*Proudly sponsored by **PyMC Labs**, the Bayesian Consultancy. **Book a call**, or **get in touch**!*

In this episode, we dive deep into gravitational wave astronomy, with Christopher Berry and John Veitch, two senior lecturers at the University of Glasgow and experts from the LIGO-VIRGO collaboration. They explain the significance of detecting gravitational waves, which are essential for understanding black holes and neutron stars collisions. This research not only sheds light on these distant events but also helps us grasp the fundamental workings of the universe.

Our discussion focuses on the integral role of Bayesian statistics, detailing how they use nested sampling for extracting crucial information from the subtle signals of gravitational waves. This approach is vital for parameter estimation and understanding the distribution of cosmic sources through population inferences.

Concluding the episode, Christopher and John highlight the latest advancements in black hole astrophysics and tests of general relativity, and touch upon the exciting prospects and challenges of the upcoming space-based LISA mission.

*Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at **https://bababrinkman.com/** !*

**Thank you to my Patrons for making this episode possible!**

*Yusuke Saito, Avi Bryant, Ero Carrera, Giuliano Cruz, Tim Gasser, James Wade, Tradd Salvo, William Benton, James Ahloy, Robin Taylor,, Chad Scherrer, Zwelithini Tunyiswa, Bertrand Wilden, James Thompson, Stephen Oates, Gian Luca Di Tanna, Jack Wells, Matthew Maldonado, Ian Costley, Ally Salim, Larry Gill, Ian Moran, Paul Oreto, Colin Caprani, Colin Carroll, Nathaniel Burbank, Michael Osthege, Rémi Louf, Clive Edelsten, Henri Wallen, Hugo Botha, Vinh Nguyen, Marcin Elantkowski, Adam C. Smith, Will Kurt, Andrew Moskowitz, Hector Munoz, Marco Gorelli, Simon Kessell, Bradley Rode, Patrick Kelley, Rick Anderson, Casper de Bruin, Philippe Labonde, Michael Hankin, Cameron Smith, Tomáš Frýda, Ryan Wesslen, Andreas Netti, Riley King, Yoshiyuki Hamajima, Sven De Maeyer, Michael DeCrescenzo, Fergal M, Mason Yahr, Naoya Kanai, Steven Rowland, Aubrey Clayton, Jeannine Sue, Omri Har Shemesh, Scott Anthony Robson, Robert Yolken, Or Duek, Pavel Dusek, Paul Cox, Andreas Kröpelin, Raphaël R, Nicolas Rode, Gabriel Stechschulte, Arkady, Kurt TeKolste, Gergely Juhasz, Marcus Nölke, Maggi Mackintosh, Grant Pezzolesi, Avram Aelony, Joshua Meehl, Javier Sabio, Kristian Higgins, Alex Jones, Gregorio Aguilar, Matt Rosinski, Bart Trudeau, Luis Fonseca, Dante Gates, Matt Niccolls, Maksim Kuznecov, Michael Thomas, Luke Gorrie, Cory Kiser and Julio*.

Visit https://www.patreon.com/learnbayesstats to unlock exclusive Bayesian swag 😉

**Takeaways: **

⁃ Gravitational wave analysis involves using Bayesian statistics for parameter estimation and population inference.

⁃ Nested sampling is a powerful algorithm used in gravitational wave analysis to explore parameter space and calculate the evidence for model selection.

⁃ Machine learning techniques, such as normalizing flows, can be integrated with nested sampling to improve efficiency and explore complex distributions.

⁃ The LIGO-VIRGO collaboration operates gravitational wave detectors that measure distortions in space and time caused by black hole and neutron star collisions.

⁃ Sources of noise in gravitational wave detection include laser noise, thermal noise, seismic motion, and gravitational coupling.

⁃ The LISA mission is a space-based gravitational wave detector that aims to observe lower frequency gravitational waves and unlock new astrophysical phenomena.

⁃ Space-based detectors like LISA can avoid the ground-based noise and observe a different part of the gravitational wave spectrum, providing new insights into the universe.

⁃ The data analysis challenges for space-based detectors are complex, as they require fitting multiple sources simultaneously and dealing with overlapping signals.

⁃ Gravitational wave observations have the potential to test general relativity, study the astrophysics of black holes and neutron stars, and provide insights into cosmology.

**Links from the show:**

- Christopher’s’ website: https://cplberry.com/
- John’s website: https://www.veitch.me.uk/
- Christopher on GitHub: https://github.com/cplb/
- John on GitHub: https://github.com/johnveitch
- Christopher on Linkedin: http://www.linkedin.com/in/cplberry
- John on Linkedin: https://www.linkedin.com/in/john-veitch-56772225/
- Christopher on Twitter: https://twitter.com/cplberry
- John on Twitter: https://twitter.com/johnveitch
- Christopher on Mastodon: https://mastodon.scot/@cplberry@mastodon.online
- John on Mastodon: https://mastodon.scot/@JohnVeitch
- LIGO website: https://www.ligo.org/
- LIGO Gitlab: https://git.ligo.org/users/sign_in
- Gravitational Wave Open Science Center: https://gwosc.org/
- LIGO Caltech Lab: https://www.ligo.caltech.edu/page/ligo-data
- Exoplanet, python package for probabilistic modeling of time series data in astronomy: https://docs.exoplanet.codes/en/latest/
- Dynamic Nested Sampling with dynesty: https://dynesty.readthedocs.io/en/latest/dynamic.html
- Nessai, Nested sampling with artificial intelligence: https://nessai.readthedocs.io/
- LBS #98 Fusing Statistical Physics, Machine Learning & Adaptive MCMC, with Marylou Gabrié: https://learnbayesstats.com/episode/98-fusing-statistical-physics-machine-learning-adaptive-mcmc-marylou-gabrie/
- bayeux, JAX models with state-of-the-art inference methods: https://jax-ml.github.io/bayeux/
- LBS #51 Bernoulli’s Fallacy & the Crisis of Modern Science, with Aubrey Clayton: https://learnbayesstats.com/episode/51-bernoullis-fallacy-crisis-modern-science-aubrey-clayton/
- Aubrey Clayton’s Probability Theory Lectures based on E.T Jaynes book: https://www.youtube.com/playlist?list=PL9v9IXDsJkktefQzX39wC2YG07vw7DsQ_

**Transcript**

*This is an automatic transcript and may therefore contain errors. Please **get in touch** if you’re willing to correct them.*

##### Transcript

In this episode, we dive deep into

gravitational wave astronomy with

2

Christopher Berry and John Vich, two

senior lecturers at the University of

3

Glasgow and experts from the LIGO -VIRGO

collaboration.

4

They explain the significance of detecting

gravitational waves, which are essential

5

for understanding black holes and neutron

stars collisions.

6

This research not only sheds light on

these distant events, but also helps us

7

grasp

8

fundamental workings of the universe.

9

Our discussion focuses on the integral

role of Bayesian statistics, detailing how

10

they use nested sampling for extracting

crucial information from the subtle

11

signals of gravitational waves.

12

This approach is vital for parameter

estimation and understanding the

13

distribution of cosmic sources through

population inferences.

14

Concluding the episode, Christopher and

John highlight the latest advancements,

15

in black hole astrophysics and tests of

general relativity, and touch upon the

16

exciting prospects and challenges of the

upcoming space -based LISA mission.

17

So strap on for episode 101 of Learning

Bayesian Statistics, recorded February 14,

18

2024.

19

Hello my dear Bayesians!

20

Today, I want to thank Julio

21

joining the Good Basion tier of the show's

Patreon.

22

Julio, your support is invaluable and

literally makes this show possible.

23

I really hope that you will enjoy the

exclusive sticker coming your way very

24

soon.

25

Make sure to post a picture in the slide

channel.

26

And now, on to the show.

27

Christopher Barry, John Vich, welcome to

Learning Basion Statistics.

28

Thank you very much for having us.

29

Yes, thank you a lot for taking the time,

even more time than listeners suspect, but

30

we're not gonna expand on that.

31

But yeah, I'm super happy to have you on

the show and we're gonna talk about a lot

32

of things, physics, of course

astrophysics, black holes and so on.

33

But first,

34

How would you both define the work you're

doing nowadays and how did you end up

35

working on this?

36

I can go first.

37

I guess I'm slightly older than

Christopher.

38

I started doing gravitational waves when I

was a physics student at Glasgow.

