Learning Bayesian Statistics

Alexandre Andorra
  • 4.4 (16)
  • Technology
  • Updated fortnightly

Are you a researcher or data scientist / analyst / ninja? Do you want to learn Bayesian inference, stay up to date or simply want to understand what Bayesian inference is? Then this podcast is for you! You'll hear from researchers and practitioners of all fields about how they use Bayesian statistics, and how in turn YOU can apply these methods in your modeling workflow. When I started learning Bayesian methods, I really wished there were a podcast out there that could introduce me to the methods, the projects and the people who make all that possible. So I created "Learning Bayesian Statistics", where you'll get to hear how Bayesian statistics are used to detect black matter in outer space, forecast elections or understand how diseases spread and can ultimately be stopped. But this show is not only about successes -- it's also about failures, because that's how we learn best. So you'll often hear the guests talking about what *didn't* work in their projects, why, and how they overcame these challenges. Because, in the end, we're all lifelong learners! My name is Alex Andorra by the way. By day, I'm a Senior data scientist. By night, I don't (yet) fight crime, but I'm an open-source enthusiast and core contributor to the python packages PyMC and ArviZ. I also love Nutella, but I don't like talking about it – I prefer eating it. So, whether you want to learn Bayesian statistics or hear about the latest libraries, books and applications, this podcast is for you -- just subscribe! You can also support the show and unlock exclusive Bayesian swag on Patreon!

  1. 19 hr ago

    #163 How to make your models sample faster, with Adrian Seyboldt & Eliot Carlson

    Support & Resources → Support the show on Patreon → Bayesian Modeling Course (first 2 lessons free) Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work Takeaways: Q: What is mass matrix adaptation, in plain terms? A: Mass matrix adaptation is best understood as an automatic, fairly dumb, but very effective reparameterization of your model. The simplest version, the diagonal mass matrix, just rescales each parameter so its posterior standard deviation becomes one, which is exactly what you'd do by hand if you had the patience. Every time you sample a PyMC or Stan model, this kind of reparameterization is happening under the hood. Q: How does Nutpie's approach to mass matrix adaptation differ from Stan and PyMC's default? A: Stan and PyMC's default sampler only use one source of information for diagonal mass matrix adaptation: the posterior standard deviation estimated from warm-up draws. Nutpie also uses the gradients of the log density, which HMC is already computing at every step to build its trajectory. For a standard normal distribution, the covariance of the gradients is exactly the inverse covariance of the draws, so Nutpie takes the geometric mean of the two resulting standard deviations. There's no guarantee it's always better, but in practice it usually is. Q: What problem does "Preconditioning Hamiltonian Monte Carlo by Minimizing Fisher Divergence" actually solve? A: Preconditioning HMC means transforming your target distribution into one that's friendly to sample, but doing that well requires knowing things about the distribution, like its covariance, that sampling itself is supposed to discover. This chicken-and-egg problem is usually handled by sketching a rough estimate from a handful of early warm-up draws, which can burn a large share of total sampling time. Adrian and Eliot's paper formalizes how to make better use of a second signal, the score function, that HMC already computes for free but that Stan-style preconditioning ignores. Chapters: 00:00:00 What is HMC preconditioning? 00:09:03 A more robust low-rank mass matrix 00:11:58 What is mass matrix adaptation? 00:18:06 What does preconditioning HMC mean? 00:20:57 What is normalizing flow adaptation, and when does a linear mass matrix fall short? 00:23:50 When does normalizing flow adaptation actually help, and when is classic mass matrix adaptation enough? 00:27:13 What is Fisher divergence? 00:30:10 Why is HMC's trajectory, not its density, the right target for preconditioning? 00:33:04 What are the diagonal, dense, and low-rank-plus-diagonal versions of mass matrix adaptation? 00:46:25 How much faster is low-rank-plus-diagonal adaptation? 00:51:07 What's the practical recommendation for using Nutpie and its mass matrix adaptation? 00:54:31 Why does low-rank adaptation sometimes fail spectacularly? 01:01:35 Where does this research fit in the bigger picture of HMC? 01:12:12 How could centered vs. non-centered parameterization be chosen automatically? Thank you to my Patrons for making this episode possible! Links from the show here

    #163 How to make your models sample faster, with Adrian Seyboldt & Eliot Carlson

  2. 20 hr ago ·  Bonus

    Bayesian Statistics vs. Epistemology

    Today's clip is from episode 160, featuring Vaden Masrani. In this conversation, Vaden explores the tension between Bayesian statistics and Bayesian epistemology, and why he sees them as fundamentally different. He explains why Bayesian epistemology can run into problems when trying to explain where hypotheses themselves come from, and argues that an emphasis on finding supporting evidence can encourage confirmation bias rather than genuine scientific inquiry. He also discusses Hempel's paradox, Popper's idea of falsification, and why these philosophical problems don't necessarily undermine Bayesian statistics itself. Full discussion here Support & Resources → Support the show on Patreon → Bayesian Modeling Course (first 2 lessons free): Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work!

