Normal distribution

And if those names sound familiar,

it's because Bill wrote PyMC's original Gaussian process submodule during a Google Summer of Code years ago.

And Jesse is a returning guest who came on to talk state space models and Kalman filters back in episode 124.

This time, they are both here to talk about Gaussian processes and specifically about PTGP, a brand new opinionated GP library built on top of PyTensor and PyMC, with a lot of help from Jesse's work on PyTensor's rewrites system.

We get into what a kernel actually is, what length scale and amplitude really mean, why GPs are so expensive to fit exactly, and how PyTensors rewrites let PTGP stay fast without hiding the math from you.

We also talk about HSGP, inducing points, and when to reach for which approximation.

But thanks Bill for saving my feelings.

Yeah, actually, let's do your origin story.

Most statistical methods assume that data is what's called normally distributed.

And we'll get to this if you've ever heard of the bell curve.

What this is, is when you sample something long enough, It will create what's called a bell curve and the bell curve looks like this, this figure right here.

Where if we draw a line down this middle that's going to represent our mean or average where 50% are on one side and 50% are on the other, but what the bell curve does is it tells us something about the population.

So when we look at the mean, for example, of a normal distribution, 50% lays on one side, 50% lays on the other, but then we have something called a standard deviation, okay? Standard deviation is a measure of what we call variation, the variation between scores, okay? And what the basic definition of a standard deviation is it's the average distance between individual scores and the mean.

So it's telling us what the average differences between individual scores are.

If someone scores below an 85, we'll do further testing to see if they have some type of developmental cognitive issue.

When people score above a 115, then we start looking to see, well, why is it that they are scoring so much higher than the average population? And so this is kind of what's unique about the standard population.

Now, this doesn't matter what the shape of the distribution is.

Like you said, well, I'm drawing them as Gaussians, but this could be Pareto.

This could be like long-tailed, fat-tailed kind of stuff.

It could be very skewed.

I think 120 or something is a genius, and at 80...

And it's equidistant, right? So we believe systems are Gaussian, they're normal.

You know, that's how we learn.

If you do any statistics, you're taught that in first year.

It really all about the mechanics memory You know How do we retrieve an identity consumed by time? And how do build archive strong enough to hold someone known globally ?

Okay lets unpack this starting with he case From the source that really highlights fragility of identify Lets look facts surrounding Phillip Sidner Right the Antioch Case Yeah so his remains Specifically just human skull were found thirty five years ago We are talking about nineteen ninety one Which I mean forensics was completely different back then Completely Mm The reporting notes would been forty years old at the time .But detail that really stops you your tracks Is how was found It wasn't coordinated police search No grid search no trained dogs No Just neighborhood dog A Dog Found Skull In An Antioch Neighborhood On Barksdale Lane Randomness That crucial Think About Police Search For Missing Person They Apply Logic Like Looking Cell Phone Pings Last Known Locations Exactly When Pet Dog stumbles upon Remains Its Total chaos bypasses All logic Have To Consider Landscape Time Source Text Point Out Antioch Neighborhood Looks Very Different Now Than Did Thirty Years Ago Oh I Mean Thirty -five Years Growing City Practically Geological Era Really Talking paving Over Dirt Cutting Down Old Trees Laying Concrete Foundations Entire Subdivisions Physical Geography Barksdale Lane Nineteen Ninety One Been Layered Over Again And physical transformation represents Literal Burying Past Earth Absorbs Evidence Human Development Seals It In Seals Right In Original Residents Move Away New People Move In Collective Memory Whatever Happened Gets Completely Overwritten Makes Finding Crazy Stark Collision Past Present Forces Unresolved History Modern Concrete Instead Lucky Discovery Leading Quick Answer Investigation Hits Massive Decades Long Wall Yeah Thirty Year Roadblock hits Colossal Mistake Initial Anthropology Report Nineteen Ninety One Incorrectly Identified Belonging Woman Devastating Push Back Genuinely Shocked Official Trained Forensic Anthropologist Get Something Fundamental Biological Sex Completely Wrong Hard Wrap Head Around Today What Cascading Consequences Single Error Raises Important Question Requires Us Look Critically Fallibility Historical Science Wasn't Precise Back Then Not At All View Forensics Through Lens Of Infallible Binary Data Dna Match Nineteen Ninety One Anthropologists Were Heavily Reliant Morphological Characteristics Visually Assessing Shape Bone Precisely That Physical Bumps Ridges Prominence Brow Ridge Jawline Mastoid Process Behind Ear Make Judgment Call Essentially Generally Speaking Male Skulls Tend Be More Robust Human Variation Exists Bell Curve Everyone Fits Perfectly Box Or Box exactly skull Actually Ambiguous Parts Skeleton Determining Sex Compared Pelvis Skull Sits Middle Bell Curve Visual Assessment Highly Vulnerable Subjective Error Wow consequences Subjective Error Absolute Detective Nineteen Ninety One Official Report Jane Doe Gospel Law Enforcement Rigid Literal Binary Filters If Reports Says Female Systematically Eliminate Everysingle Missing Mail Database Pulling Dental Records Probably Discard Any Tips About Missing Men Antioch Area One Mistake Effectively Erased Philip Sydney Own Investigation They spent years looking for a ghost, a woman who didn't even exist in the context of those remains.

He was physically found but systematically lost all over again.

And you know, the tragedy is compounded by a secondary failure, one that happens outside the police station.

It's a dangerous shithole." Then why do you go back to Syria on vacation twice a year? Right? Why, why, why are you constantly sending money and, and, and going back to these places? Right? W- why, if it's, if it's so awful, are, you know...

Do you go back to Pakistan to pick a wife and bring her back to England? Why? Well, 'cause you're just-- You're here and, and for the reasons that, you know, are elucidated in Bell Curve and elsewhere and, and that every one of these people knew.

This is the Rothfeld Brockwell report.

Jeff Tucker was there.