39

I got involved with the LIGO, actually the

GEO experiment first of all, which is the

40

Gravitational Weight Detector in Germany.

41

Its bigger brother is the LIGO and the

LIGO detectors that we're going to talk

42

about more today.

43

And ever since then, I mean, thought the

project was fantastic.

44

I'll you all about it.

45

I just wanted to get involved in the

discoveries of gravitational waves and

46

what they can tell us about black holes

and so on.

47

I got involved back in my PhD.

48

My PhD was largely about gravitational

waves we could maybe detect in the future

49

with an upcoming space -based mission

called LISA, due for launch in the 2030s.

50

I remember

51

my advisor telling me, I hope you're OK.

52

There's not going to be any real data.

53

And I was like, yes, that's great.

54

I just want to play around with the theory

stuff.

55

And then I guess fate conspired against

me.

56

After my PhD, I moved to the University of

Birmingham.

57

That's where I first started working with

John.

58

We were at University of Birmingham

together.

59

And I got involved in LIGO, VEGO data

analysis.

60

And we happened to make our first

detection just a couple of years after I

61

joined in 2015.

62

And we've been very busy since then

analyzing all the signals, figuring out

63

the astrophysics of them.

64

So each individual source and then putting

them together to understand the population

65

underneath.

66

So now we're both at the University of

Glasgow working on analyzing these

67

gravitational wave signals and

understanding what they can teach us about

68

the universe.

69

Yeah.

70

So as Liesner can already tell, I guess,

71

Fascinating topics, lots of things to talk

about and dive into.

72

But maybe to give us a preview of things

we're going to talk about a bit more.

73

You guys are also using some patient stats

writing in these analysis, am I right?

74

Yeah, so I think we look at, I guess, two

levels of Bayesian stats.

75

So the first is what we refer to as

parameter estimation.

76

So given a single signal trying to figure

out what are the properties of the source.

77

So the signals we most often see are, say,

two black holes spiraling in together.

78

So we look at the patterns of

gravitational waves that it emits.

79

And from this, we can match templates and

then infer.

80

These are the masses of the two black

holes.

81

This is the orientation of binary, the

distance to the binary, and parameters

82

like that.

83

So we use Bayesian stats and the sampling

algorithms like nested sampling to mop out

84

a posterior probability distribution.

85

And then I guess the second level of this,

we do what we call a population inference,

86

so a hierarchical inference of given an

ensemble of different detections,

87

correcting for our selection effects that

we can detect some signals easier than

88

others.

89

What is the underlying astrophysical

distribution?

90

So what is the distribution of masses of

black holes out there in the universe?

91

Yeah.

92

So fascinating things.

93

And John, you want to maybe add something

to that?

94

Just as a teaser, we're going to dive a

bit later in the episode into what you

95

guys actually do.

96

So as Christopher just said, nested

sampling, population inferences, but

97

anything you want to add?

98

teaser for Easter.

99

I would add something about the background

of how it works within the LIGO scientific

100

collaboration.

101

So when I started doing my PhD, my

advisor, Graham Wohn, taught me about

102

Bayesian statistics, Bayesian inference,

and I never learned it as an undergraduate

103

at all.

104

I just leave my mind, like, here we have

this mathematical theory of learning.

105

Why are we using this everywhere?

106

And in those days, it really wasn't being

used very much in LIGO.

107

because a lot of the people that started

the collaboration were coming from a

108

physical perspective and they were very

frequentists.

109

They were counting and cutting all of

their events to try and measure the

110

discovery that takes place on it or

whatever.

111

So it was kind of novel in that patient's

way back then.

112

But since then, as Christopher said, it's

been applied all over the place to all

113

kinds of different problems.

114

So it's been quite exciting to watch that

back over the years.

115

I remember we had a...

116

We had our first detection and we were

lighting up our results.

117

And I think at that time still a lot of

the collaboration was very frequent.

118

So we were writing in our papers, we have

a posterior probability distribution for

119

the masses and there are people going,

hey, what's that?

120

What's a posterior?

121

We've never come across this before.

122

Can you explain it to us?

123

And now it is very much accepted.

124

And yeah, everyone has a new detector.

125

Where are the masses?

126

I want to see this probability

distribution.

127

What do you think drove that evolution and

that change?

128

I think Bayesian statistics is very

popular in other parts of astronomy.

129

So in a sense, it was kind of inevitable

that it would make its way over to

130

gravitational wave astronomy as it's only

a matter of time.

131

But I think the problems that we were

trying to solve, particularly for the

132

parameter estimation,

133

type analysis did lend itself to a

Bayesian analysis because you have a

134

unique event.

135

You you're not, we only see a very small

number of gravitational waves.

136

We see them all the time, but it's still

measurable.

137

The dozens, not the millions.

138

So we have to make the most of every

single one.

139

The second one, the ratio is rather low.

140

So graphs from the other side.

141

is also very important if you want to do

science.

142

Yeah, that makes sense.

143

And so it was mainly driven by just

patient stats entering a need in what you

144

wanted to do basically, which is something

I often see in fields where psychology,

145

from what I've seen in the last few years,

for instance, psychometrics, things like

146

that, have seen a big rise in patient

statistics because they have been able to

147

answer the questions that researchers had

and that they could not answer with the

148

tools they had before.

149

So basically, a very practical, oriented

view of things.

150

And then afterwards, let's say the more

epistemological philosophical side of

151

things enters to also justify that.

152

But...

153

But most of the time it's a very practical

driven mindset, which is great, right?

154

Because in the end, why you care about

that is just, is that the right tool to

155

answer the questions I have right now?

156

And yeah, for what it's worth.

157

Yeah, go ahead, John.

158

The pragmatism is what's put in the table

at the end of the day, but during my PhD,

159

I was trying to look...

160

or not the kind of black hole binaries

that we'll talk about later, but from

161

monochromatic waves.

162

So you imagine doing a Fourier transform

of some data and you have a single spike,

163

and it has a bit of modulation on it.

164

But really there's no information about

that spike in any area of the prime space

165

outside of the spike.

166

So I learned about Bayesian statistics and

tried to do MTMC on this problem, which

167

was kind of like the most pathological

problem that you'd be trying to do MTMC

168

on.

169

that basically reduces itself to doing an

exhaustive search for the ground or space.

170

So I was kind of convinced by the

epistemology originally rather than the

171

thesis and the only nature that we used

for the sake.

172

Yeah, yeah.

173

Yeah, yeah.

174

That makes sense.

175

And as you were saying also that patient

studies is popular in other parts of

176

physics.

177

That's definitely true in a sense that,

for instance, in the core developers of

178

MC, of Stan, you have a lot of physicists,

often coming from statistical physics and

179

historically even the algorithms that we

even use, MCMC algorithms, have been

180

developed mainly by physicists or for

physics purposes.

181

So there is really this integration here

almost historically.

182

And that made me think that if listeners

are interested, there is an interesting

183

package that's called Exoplanet.

184

And that's basically a toolkit for

probabilistic modeling of time series data

185

in astronomy, but with a focus on

observations of exoplanets.

186

So that's different from what you guys do,

but that's using PIMC as a backend.

187

So that's why I know it.

188

And that's...

189

mainly developed by Dan, Firm and Macky,

if I remember correctly.

190

I'll put that in the show notes for people

who are interested because that is

191

definitely something to check out if you

are doing that kind of models.

192

And that made me think that I didn't even

thank our matchmaker because today is

193

February 14th, but actually this episode

was made possible thanks to a matchmaker,

194

Cupid, if you want, of patient statistics,

Johnny Highland.

195

Thanks a lot for putting me in contact

with Christopher and John.

196

Johnny is a faithful listener and I am

very grateful for that and for putting me

197

in contact with today's guests.

198

And so you mentioned already, Christopher,

that you two work on the LIGO -VIRGO

199

collaboration.

200

Maybe...

201

Yeah, tell us a bit more about that

collaboration, what that is about, and

202

what the goal is, so that listeners have a

clear background.

203

And then we'll dive into the details.

204

So yes, LIGO -VIRGO -CAGRA is a

collaboration of collaborations.

205

So each of LIGO -VIRGO and CAGRA operate

their own gravitational wave detectors.

206

So these are remarkable experimental

achievements.

207

We're talking devices that can measure

208

Distortions in space and time is what

we're looking for.

209

So in effect, what we do is we time how

long it takes a laser to bounce up and

210

down between some mirrors in one direction

compared to another.