    Bayesian Statistics vs. Epistemology

  3. 7 Aug ·  Bonus

    Bayesian Epistemology Is "Bayes' Theorem Without the Data"

    Today's clip is from episode 160, featuring Vaden Masrani. In this conversation, Vaden lays out a sharp critique of Bayesian epistemology - the roughly hundred-year-old philosophical tradition, popular in some Oxford-adjacent circles, that treats subjective probability estimates as legitimate even when there's no data behind them. Vaden's core objection: doing Bayes' theorem on numbers you made up in your head is like fitting a regression line to an empty scatter plot - the math looks rigorous, but there's nothing underneath it. He argues this "math-washing" can trick people into thinking a decision is well-informed simply because it's dressed up in probability language, when frequentists and data-driven Bayesians alike would say the same thing: no data, no model. Get the full discussion here Support & Resources → Support the show on Patreon → Bayesian Modeling Course (first 2 lessons free): Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work!

    Bayesian Epistemology Is "Bayes' Theorem Without the Data"

  4. 3 Aug ·  Bonus

    Why Bayesians Have an Edge in AI

    Today's clip is from episode 162, featuring Chris Krapu. In this conversation, Chris explains why Bayesian thinking remains surprisingly valuable in today's AI landscape - even when the models themselves aren't explicitly Bayesian. Rather than uncertainty estimation, Chris highlights a different advantage: Bayesian training provides a deep intuition for concepts like priors, sampling, rejection sampling, and high-dimensional geometry, making it much easier to understand and apply modern AI research. He also discusses why Bayesian methods are becoming increasingly relevant for evaluating agentic AI systems, where complex workflows and limited evaluation data make hierarchical models and sensible priors especially powerful. Get the full discussion here Support & Resources → Support the show on Patreon → Bayesian Modeling Course (first 2 lessons free): Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work!

    Why Bayesians Have an Edge in AI

  5. 28 Jul

    #162 Bayesian Hydrology & GPU AI, with Christopher Krapu

    Support & Resources → Support the show on Patreon → Bayesian Modeling Course (first 2 lessons free) Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work Takeaways: Q: How does putting a Gaussian process on unknown coordinates fix noisy location data in mineral prospecting? A: In mining and geostatistics, the classic Gaussian process model, known there as kriging, assumes you know exactly where each sample was taken. Chris’ project broke that assumption on purpose: the recorded coordinates for each core sample were only accurate to within a rough radius. By treating the true locations as latent variables and putting a Gaussian process over them jointly with the measurements, the model could still reconstruct the underlying gold-concentration field, even though the exact sampling locations were never known precisely. It's a demonstration that Gaussian processes can absorb structural uncertainty that looks, at first glance, like it should make the problem impossible. Q: What is "Poverty Bayes," and what did it cost to train a two-million-parameter Bayesian model? A: Poverty Bayes was Chris’ experiment in seeing how cheaply a large Bayesian model could be trained using modern cloud infrastructure. He fit a hierarchical logistic regression with close to two million parameters, using PyMC's Hamiltonian Monte Carlo on a single A100 GPU rented through Modal, a serverless platform that deploys a Python script straight to GPU hardware with almost no setup. He'd originally guessed it would cost around five dollars, the price of a Big Mac, but the real bill came in an order of magnitude lower. A model that would take a Gibbs sampler weeks to run, and that once required a research lab's dedicated GPU, now costs pocket change and a few minutes of setup. Q: What's the current bottleneck in Bayesian-at-scale tooling? A: Chris argues the software has largely caught up: PyMC's JAX backend and NumPyro make GPU-accelerated Bayesian modeling work out of the box for most problems. What's missing is common knowledge. Companies are clearly running large Bayesian models in production, but the results stay behind corporate firewalls. Chris’ proposal is a community benchmark effort: which frameworks handle a million-parameter Markov random field on a given GPU out of the box, since this kind of expensive, slow-running benchmark is a poor fit for standard CI pipelines but valuable for the field to know. Chapters: 22:57 When does GPU acceleration actually pay off for a Bayesian model? 26:33 What did it cost to train a two-million-parameter model on Modal? 30:36 What happened when Chris asked 200 different LLMs to flip a coin? 34:50 Where do Bayesian ideas show up in the agentic AI systems Chris builds at Nvidia? 40:16 Are statisticians being made obsolete by large language models? 41:19 How does putting a Gaussian process on unknown coordinates fix noisy data in mineral prospecting? 58:05 What is Chris looking forward to working on next? Thank you to my Patrons for making this episode possible! Links from the show here