211

We're looking for a part of less than one

part in 10 to the 21.

212

So it's equivalent to measuring the

distance between the Earth and the sun to

213

the diameter of a hydrogen atom, or the

distance from here to Alpha Centauri to

214

the width of a human hair.

215

So over many decades,

216

experimentalists have developed the

techniques to build these detectors to

217

design them.

218

And we're now in a very fortunate

situation that we have multiple of these

219

detectors operating across the world.

220

So we have two LIGO detectors in the US,

one in Livingston, Louisiana, one in

221

Washington, in Hanford.

222

And we've got Virgo in Italy, just outside

Pisa, Kagra underground in Japan, and

223

coming decade another LIGO to be built in

India.

224

And each of these observatories is looking

for gravitational wave signals.

225

The ideal source for gravitational waves

would be a binary of two black holes or

226

two neutron stars, very dense objects

coming together, merging very quickly,

227

very strong gravity, very dynamical

objects.

228

And we can detect these gravitational

waves and with those do astronomy.

229

So instead of using a telescope to make

observations with light, we're using these

230

gravitational wave detectors to look for

gravitational waves in undercover.

231

the astrophysics of these sources.

232

Yeah.

233

Yeah.

234

Thanks.

235

So that's a very clear explanation.

236

It's a bit like being able to hear the

universe itself only looking at it, right?

237

So that's another way of getting

information about the universe that maybe

238

allows us to also answer questions that we

had, but we were not able to answer only

239

with a telescope data.

240

Is that the case or is that mainly

241

information that's parallel and similar.

242

Yes.

243

Go ahead.

244

Yeah, I think that's one of the most

exciting things about this is completely

245

set in the electron spectrum using the

structural squeezing space itself by these

246

buckles and neutrons.

247

The waves that we've been offering are of

an oil from the sea.

248

So, as you said, the detectors are picking

up

249

essentially the equivalent of sound waves,

bulk motion of the material rather than

250

the jiggling of atoms.

251

We're talking about the jiggling of whole

stars, movement of them in their orbits.

252

And because you're looking at the bulk

motion rather than the surface of the

253

object, you can see right into the heart

of what's going on in some of these very

254

violent events.

255

In principle, we should be able to see

also inside supernovae if there are

256

enough...

257

motion of material during the core

collapse.

258

That would also give off gravitational

waves that we could see, although their

259

thoughts would be much weaker than those

that we're looking at in the moment.

260

I see.

261

One thing that's particularly nice we can

do as well is really test how gravity

262

behaves in very extreme environments.

263

John, I don't know if you want to mention

something about looking at the ring down

264

of black holes.

265

Sure.

266

I mean, as Christopher says, there's a

very detailed prediction for how two stars

267

should approach each other in their own

spiral over time.

268

And the equations are horrendously

complicated.

269

talking about the full view of general

relativity.

270

But once they've collided and they form a

larger black hole, suddenly everything

271

becomes rather simple and acts just like a

wine glass that's been excited with a fork

272

and then it actually decays down and

settles into its final state.

273

Therefore a black hole that happens

extremely fast because they want to

274

settle down as quickly as they possibly

can, if you like.

275

So the notes that we give off are

milliseconds long rather than seconds

276

long.

277

But the frequencies in the damping times

of those notes are measurable with their

278

picture waves.

279

And by looking at them and comparing them

to each other, we can check to see that

280

the predictions of the theory are indeed

what we would see in the world.

281

So far, they seem to be the case.

282

Yeah.

283

Something I'm wondering is that these

collisions that you're talking about, they

284

are happening millions of light -wears

away.

285

How are we even able to study them and

also maybe tell us what we already have

286

learned from them?

287

They're really quite rare events, the

types of collisions that we're seeing.

288

I mean, this is why there are millions,

hundreds of millions or even billions of

289

light years away is because they're so

rare in the universe that we need to look

290

out a very long way before we see one

often enough to make the detections often.

291

So they do happen in local galaxies as

well as the reason to think it wouldn't,

292

but it's just they're so rare.

293

I've seen one near black source.

294

Yeah.

295

Yes, they are remarkably energetic.

296

The amount of energy that is output as

gravitational waves when you've got, say,

297

two black holes coming together is

phenomenal.

298

For just that moment as they smash in

together, more energy, so the luminosity,

299

the amount of energy per unit time emitted

right at that peak is higher in

300

gravitational waves than if you were to

add up.

301

or the visible light from all the stars

that you could see in the universe.

302

So it's a phenomenal amount of energy just

over a very short way.

303

So yeah, we just need to be listening to

the universe to see these, to discover

304

these sources and find out what they're

trying to tell us.

305

The energy flux from these black hole

collisions, despite the fact that they're

306

hundreds of millions of light years away,

is actually comparable to the flux from

307

the full moon.

308

So the brightest object in the night sky,

309

is surpassed by gravitational wave

signals, except we can't see the

310

gravitational waves because they don't

interact very strongly with matter.

311

And it's only by building these incredibly

sensitive detectors to pick up their

312

effect on distances that we can still look

at.

313

Yeah, that's just fascinating to me that

we're even able to see...

314

like hear these waves in a way.

315

So, yeah, just to finally point home,

there's so much energy that you're

316

carrying away, but the effect is so tiny,

as Chris said, 10 to the minus 21, no

317

less.

318

Yeah.

319

If you think about how those two things

could be true at once, it's telling you

320

that it takes an enormous amount of energy

to produce a tiny distortion in space.

321

So it's very, very difficult to walk

space.

322

And that's...

323

the consequences of general malpractice.

324

Yeah.

325

And then, so I think now it's a good time

for you to tell us.

326

So maybe Christopher, you can tell us

that.

327

How do you use patient stats to extract as

much information as possible from these

328

tiny wave signals?

329

How is base useful in this field?

330

And how do you also actually do it?

331

Are you able to use any...

332

widespread open source packages or do you

have to write everything yourself?

333

How does that work concretely?

334

Yes, so for the type of sources we've been

seeing these binaries, we have predictions

335

for what the signal should look like.

336

So we have a template that is a function

of the parameters and we have a decent

337

understanding of the properties of our

noise.

338

So the data is a combination of the signal

plus some noise which you assume to be

339

stationary over the short time scales that

we're analyzing and characterized such

340

that the noise at individual frequencies

is uncorrelated.

341

So if you like, you get your data,

transform it to the frequency domain,

342

subtract out your template, you should be

just left with noise, which is Gaussian at

343

each frequency bin.

344

And so you have a lot of Gaussian

probabilities that you combine to get.

345

So that gives us our likelihood.

346

You map that out, you change your

parameters for your template.

347

evaluate that at another point in

parameter space, map that out with your

348

suitable prior, and you end up with your

posterior probability for a single event.

349

The number of parameters that we're

typically dealing with is something like

350

15 for typical binary.

351

Maybe that goes up to 17 when we add in a

couple of extra ones, a few more if we're

352

maybe looking at tests of general

relativity.

353

So it's enough that exploring the

parameter space can't be just done by

354

gridding it up and exploring it.

355

We generally use some kind of stochastic

sampling algorithm.

356

But it's not one of these problems, at

least yet, where we've got millions of

357

parameters and it's a really high

parameter space.

358

In terms of the algorithms that we use to

explore parameter space, we've got a long

359

history of using MCMC and nested sampling

for these.

360

And John's really the expert on this.

361

So, John, do want to say some more about?

362

We'll get to that, yeah.

363

Oh, you are done?

364

OK, perfect.

365

So yeah, John, maybe if you can tell us.

366

Yeah, maybe let's start with nested

sampling that you use a lot for your

367

inferences.

368

So can you talk about that, why that's

useful, and also why you end up using that

369

a lot in your work?

370

Which problem does that solve?

371

So nested sampling is an alternative to

MCMC.

372

I don't know if you're...

373

listeners will all have encountered it

before.

374

If you're a regular user of MCMC though,

it's definitely worth a look.

375

It was invented in 2006 -2007 by John

Scaling.

376

He was a physicist.

377

The idea is that you're actually trying to

evaluate the evidence, the normalization

378

constant of the posterior to allow you to

do model selection in a basic way.

379

But as a by -product, it can generate

samples from the Bistidia as well.

380

So this popped up around about the time

that I started a full stock position in

381

Birmingham and thought, well, why don't we

give it a go and apply it to the problem

382

of compact binaries.

383

So at that point, there was no off -the

-shelf package available to do this.

384

And so we had to create our own.

385

That was all coded up in C for so time.

386

It wasn't such a big thing.

387

There was thousands of lines of code and

all that.

388

But yeah, so the reason is that you might

prepare it for MCMC.

389

People were trying to solve the same

problem with parallel tempered MCMC.

390

The compact binary parameter space has a

fair amount of degeneracies, multiple

391

data, and in amongst those modes.

392

They make it difficult to sample the

waveforms are facilitated in a nonlinear

393

problem.

394

It can be quite complicated.

395

Getting a decent exploration of the prior

was proving to be difficult for the MCMC.

396

Hence the need for parallel tempering.

397

And this is something that works a little

bit differently because it starts off by

398

sampling the whole prior in the first

place.

399

So you know, say thousands of points,

they're called live points.

400

scatter them across the entire prior and

then compute the likelihood for every one

401

of those.

402

If you then eliminate the point that has

the lowest likelihood and replace it with

403

one that has the higher likelihood of the

lowest one, then people still have a

404

thousand points, so they will all have a

likelihood higher than the worst one.

405

And you can see that, roughly speaking,

the volume of that remaining set of points

406

will be about

407

999 thousandths of the original one just

by random large numbers.

408

And so if you repeat that process, always

replacing the point of the next iteration,

409

you'll have 999 thousandths of 999

thousandths of the original.

410

And so eventually you'll shrink in a

geometric fashion the volume that your

411

points are contained within.

412

And...

413

In doing so, you're walking uphill, you're

moving towards the peak of the posterior.

414

So, what I have seen to see it is

guaranteed to terminate once you have held

415

the climb up, which was a nice feature.

416

And it gives you the evidence for doing

multi -selection.

417

Once you've done the entire chain, you can

resample those points from the chain and

418

weight them according to the posterior to

produce either independent samples or

419

weighted.

420

posterior samples are to meet.

421

Yeah, so it's a really effective

algorithm.

422

I like it because it's reliable.

423

And as I say, your run is guaranteed to

finish.

424

It might take a long time, but it will get

there.

425

There are of course, places where it falls

down.

426

If you don't have an upline, you can end

up missing a mode.

427

The challenge is really how do you explore

that constrained prior distribution.

428

And so over the years, there have been

different approaches to doing that.

429

The one that I started, I was coding in

Oracle Struct, was using MCMC inside the

430

nested sampling.

431

So just do a little MCMC chain to draw the

next sample, which works fine, especially

432

because we already knew how to do MCMC's

for this problem quite well.

433

But other people have invented the

ellipsoidal multiness algorithm, was one

434

of the first very popular.

435

off -the -shelf solutions and that was

used also for gravitational waves.

436

These days there are more modern, I

packages that do everything you need,

437

either with MCMC or with side sampling or

more complicated things like normalizing

438

flows.

439

I should mention the Bowman or most of the

gravitational wave using dynasty, which is

440

next to sampling.

441

myself and the students, there's no force

with it.

442

That's the image that connects it

something with artificial intelligence

443

that attempts to use some machine learning

to accelerate this whole process.

444

Well, that sounds like fun.

445

Yeah, I'm definitely going to link to

Genesty.

446

So the package you're using right now to

do the NST sampling in the show notes and

447

If you have anything you can share on this

new package you're working on, for sure,

448

please add that to the channel.

449

These listeners will be very interested.

450

And maybe you want to add a bit more about

this project.

451

So how would you use machine learning in

this way to help you do the nested

452

sampling?

453

Yeah, I can say something about that.

454

It's a cool idea.

455

I mean, the...

456

Enabling technology for this is a tool

called the normalizing flow.

457

And I don't know if you've talked about it

in podcast before, but they have a way of

458

approximating complicated distributions

using single ones with a remapping of the

459

coordinate system.

460

So in that context, we were trying to make

a good fit to the jump proposal for the

461

sample, if you like, because that has to

evolve.

462

with the scale of the problem as the

nested sample proceeds.

463

The mode shrinks and it can shrink by a

factor of 10 to the 20 over the course of

464

the run.

465

So you're going to need something adaptive

to continue to have good efficiency.

466

So we took this normalizing flow technique

and applied it to this problem of fitting

467

the existing samples.

468

And then the advantage being that it

allows you to draw independent samples, a

469

bit like the ellipsoidal.

470

technique, but it doesn't require a fixed

shape.

471

So it's able to make more complicated

shapes for distribution.

472

Yeah, I'll pop the link in and people are

very welcome to give a go.

473

Yeah, for sure.

474

Yeah.

475

So folks give it a go, try it.

476

If you see issues, report them on the

GitHub, even better.

477

If you can do a PR, I'm sure John will

appreciate it.

478

And actually, so that could not be better

because I will refer people to episode 98

479

of the podcast where I talked with Maridu

Gabriel, who is one of the persons

480

developing these kinds of methods.

481

And we talked exactly about that.

482

Adaptive MCMC augmented with normalizing

flows.

483

And we...

484

talked in the episode about how it offers

a powerful approach, especially for

485

sampling multimodal distributions, how it

also scales the algorithm to higher

486

dimensions, how you can handle discrete

parameters, and how all these ongoing

487

challenges in the field.

488

So if you're interested in the nitty

gritty details of what John just

489

mentioned, I recommend listening to

episode 98 because, well, Marilou is

490

really a f***.

491

One of the persons developing all that

stuff.

492

Sounds super interesting Alex.

493

I'm amazed at the power of some of these

new techniques.

494

There's a revolution going on at the

moment in this area.

495

It's a good time to be involved.

496

Yeah, I know for sure.

497

I will link to that.

498

Also, Colin Carroll, who is one of the

PIMC developers, he also has a new

499

package, well, working on a new package

called Biox.

500

And I know that they implemented these

normalizing flow algorithm.

501

And so now you can use that in PyMC

directly through BIOX and to use that kind

502

of algorithm and handle your multi

-dimensional, multi -model distributions

503

more easily.

504

So I also link to that because it's

definitely super interesting if you have

505

lots of weird distributions.

506

Like that.

507

And Christopher, to come back to you, you

also mentioned that you guys do population

508

inferences.

509

And that's hierarchical models where you

use a bunch of observations to infer the

510

underlying distribution of the sources of

the signal, if I understood correctly.

511

So what does that look like?

512

What do you guys do here?

513

Yeah, so we do the calculation in a couple

of stages that we always run the parameter

514

estimation to get the events parameters

for just one signal of time first.

515

And so the result of that is a set of

posterior samples calculated with a

516

fiducial prior.

517

And what we want to do is then divide out

that prior, put in a population model, see

518

how well that fits.

519

So calculate the, I guess, the evidence.

520

under the assumption of a particular set

of hyperparameters.

521

And then we have an inference one level up

where we vary the population parameters,

522

the hyperparameters for the population

model, explore that to see what fits work.

523

So that really is starting to get the

astrophysics.

524

So looking at the distribution of masses,

are there more low mass black holes and

525

high mass black holes?

526

How does that scale?

527

Is there a little?

528

bumps in the distribution and things like

that.

529

So, yeah, it's next level up.

530

The likelihood isn't quite as expensive as

evaluating the waveforms, but we have some

531

data handling issues of reading in order

of the posterior samples.

532

And key to this is, as I alluded to, is

correcting for the selection effects so

533

that we need to account for the fact that

with our gravitational wave detectors, we

534

can preferentially see some sources over

other sources.

535

So if you were just to look at our

536

distribution of sources that we detect,

you'll see, hey, there are lots of 30

537

solar mass black holes, there aren't too

many 10 solar mass black holes, and if you

538

didn't know about our selection effects,

you can actually assume, okay, the

539

universe is full of 30 solar mass black

holes, and 10 solar mass ones are much

540

rarer.

541

Whereas because our detectors are more

sensitive to the high mass signals, those

542

are intrinsically louder, so we can see

them further away, we can see more of

543

them.

544

Once you correct for the selection

effects, you actually see it's the other

545

way around, there are many more

546

At least there should be many more 10

solar mass black holes than 30 solar mass

547

black holes.

548

And the fact we don't see so many 50 solar

mass black holes, 90 solar mass black

549

holes, tells you that the distribution

does drop off quite rapidly.

550

So this is a field that's growing quite

nicely as we get more and more detections.

551

Your uncertainties on the population

basically go as the square root of the

552

number of detections.

553

what we're seeing a lot of work on is what

does one assume for the population model.