    #162 Bayesian Hydrology & GPU AI, with Christopher Krapu

  6. 22 Jul ·  Bonus

    The Next Step Beyond LLMs: Foundation Models for Inference

    Today's clip is from episode 161, featuring Luigi Acerbi. In this conversation, Luigi explains one of the biggest engineering bottlenecks facing transformer-based probabilistic models—and how his group found a way around it. The core challenge is that many inference models treat data as an unordered set, making them naturally permutation invariant. That's statistically elegant, but computationally painful: every time a new data point arrives, the model has to recompute attention over the entire dataset from scratch, preventing the kind of KV caching that makes modern language models so efficient. Luigi walks through his team's solution: a hybrid architecture that keeps the original context fully set-based while introducing a causal-attention buffer for newly arriving data. The result is dramatically faster inference- up to 100× faster in some settings - opening the door to applications like reinforcement learning, active data acquisition, and, ultimately, Luigi's long-term vision of a foundation model for Bayesian inference. Get the full discussion here Support & Resources → Support the show on Patreon → Bayesian Modeling Course (first 2 lessons free) Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work

    The Next Step Beyond LLMs: Foundation Models for Inference

  7. 16 Jul

    #161 Amortized Inference & Neural Processes, with Luigi Acerbi

    Support & Resources → Support the show on Patreon → Bayesian Modeling Course (first 2 lessons free) Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work Takeaways: Q: What is Variational Bayesian Monte Carlo (VBMC) and how is it different from Bayesian optimization? A: VBMC borrows the machinery of Bayesian optimization but aims at a different target. Bayesian optimization fits a Gaussian process surrogate to an expensive function and uses it to hunt for the optimum. VBMC instead treats the log-posterior as the function to model, evaluates it at a few carefully chosen points, and keeps the whole reconstructed shape rather than just its peak. That gives you the full posterior, not a single best-fit value. Where MCMC might need tens of thousands to millions of evaluations, VBMC often reconstructs a good posterior approximation from a few hundred, which matters when each evaluation is slow. Q: When should you reach for PyVBMC, and when is it the wrong tool? A: Two symptoms tell you PyVBMC might help. First, speed: if a single evaluation of your log density takes on the order of a second, running MCMC over tens of thousands of evaluations becomes painful, and PyVBMC's few-hundred-evaluation budget pays off. Second, dimensionality: because it leans on a Gaussian process surrogate, it works well up to roughly 10 to 15 parameters and degrades beyond that. If your model already runs fine in Stan or PyMC, you do not need it. It shines for expensive, low-dimensional models common in science and engineering, where you are modeling a process rather than composing nice distributions. Full takeaways here Chapters: 00:18:13 What is Variational Bayesian Monte Carlo (VBMC) and how does it differ from Bayesian optimization? 00:30:21 When should you use VBMC versus BADS in practice? 00:31:20 What is Bayesian Adaptive Direct Search (BADS) and how does its hybrid optimization strategy work? 00:39:18 What are neural processes, and why are transformers a natural neural process architecture? 00:45:54 What is the Amortized Conditioning Engine (ACE) and what problem does it unify? 00:55:42 What do PriorGuide and the new autoregressive buffer paper solve for amortized inference? 01:02:03 How does the new autoregressive buffer speed up predictions in transformer probabilistic models? 01:06:11 What is Luigi Acerbi's vision for a foundation model for inference? 01:09:26 What is ALINE and how does it add active data acquisition to amortized inference? 01:12:43 How does Luigi Acerbi connect LLM agents, Bayesian decision theory, and the nature of intelligence? 01:18:44 For a PyMC, Stan, or NumPyro user, where should you start with VBMC, BADS, or BayesFlow? Thank you to my Patrons for making this episode possible! Links from the show here