554

So when we started off with, I guess,

following what is common in astronomy, we

555

put a power law through for the masses,

just infer the power law index basically

556

in the normalization for the overall rate

and see how that worked.

557

Then we like that's a bit simplistic.

558

Let's add in a couple more parameters.

559

Let's have

560

say a little peak, a Gaussian add on top

of that to get peak.

561

Let's say have two parallels with the

break, see how those fit.

562

Let's put in another peak.

563

And now people are looking at semi

-parametric models.

564

So OK, what if we add a spline on top of

that?

565

See how we can vary that.

566

Or what if we do something really

flexible, so allow a bunch of kernels to

567

come together and further the population

to get out of there?

568

So a lot of.

569

A lot of the work at the moment is trying

to see what is a good fit for the data and

570

then checking is this overly complex?

571

Are we overfitting?

572

Is there a little bump there?

573

Is that just because of a pass on

fluctuation that we've only seen so many

574

events?

575

So a small number of statistics means

there's a few more here and a few fewer

576

there.

577

Or is there actually some feature of the

underlying population, which may be a hint

578

to how stars are formed?

579

I think it's quite an interesting time at

the moment from this testing out models,

580

trying to determine do they fit the

observations quite well.

581

And I'm very excited for getting the

results of our upcoming observing runs

582

when we're having a much larger number of

detections and we'll really be able to

583

constrain the models to higher accuracy

and precision.

584

Yeah, so that's super interesting.

585

And so here to understand what you're

doing, it's like your...

586

hearing different sounds and you're trying

to infer not really what the sound is

587

about, but what is emitting that sound?

588

What is the source of that sound?

589

And the issue is that these sounds can be

emitted by a lot of entities and a lot of

590

these sources you don't really care about

because I know they are on earth, they are

591

like, but what you're interested in are

the sources.

592

outside, which are in space and which tell

you something about the universe, which

593

here would be mainly neutron stars and

black holes colliding.

594

How weird was that characterization?

595

Yes, I guess maybe a nice analogy might

be, imagine you have a room full of people

596

and you're trying to judge the composition

of the room.

597

And some of the people there, you have a

bunch of librarians who are very quiet.

598

And you have some heavy metal stars who

are very, very loud.

599

And so you've made your recording of the

audio in the room, and then you need to

600

try and reconstruct that.

601

OK, I can only hear one librarian.

602

But given that the librarians are very

quiet, there's probably a whole host of

603

other librarians who I just missed because

they're being too quiet.

604

and I can hear lots of electric guitars

going on, so I know there's some rock

605

stars here, but I know they're very loud

and easy.

606

I probably will have detected 100 % of

those, so correct for those bias from the

607

detection.

608

We're very fortunate actually in

gravitational wave detection that we can

609

calculate our selection effects.

610

It's quite easy for us to determine what

sources we can detect and what we can't.

611

This is a standing problem in astronomy

that you're

612

We only have one universe, so we need to

make sure we understand what we're seeing.

613

And you can know what you detect, but it's

very hard to know what you're not

614

detecting.

615

So a lot of astronomy is trying to correct

for these.

616

And if you have a telescope, that can be

very difficult because you've got to

617

calculate, OK, not just what did I see,

but what could I have seen?

618

So that would depend on where I was

pointing the telescope.

619

It would depend on the weather on a

particular day and how cloudy it was.

620

Whereas with our gravitational wave, it's

much simpler.

621

What we do is we can inject the

terminology we use.

622

We simulate signals, put those into our

data, run our detection pipelines on that,

623

and see what fraction of the signals that

we injected would we recovered and from

624

that work out.

625

As a function of source parameters, what

was the probability that something was

626

detected?

627

And then use that in renormalizing our

likelihood to establish.

628

Okay, how many of these sources should

have there have been given that we saw

629

this money?

630

Okay, it helps a lot that gravitational

waves are not blocked by anything in the

631

universe that we know about except for

other black holes But even then other

632

black holes tend to be very small So when

we are able to calculate exactly what the

633

source is doing it means that we've got a

very good idea of what we will see.

634

It doesn't really matter what's in the

entropy space.

635

The two veins of astronomy are dust and

magnetic fields, and gravitational waves

636

are just don't really care about any of

those two things.

637

Yeah, okay.

638

I see.

639

And that's actually a good thing.

640

Indeed, that's quite a luxury to be able

to compute your own selection bias.

641

That's pretty amazing.

642

Me, who've done a lot of political

science, you usually cannot do that, so

643

I'm very jealous.

644

And can you tell us actually where does

that noise come from?

645

Because it seems like you're saying there

is a lot of noise in your observations.

646

Thankfully, you are able to tame that

somewhat easily.

647

Can you tell us a bit more about that?

648

And John, it seems like you want to add

something about that.

649

Most of the noise, all the noise is not of

extraterrestrial origin.

650

It's coming from the detectors and coming

from the environment around the detectors.

651

So in order to understand that you have to

know a little bit about how to light over

652

a porp.

653

So imagine a giant in all shape, four

kilometres long, in bits of light, with

654

the letters at the ends of the arms

shining a laser into the coin, if like.

655

It gets split into two and sent down both

arms, bounces off them into the end and

656

then comes down.

657

and if they aren't the same length then

the light will constructively interfere or

658

destructively, I may have that wrongly

written.

659

The point is if they aren't at different

lengths or if they're changing lengths

660

then the pattern of the light that comes

out will change over time.

661

So we are really worried about anything

that can change that output of the laser

662

in the detector.

663

And so that could be due to the laser

itself.

664

All lasers have some noise in them.

665

So the lasers that they use in these

detectors are some of the most stable

666

lasers that you can use.

667

have been invented from scratch basically

for this one.

668

It could be the thermal motion of the

atoms in the matrix of the complex.

669

It would be better in that, simply having

a wide enough laser beam approaching the

670

whole surface of the metal, cancelling out

the mean motion to the low enough level to

671

get it ready.

672

But the laser also

673

You know, there's energy and that energy

fishes on the mirrors of radiation, which

674

causes the mirrors to move a little bit.

675

And now, think about the algorithms, the

laser energy is carried by photons, which

676

are ultimately quantum objects, so they

get off the radar distinctly.

677

Kind of raindrops on the roof, if you

imagine, or if you're in a tent, you get

678

raindrops of rain.

679

That's kind of what it's like.

680

The lasers are enormously hard.

681

still they are made of individual photons.

682

And so there's a shot noise associated

with them, just due to the statistical

683

fluctuation in the number of photons that

are writing per second.

684

Then we've got the environment as well,

which is especially dominant at low

685

frequencies.

686

So we can't sense anything below about 10

Hertz with these detectors that are above

687

the ground.

688

because of seismic motion.

689

Now we do have a lot of techniques to try

and screen the mirrors out in the motion

690

of the Earth.

691

They're hung on suspended optics, which

act as a natural filter to prevent ground

692

motion from propagating through to the

mirror.

693

But even so, we need to have active

oscillation systems as well.

694

And on top of all of that, even if you

manage to screen out all the mechanical

695

coupling,

696

There's unfortunately the gravitational

coupling that we can't spin out because we

697

actually want to measure gravity in the

first place.

698

So if you imagine a seismic wave as a

pressure wave in the rock, I mean, when

699

pressure is high, the rock is actually

compressed slightly.

700

And because it's compressed, it's denser

than average.

701

And because it's denser than average, it

exerts a gravitational pull on the mirrors

702

that tends to pull them along.

703

with the seismic waves.

704

So this tiny effect, I mean, you've

probably never even thought about it, but

705

it's there as a small gravitational

coupling of seismic waves to the detector.

706

And you can't really get around these

things tall on the earth.

707

And so that's why one of the challenges

that we're working on at the moment is

708

looking at sending a detector into space,

which is hopefully going to open up a

709

whole new range of...

710

objects for us to look at.

711

Yeah, thanks a lot, That's definitely

clear, and I didn't have, indeed, any idea

712

of all these sources of noise, which is

pretty incredible that we're able to

713

filter that out, knowing that already the

signals you're looking at are already so

714

weak.

715

So it feels pretty incredible to still be

able to do it, even though the signals are

716

weak.

717

and the result of noise.

718

It's really amazing the technology that is

required to do these experiments has been

719

developed decades and decades for people

to develop it and almost all aspects of

720

the detectors have to be invented for that

purpose.

721

There's very little off -the -shelf

technology and of course the spinoffs from

722

that then taken up in other areas but it's

the pure science that was driving the

723

development of the law.

724

Yeah, exactly.

725

It's like, it's not even as if the all the

engineering of these was already available

726

and you could just go on Amazon and buy

it, right?

727

You have like everything has to be

developed custom for these and you don't

728

even know if that's going to work before

you actually try it out.

729

So that's like all these endeavors are

absolutely incredible.

730

And so that makes me think and I think on

these Christopher, you will have stuff to

731

add.

732

Because, so if I understood correctly, all

these detectors that we have right now are

733

on Earth.

734

These gravitational waves detectors.

735

Hopefully, we'll be able to do a video

documentary on Learned Bay stats in one of

736

these detectors.

737

It's just some of the backstage I'm

telling to the listeners.

738

We'll see if that's possible.

739

But, so these detectors are on Earth.

740

If you go to space and were able to put

one of these detectors around the earth or

741

I don't know, in space floating somewhere,

I'm guessing that solves these problems,

742

even though there are other sources of

issues if you do that in space.

743

But if I understood correctly, the LISA

mission is space -based.

744

And so is that a way of doing that?

745

Can you tell us a bit more about that?

746

Christopher and...

747

Yeah, mainly tell us what the discoveries

will be with that.

748

Also the data analysis problems that will

engender, especially when it comes to the

749

size of the data, I'm guessing.

750

Yeah.

751

So Lisa's Space Space Gravitational Wave

mission, it's led by the European Space

752

Agency with NASA as a junior partner

there.

753

And the idea is we...

754

launch a constellation of satellites, so

three satellites that will orbit around

755

the Sun lagging behind the Earth in a

triangular formation and we bounce the

756

lasers between them to make the same sort

of measurements that we do for

757

gravitational waves but over a much larger

scale, so really massive arms.

758

So this is great because we can avoid the

ground -based noise that John mentioned

759

and this

760

is really good.

761

So for Lisa, we're not trying to see

exactly the same sources as with our

762

ground -based detectors, but we're trying

to look for lower frequencies.

763

So one of the things we've learned in

astronomy over the last century or so is

764

that each time you're observing the

universe in a new way, you discover new

765

things.

766

So we want to look at a different part of

the spectrum of gravitational waves.

767

So Lisa's most sensitive is the millihertz

range, so much lower frequencies.

768

And a much lower frequency gravitational

wave,

769

corresponds to a bigger source.

770

So these could be the same type of binary,

but just much further apart in that orbit,

771

so much earlier before they come in and

merge much further apart.

772

Or we could be looking at much more

massive objects, so massive black holes.

773

We believe at the center of every galaxy

is a massive black hole.

774

Our own galaxy has one about four million

solar masses, four million times the mass

775

of our sun.

776

And we think galaxies merge, and so the

massive black hole should merge.

777

And so we'd be able to see these out to a

much greater distance.

778

So Lisa's objective is to see what we can

observe in the gravitational wave sky at

779

these much lower frequencies.

780

And there's a whole host of different

sources.

781

So these massive black hole mergers we

should be able to see out across the

782

entire history of the universe.

783

We should be able to see regular stellar

mass black holes.

784

So black holes formed from.

785

stars at the end of their lives spiraling

into these supermassive black holes.

786

It's a topic I've studied quite a lot.

787

Those signals are extremely complicated.

788

The orbits they undergo are very

intricate, which is great if we observe

789

one because we can measure the parameters

to tiny, tiny precision, to one part in a

790

million, something like that.

791

But it's a huge pain from a data analysis

point of view because you've got to find

792

the part of parameter space where this is.

793

And we're also going to see

794

huge numbers of binaries in our own galaxy

of white dwarfs, maybe neutron -style

795

white dwarfs, so the wide binaries here.

796

And so the real data analysis problem for

LISA will be how to fit all of this

797

information all at once, because with our

ground -based detectors, at least at the

798

moment, we basically just see here's a

signal and then here's another signal.

799

So you can analyze each signal in

isolation.

800

With Lisa, you cannot you see everything

all at time.

801

Some of these lights, they don't

supermassive black hole mergers might be

802

quite short to compare to place a

localized in time, but they will still be

803

overlapping these long lives.

804

So the the in spiraling objects or the

very wide bindings will basically be there

805

for the entire mission or a large fraction

of the mission.

806

So to analyze the data, you need to fit

everything or this is what we call a

807

global fit problem.

808

And you

809

So you potentially have hundreds of

thousands of sources, each with a dozen

810

parameters or so, maybe less than simpler

sources.

811

But you've got to do all of these all at

the same time.

812

And it potentially does matter how you do

this, because things like the massive

813

black hole binaries are extremely loud, so

signal -to -noise ratios of thousands.

814

So if you get that wrong by just a little

percentage,

815

residual power in your data stream would

be enough to bias your measurements of the

816

quieter signals underneath.

817

So this is a huge, I think possibly the

most complicated data analysis problem in

818

astronomy and we're just starting to

figure out how we're going to tackle this.

819

So yeah, space -based detectors I think

extremely exciting, a whole host of new

820

sources that we can see, a new host of

astrophysics that we can unlock through

821

these observations, but also

822

some extremely complicated data analysis

challenges that need to be tackled and

823

solved before the mission launches in the

2030s.

824

And what's the timeline on this mission?

825

Are we close to launch?

826

Where are things right now?

827

So just in the last couple of months, the

mission was approved by ESA.

828

So that's them looking at the designs and

going, OK, we think we can build this.

829

And now the serious work on putting it

together comes.

830

So it's due to launch in the 2030s,

exactly when that be, I'm sure.

831

People are very confident on when it will

be, but we know space -based missions are

832

hard.

833

So it might, maybe, maybe it's a little

early to say exactly what date it will

834

launch.

835

But it will go up and then there'll be a

little period of commissioning and then it

836

will start observing.

837

So in the late 2030s, we should hopefully

get the observations from that.

838

So the current timeline, 2035 for launch,

which I guess is...

839

Good news to any of your listeners who are

inspired by the problems that we're

840

talking about and think this is really

cool and think that maybe they'd like to

841

tackle these problems.

842

There's certainly enough time to go out,

get a degree, start a PhD in the field

843

before we get the real data.

844

Yeah, for sure.

845

Exactly.

846

And also, historically, these kind of huge

missions tend to take a bit of delay.

847

So, you know, like...

848

You can start your PhD on this.

849

I mean, that's better to launch later than

to launch on time, but have a mission that

850

fails, right?

851

Yes.

852

We're talking a billion euro cost of these

things.

853

So you definitely don't want to explode on

the launch pad.

854

Exactly.

855

Way better to take a few more months and

do some double checks than just launch

856

because we said we would launch on that

arbitrary date.

857

Yeah, the space agencies do take these

things.

858

It's been fascinating seeing the order,

the things that needed to be rubber

859

stamped to get the approval for the

mission.

860

So very good work people getting that

done.

861

So there are also other proposed space

-based missions, some potential ones in

862

China.

863

There's a potential follow -up mission, I

guess, slightly in the future, maybe in

864

Japan that's been proposed for a few

years.

865

status of these, I guess, it's difficult

getting the funding for these things.

866

So I think it's an exciting time in the

field.

867

Hopefully we'll expand the range of

gravitational waves we can detect and

868

that'll be great.

869

Yeah, yeah, for sure.

870

And I mean, that must be...

871

So I don't know how directly involved you

are on these, Lounch, but I'm guessing

872

that if you're still working on these

when...

873

the mission launches, I'm pretty sure the

day of the launch, you will be pretty

874

nervous and excited.

875

Have you already lived that actually, or

would that be new to you?

876

So I mean, the closest analogy would have

been there was a technology mission to

877

test some of the key components of Lisa

called Lisa Pathfinder that went up a few

878

years ago, an extremely successful

mission.

879

And so watching that from the sidelines,

my PhD was on LISA.

880

If this mission didn't work, then there'd

be no LISA mission.

881

So all my PhD work would be in vain.

882

But thankfully, it worked very well and

worked better than what was hoped for, in

883

fact.

884

So that was great.

885

And I guess that's a real testament to the

experiment, as saying I was feeling

886

worried because it was my PhD work.

887

But there really people in the field who

have spent their entire careers working on

888

this technology, you know, multiple

decades.

889

So it's all.

890

Yeah, real testament to their

determination, I guess, their vision going

891

into a field right at the beginning before

anything worked to look at these things.