    #161 Amortized Inference & Neural Processes, with Luigi Acerbi

  8. 29 Jun

    Bayesian Statistics vs Epistemology, with Vaden Masrani

    Support & Resources → Support the show on Patreon → Bayesian Modeling Course (first 2 lessons free) Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work Takeaways: Q: What's the difference between Bayesian statistics and Bayesian epistemology? A: Bayesian statistics uses Bayes' theorem on actual data: you put a prior over parameters, combine it with a likelihood, and the data is allowed to tell you your model is wrong. Vaden loves it. Bayesian epistemology, in his tongue-in-cheek phrase, is "Bayesian statistics minus the statistics" - taking Bayes' theorem as a general account of how anyone should reason under uncertainty, including about events where there is nothing to count. The first is falsifiable and grounded; the second, he argues, lets people attach authoritative-sounding numbers to pure belief. Q: Why is it a problem to put a probability on a one-off future event like human extinction? A: Because there are no statistics behind it. Vaden's trigger example is Toby Ord's The Precipice, where a data-derived probability (supervolcanoes per millennium) is placed side by side with a probability of extinction-by-superintelligence that came from no data at all. His reaction is the statistician's first instinct: where are the numbers coming from, and what could ever make them come out differently? A subjective degree of belief is fine as a hunch. The trouble starts when it is communicated as though it were an objective, data-grounded frequency. Q: What does Vaden Masrani actually like about Bayesian statistics? A: The freedom to encode domain knowledge as a prior and have the result respect common sense - estimating an average human height, you can rule out zero and a hundred feet before seeing a single measurement. But the part he keeps stressing is falsifiability: you fit the model, compare it to data, and the data can tell you the model was bad. That contact with reality is exactly what makes the statistics legitimate and what the epistemology lacks. On Bayesian-versus-frequentist for engineering problems, he says he has no dog in the fight -- both are useful, and any working statistician uses both. Full takeaways here Chapters: 00:24:01 What's the difference between Bayesian statistics and Bayesian epistemology? 00:33:12 How can Bayesian epistemology lead to bad real-world decisions? 00:36:36 Is Bayesian or frequentist statistics better for real-world problems? 00:39:31 What is the problem of induction, and how does Bayesian epistemology try to solve it? 00:43:50 What are the main logical problems with Bayesian epistemology? 00:48:40 What is Popper's critical rationalism, and how does falsifiability fit in? 00:52:31 How does critical rationalism work when you can't run a clean experiment? 01:15:03 Why should you treat criticism as a gift, even when it hurts? 01:19:54 How do Stoicism and equanimity help you handle criticism? 01:23:19 Why does critical rationalism apply to everyday life, not just science? Thank you to my Patrons for making this episode possible! Links from the show here

    Bayesian Statistics vs Epistemology, with Vaden Masrani
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About

Are you a researcher or data scientist / analyst / ninja? Do you want to learn Bayesian inference, stay up to date or simply want to understand what Bayesian inference is? Then this podcast is for you! You'll hear from researchers and practitioners of all fields about how they use Bayesian statistics, and how in turn YOU can apply these methods in your modeling workflow. When I started learning Bayesian methods, I really wished there were a podcast out there that could introduce me to the methods, the projects and the people who make all that possible. So I created "Learning Bayesian Statistics", where you'll get to hear how Bayesian statistics are used to detect black matter in outer space, forecast elections or understand how diseases spread and can ultimately be stopped. But this show is not only about successes -- it's also about failures, because that's how we learn best. So you'll often hear the guests talking about what *didn't* work in their projects, why, and how they overcame these challenges. Because, in the end, we're all lifelong learners! My name is Alex Andorra by the way. By day, I'm a Senior data scientist. By night, I don't (yet) fight crime, but I'm an open-source enthusiast and core contributor to the python packages PyMC and ArviZ. I also love Nutella, but I don't like talking about it – I prefer eating it. So, whether you want to learn Bayesian statistics or hear about the latest libraries, books and applications, this podcast is for you -- just subscribe! You can also support the show and unlock exclusive Bayesian swag on Patreon!

Information

  • Creator
    Alexandre Andorra
  • Years Active
    2019 - 2026
  • Episodes
    213
  • Rating
    Clean
  • Copyright
    © 2025 Alexandre Andorra
  • Show Website
    Learning Bayesian Statistics

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