892

It's also honestly quite remarkable that

we somehow managed to convince the funding

893

agencies to fund these things for so long

before there would be scientific returns.

894

So, yeah, we're extremely grateful that

they had the forethought and the patience

895

to invest in something so long before it

would give returns.

896

Yeah, definitely.

897

Yeah, that must be absolutely fascinating.

898

John, anything you want to add on that?

899

I think Christopher is doing a great

overview of WISA, which indeed will be an

900

enormous challenge on the ground.

901

There are also plans to take things

forward into the 2030s and beyond.

902

Currently, there are two major...

903

detectors in the kind of scoping design

stage.

904

One is led by the Europeans called the

Einstein Telescope and the other one is

905

led by the US called Cosmic Explorer.

906

They're taking different approaches.

907

They're both going by detectors.

908

The challenge there is to lower the noise

floor.

909

So giving them a sort of order of

magnitude improvement in the range that

910

you can see things to, which translates to

911

thousand -fold increase in the volume that

you can see things to, more or less.

912

At these kinds of distances, you do

actually have to worry about the size of

913

the universe, getting in the way of these

calculations.

914

But yeah, these new experiments will

require a new infrastructure.

915

So they're also going to require a new

batch of experiments from national,

916

indeed, European land.

917

best friend.

918

A lot of the data analysis challenges for

those are kind of similar to the ones that

919

we're tackling with the current generation

of ground -based detectors.

920

But the major difference is that the

signals would be much longer because the

921

low frequency end is really the target for

improvement.

922

I think that's the way that the binaries

chop.

923

I mean, okay, I told you that they sort of

make this characteristic, whoop, type

924

noise.

925

Maybe you can find a sample.

926

and pluck out my pale imitation.

927

The lower in frequency you start, the

longer the signal will be.

928

That multiplies the amount of data that

you have to analyze, which with a Bayesian

929

problem can be a bit challenging.

930

If you're doing many millions of light

-weighting evaluations, you don't want

931

each light -weighting evaluation to be

expensive.

932

And also the signal -to -noise ratio will

be huge.

933

Least effects are 10 higher.

934

So you will run into problems with our

uncertainties on the nature of the

935

sources.

936

So the models that we have are very good

theoretical models at the moment and

937

they're good enough for the current

generation of detectors, but they will

938

break down once observations become good

enough.

939

They will probably show the crops in

theories, which I should say is probably

940

not a fundamental part in the theory.

941

I think most people probably would put

their money on general relativity being

942

correct.

943

The problem is that there is a translation

layer between general relativity and the

944

types of temperament we can use it that

requires approximations and shortcuts and

945

models to be created.

946

So there's challenges with modeling and

balance that are quite difficult to

947

overcome and people are searching that as

well at the moment.

948

Yeah, fantastic.

949

Thanks a lot, guys.

950

That's really fantastic to have all these

overviews of the missions.

951

And actually, I'm wondering, so with all

that work that you've been doing, all

952

these studies that you've been talking

about since we started recording, we've

953

been able to study actually what

954

we want to do, right?

955

So study the astrophysics of black holes

and also some tests of general relativity,

956

as you were saying, Christopher.

957

Can you tell us about that and mainly what

are the current frontiers on those fronts?

958

What are we trying to learn with the

current missions?

959

That's a big question.

960

So general relativity, I guess, we really

want to find somewhere where it doesn't

961

work.

962

So for the point of view of understanding

gravity, there's this tension within

963

physics that how do you reconcile general

relativity with quantum theory?

964

And that is rather tricky and the whole

host of different theoretical frameworks

965

to try and reconcile this.

966

But we don't know for certain what the

answer is.

967

And finding some hint where general

relativity breaks down would give a

968

pointer in the right direction.

969

Of course, finding a place where general

relativity breaks down is very difficult.

970

The place where I think it makes sense to

look most is the most extreme environment.

971

So where is gravity strongest?

972

Where is the spacetime most dynamical?

973

Where do things change the quickest?

974

So black hole mergers, I think, are

really, and the gravitational wave

975

signals, they admit, are the

976

best place to look for that.

977

So that's why we're looking there.

978

And what we'd really love to find is some

deviation from general relativity that we

979

could actually be certain is a deviation

from general relativity and not just a

980

noise artifact.

981

So I think we're pursuing a whole host of

different things to look for deviations

982

there.

983

On the astrophysics point of view, there's

just so much we don't know about the

984

progenitors of these sources.

985

So how do

986

we end up with black holes and neutron

stars.

987

So stars are pretty important in

astronomy.

988

Exactly how they work is kind of

complicated.

989

So there's a lot of uncertainties in that.

990

And I think it's really quite remarkable

how rapidly the field has progressed.

991

So back in 2015, before we made our first

detection, it wasn't at all certain that

992

we would find pairs of black holes

orbiting each other and merging.

993

We knew there would be neutron stars.

994

But we didn't know they're black holes

because we'd never seen them.

995

They're really hard to see other than

gravitational waves.

996

That's kind of why we built the

gravitational wave detectors.

997

But we hadn't seen any of them.

998

So our first detection confirmed, yes,

they exist.

999

And they exist in sufficient numbers that

we can actually detect them.

Speaker:

And then the follow up was when we

measured the masses, they were about 30

Speaker:

times the mass of our sun.

Speaker:

We'd never seen black holes in that mass

range before.

Speaker:

We now know, yep, there's quite a few of

them.

Speaker:

But whether you can form black holes that

big,

Speaker:

tells you something about the way that

stars live, how much mass they lose

Speaker:

through their lifetime.

Speaker:

So that's a key uncertainty that we don't

really understand about how stars evolve.

Speaker:

So now, as we're building up statistics,

really teasing out the details of the mass

Speaker:

distribution, what is the biggest black

hole that you can build?

Speaker:

Currently, we know there are these black

holes that form from stars collapsing.

Speaker:

And we know there are these massive stars,

massive black holes, millions of solar

Speaker:

masses.

Speaker:

lightest ones, hundreds of thousands, tens

of thousands.

Speaker:

But we don't know, is there a continuous

distribution of black holes in between?

Speaker:

So are there hundreds of thousands of mass

black holes?

Speaker:

So that's one of the key things to figure

out.

Speaker:

Is there a key thing?

Speaker:

Where do these big, really big, massive

black holes come from?

Speaker:

And how do stars evolve?

Speaker:

The details of all the different ways that

you could end up with massive black holes

Speaker:

that people theorized?

Speaker:

Which ones are correct?

Speaker:

In what ratio out there?

Speaker:

And then I guess one...

Speaker:

One additional key thing, we talked about

black holes in nature gravity.

Speaker:

We've talked about how you form black

holes in neutron stars.

Speaker:

But there's also what neutron stars are

really made of.

Speaker:

So neutron stars, from the name you might

suggest, OK, they're made of very neutron

Speaker:

-rich matter.

Speaker:

But actually, what happens inside the core

of a neutron star, we get a whole host of

Speaker:

different phase changes, really quite

exotic matter going on that we can't hope

Speaker:

to replicate in the lab here on Earth.

Speaker:

So we really don't know.

Speaker:

this behaves.

Speaker:

If we did, that would be really

informative for understanding the dynamics

Speaker:

of the particles that make those.

Speaker:

So by making measurements of the neutron

stars we observe, how much they stretch

Speaker:

and squeeze, we can hopefully get some

constraints on what neutron stars are made

Speaker:

of, which would be an exciting frontier

there.

Speaker:

John?

Speaker:

One thing that I think we can zoom out

from looking at the individual black holes

Speaker:

and neutron stars and

Speaker:

Still with the theme of trying to

understand gravity is on the other scale

Speaker:

is cosmology, the very, very largest

scales, how is the universe evolving over

Speaker:

time?

Speaker:

Hopefully with the current generation and

the next generation, we'll be able to do

Speaker:

cosmology in a completely different way

than what we have done up until now.

Speaker:

By looking at the gravitational wave

signal, so those...

Speaker:

properties of those signals, the fact that

we know exactly what they look like, their

Speaker:

amplitude and how it would case with

distance means that they can be used as an

Speaker:

independent co -coxmology.

Speaker:

Now we've already done this with the

prying intrastar signal and with black

Speaker:

holes that we've seen up to now,

relatively low numbers of sources such

Speaker:

that the constraints that we're able to

cook are not yet competitive with the best

Speaker:

constraints that we can get from other

techniques.

Speaker:

But going forward, as the numbers improve,

as the SNRs and the applies ratio

Speaker:

improves, this is going to get better and

better over time.

Speaker:

And so even if we don't see anything on

the scale of the individual black holes,

Speaker:

if this agrees with general relativity, it

could still help us en masse to pin down

Speaker:

what's going on with cosmology, where

there are many things that we don't

Speaker:

understand, including discrepancies in the

existing constraints we have.

Speaker:

No one.

Speaker:

And I'm curious, among all of these

burning issues, burning questions, if you

Speaker:

could choose one that you're sure you're

going to get the answer to before you die,

Speaker:

what would it be?

Speaker:

I don't know how long I'm going to live,

but the thing that really motivates me is

Speaker:

trying to understand whether the black

holes that we're seeing really are the

Speaker:

things that you can write down with pencil

and paper when you're teaching people

Speaker:

general relativity, or are they more

complicated than that in reality?

Speaker:

I think if there was one problem I have to

choose in this field, that would be the

Speaker:

one that I found the most interesting.

Speaker:

I think I'd really like to know the answer

to that one as well.

Speaker:

I think that might be one of the most

challenging to actually get the solution

Speaker:

to.

Speaker:

The best way to answer it might be to

travel into a black hole.

Speaker:

But then the question of whether you

observe anything before you die becomes

Speaker:

rather technical.

Speaker:

Yeah.

Speaker:

Certainly something not advised for your

listeners to give that a go.

Speaker:

Yeah, I am not sure it would end up like

Matthew McConaughey in The

Speaker:

What's the movie?

Speaker:

You know that?

Speaker:

Interstellar.

Speaker:

So Kip Thorne is one of the founders of

LIGO.

Speaker:

One of the recipients of the Nobel Prize

for Gravitational Analytics.

Speaker:

He's behind Interstellar.

Speaker:

So he advised on a lot of it.

Speaker:

Yeah, the bit at the end is not backed up

by science.

Speaker:

For sure.

Speaker:

At least for now.

Speaker:

They originally were going to have the

wormhole thing that opens up in

Speaker:

Interstellar.

Speaker:

They're going to have that detected with

gravitational waves at LIGO.

Speaker:

Unfortunately, Christopher Nolan cut that

bit.

Speaker:

Oh, that's a shame.

Speaker:

It wasn't in the film.

Speaker:

Maybe that would be for Interstellar 2.

Speaker:

We don't know.

Speaker:

So guys, thanks a lot.

Speaker:

I've already taken a lot of your time.

Speaker:

And I still have a good talk for you.

Speaker:

hours because this is really really

fascinating but it's time to call it a

Speaker:

show before that though as usual i'm gonna

ask you the the two questions i ask every

Speaker:

guest at the end of the show first one if

you had unlimited time and resources which

Speaker:

problem would you try to solve um who

wants to start

Speaker:

I think if you're really serious about the

unlimited time resources, then the most

Speaker:

pressing problem I think would be nothing

to do with adaptation waves, but it's more

Speaker:

to do with the climate breakdown.

Speaker:

So if you want an honest answer, that's my

answer, is solve climate change.

Speaker:

That's a very popular answer.

Speaker:

Get nuclear fusion working.

Speaker:

That would be very nice.

Speaker:

In our field with infinite resources, I

tackle the quantum theory of gravity and

Speaker:

get the evidence for that.

Speaker:

Would be nice.

Speaker:

Yeah, definitely.

Speaker:

That is a great answer.

Speaker:

And I think also some people answered

that.

Speaker:

So you're in good company, Christophe.

Speaker:

And second question, if you could have

dinner with any great scientific mind

Speaker:

dead, alive or fictional, who would it be?

Speaker:

Maybe Chris, the only answer for, uh,

dead, I think for this podcast, and James

Speaker:

would be my choice.

Speaker:

You may know him if you're a Bayesian.

Speaker:

Yeah.

Speaker:

Um, I think he would be very good dinner

company.

Speaker:

Um, his textbook was one of the formative

influences on me as a young Bayesian.

Speaker:

Yeah.

Speaker:

Yeah.

Speaker:

Yeah, for sure.

Speaker:

And, uh, there is a, there is a really

great, uh, YouTube.

Speaker:

series playlist by Aubrey Clayton, who was

here on episode 51.

Speaker:

So Aubrey Clayton wrote a book called

Bernoulli's Fallacy, The Crisis of Modern

Speaker:

Science.

Speaker:

Really interesting book.

Speaker:

I'll link to the episode and also to his

YouTube series where he goes through E .T.

Speaker:

Jane's book, Probability Theory, I think

it's called.

Speaker:

which is a really great book, also really

well written and already goes through its

Speaker:

chapters and explain the different ideas

and so on.

Speaker:

So that's also a very fun YouTube playlist

if you want I'm definitely going to go and

Speaker:

look that up.

Speaker:

Awesome, yeah.

Speaker:

I'll send that your way.

Speaker:

And Christopher?

Speaker:

One of my favorite books, yeah.

Speaker:

I don't know, I think I might be somewhat

boring and just go for Einstein for the...

Speaker:

of both gravity, I think he'd like to know

what we're up to.

Speaker:

And also just to see what, you know, his

thoughts were being about being such a

Speaker:

public intellectual and what it was like

being that would be being cool.

Speaker:

I could invite a guest might be

interesting to get Newton along as well,

Speaker:

and see what they think about gravity.

Speaker:

But I think that would be quite awkward in

a conversation, I get the feeling, not the

Speaker:

socially the most interactive.

Speaker:

Yeah, yeah.

Speaker:

Do you think Einstein would accept at that

point the, like all the advances in, like

Speaker:

all the ramifications of actually general

relativity and so on and the crazy

Speaker:

predictions that that was making and in

the end, most of them, like for now, at

Speaker:

least were true, but at the end of his

career, he was not really accepting that.

Speaker:

Do you think he would accept that now?

Speaker:

I think he would accept the general

relativity and he would be delighted to

Speaker:

find that we've seen some of the effects

that he never thought he observed.

Speaker:

And again, he himself knew the general

relativity couldn't be the final answer to

Speaker:

the correction of gravity.

Speaker:

So he'd probably also be interested to

know how we've seen any signs of it

Speaker:

breaking down.

Speaker:

And I think the stuff that motivated him

towards the end of his career is

Speaker:

probably...

Speaker:

still what's motivating a lot of people.

Speaker:

Well, if you are invited to such a dinner,

please let me know and I will gladly come.

Speaker:

Awesome guys.

Speaker:

I think it's time to call it a show.

Speaker:

You've been wonderful.

Speaker:

Thanks a lot for taking so much time.

Speaker:

As usual, I will put resources and a link

to your websites in the show notes for

Speaker:

those who want to dig deeper.

Speaker:

The show notes are huge for this episode,

I can already warn listeners.

Speaker:

So lots of things to look at.

Speaker:

And well, thank you again, Chris and John

for taking the time and being on this

Speaker:

show.

Speaker:

Thank you very much.

Speaker:

I may put in one thing that your listeners

might like.

Speaker:

They're interested in trying gravitational

wave data analysis.

Speaker:

Data are public.

Speaker:

They can look up the Gravitational Wave

Open Science Center, download the data

Speaker:

there.

Speaker:

Also, they'll find links to tutorials.

Speaker:

There are workshops held fairly regularly

that they can maybe sign up to to get some

Speaker:

data analysis experience.

Speaker:

And there's a whole list of open source

packages for gravitational wave data

Speaker:

analysis linked from those so they can go

and have a look at themselves.

Speaker:

Yeah, this is indeed a very good ad.

Speaker:

Thank you very much, Christopher.

Speaker:

I actually already put these links in the

show notes and forgot to mention them.

Speaker:

So thank you very much.

Speaker:

Because we're all very dedicated to open

source and open source here.

Speaker:

So if any of the listeners are interested

in that, like how these things are done,

Speaker:

You have all the packages we've mentioned

in the show notes, but also the open

Speaker:

source and open science efforts from your

collaborations, Christopher and John.

Speaker:

So definitely take a look at the show

notes.

Speaker:

Everything is in there.

Speaker:

Thank you guys.

Speaker:

And well, you can come back on the podcast

any...

Speaker:

Any time, hopefully around 2034 to talk

about Lysa and the space -based mission.

Speaker:

I'll put it in my calendar.