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Learning Bayesian Statistics: Daily Summaries Delivered
by Alexandre Andorra
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
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- 3 days ago1h 26m
#168 Speech Perception & Multilevel Models, with Santiago Barreda
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: Why would a linguist switch from lme4 to Bayesian multilevel models?A: For Santiago, it was purely practical. Mixed-effects models fit with lme4 kept failing to converge, and they couldn't handle the complex repeated-measures structures his experiments needed. His friend Noah Silbert got him into Bayesian modeling around 2015, and only afterwards did he realize he agreed with the philosophy too. His analogy: the frequentist toolbox is a furniture store, and if it doesn't sell the bed you need, you settle for the nearest one; Bayesian modeling teaches you carpentry, so the model can match what you believe is going on in your data instead of squeezing the data into a standard structure.Q: Why teach Bayesian multilevel models before t-tests and ANOVA?A: Because in linguistics essentially all data are repeated measures: listeners judge hundreds of trials, and speakers produce many tokens. Yet students traditionally spend a year or more on one-sample t-tests, paired t-tests and ANOVAs they will never use in their own research. Santiago's book jumps straight to the multilevel version of the simplest case, a one-group model with many observations per listener, which he finds no harder to grasp than a t-test since there are no reference distributions or degrees of freedom to explain.Q: Do Bayesian and frequentist analyses give different results on typical phonetics data?A: With analogous models, largely no, at least with the amount of data phonetics experiments usually have. That's why the early chapters of Santiago's book end with a comparison to the equivalent frequentist analysis, to reassure readers. His rule of thumb: if you get dramatically different results, something has probably gone wrong. The gain from going Bayesian is not different point estimates, but models that actually converge, flexible error distributions and model structures, and much richer information about the so-called random effects, which in speech research describe how listeners vary within a speech community.Full takeaways here!Chapters:09:09 Why did Santiago switch from lme4 to Bayesian multilevel models?11:50 Why is Bayesian modeling like learning carpentry instead of shopping at IKEA?18:10 How does Santiago's book differ from classic Bayesian textbooks?21:11 Why do so many students wrongly decide they're bad at math?24:01 Why is learning statistics more like learning the piano than memorizing facts?29:53 What do listeners infer about a speaker from their voice, and why are they wrong in predictable ways?43:59 How is vowel normalization like judging an object's size at a distance?49:19 How do animals use their calls to signal body size?56:15 Can we predict how accents and languages will change?01:00:15 Why did Latin die, and what counts as a separate language?01:07:28 What is Santiago working on next?Thank you to my Patrons for making this episode possible! Full links from the show here.
- 1 weeks ago22 min
How I built Learn Bayes Stats to the Top 1.5%
This one is a bonus episode, where I was the guest, on a podcast called One Thing That Worked! Get all the insights and takeaways here. In the meantime, here is how they described it:In this insightful episode of One Thing That Worked, my guest is Alex Andorra, host of Learning Bayesian Statistics Podcast. Alex reveals how he built a top-tier show that ranks among the top 1.5% of podcasts globally out of nearly 4 million shows.Discover how Alex leveraged "The Selfish Method"—creating the exact show he needed for his own career growth—to attract a hyper-dedicated audience of technical experts. We explore his core podcast growth strategy, focusing on a specialized niche and publishing biweekly episodes like clockwork since 2019.Alex also opens up about podcast revenue, handling podcast sponsors, and funding operations via Patreon while keeping the content independent. In this conversation, we break down the power of relentless consistency, the value of solving your own problems, and why learning through public failure is a superpower for creators looking to master podcasting and build an engaged community.Chapters0:00 - Intro01:25 - About Learning Bayesian Statistics Podcast05:35 - What Bayesian Statistics Is08:44 - The Main Thing That Worked11:03 - Building Network & Community 13:23 - Monetizing The Show16:17 - Main Lessons from AlexHope you like it, my dear Bayesians! As usual, you can support the show on Patreon, and reach out to me with fun ideas 🖖
- 1 weeks ago3 min
Can Neural Networks Replace MCMC?
Today’s clip is from Episode 167 of Learning Bayesian Statistics, featuring Paul-Christian Bürkner and Steve Bronder, recorded live at StanCon 2026 in Uppsala, Sweden.Paul Bürkner, creator of brms and a leading researcher behind BayesFlow, explains how neural networks can replace MCMC for Bayesian inference. Instead of evaluating likelihood and prior densities, the networks are trained on simulated data, so you can do simulation-based inference (SBI) even when the likelihood is intractable. Once trained, they give you amortized, real-time posteriors for new datasets, and they have made SBI scalable well beyond what approximate Bayesian computation could handle.Paul is also candid about the limits. Neural methods come with unstable training and no guarantees, and they can be unreliable on out-of-distribution or misspecified data, which is why MCMC is still the more trustworthy option wherever you can apply it. He ends with how his group is building diagnostics to flag when a neural posterior can’t be trusted.Full discussion hereSupport & 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!
- 2 weeks ago1h 3m
#167 Amortized Inference & GPUs for Stan, with Paul-Christian Bürkner & Steve Bronder
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 amortized Bayesian inference and how does it differ from MCMC?Instead of running MCMC on each dataset, you train neural networks on data simulated from the model, so you don't need likelihood or prior densities. Once training is done, inference on a new dataset is essentially instant: new data in, posterior out. The price is everything neural networks bring with them, from unstable training to a lack of guarantees. Paul's stated goal is to make these methods as reliable and robust as MCMC while staying orders of magnitude faster, and he's candid that he doesn't know whether the field will ever get there.Q: Why would a Bayesian model not have a usable likelihood?A: Usually not because the likelihood can't be written down in principle, but because computing it is so expensive or numerically unstable that it's intractable in practice. Paul gives two cases. First, mechanistic models built on complicated differential equations, as in physical chemistry or biology, where you can't solve through the equations to get densities and gradients in a stable, fast way. Second, big latent variable models with thousands of latent variables between the parameters and the data, where marginalizing them out is hopeless. In both cases, simulating from the model is easy: simulate the parameters, the latents and the data, throw the latents away, and learn the relation between parameters and data from the simulations.Full takeaways here!Chapters:15:33 What is amortized Bayesian inference and when should you use it instead of MCMC?23:18 Why would a Bayesian model not have a usable likelihood?26:03 What's holding back GPU computing in Stan?31:14 What are sum-to-zero constraints and why do they make models sample faster?35:55 What is a Jacobian adjustment in Bayesian statistics?39:17 How do you diagnose failures in amortized Bayesian inference?42:01 What is leave-one-group-out cross-validation for hierarchical models?45:57 Do undertrained neural posteriors overestimate or underestimate uncertainty?49:06 How do Stan developers use AI tools in their work?55:47 Should Stan and brms hide the inference algorithm from users?Thank you to my Patrons for making this episode possible!Full links from the show here!
- Oct 7, 20263 min
What Do Kernels, Length Scale & Amplitude Mean in Gaussian Processes?
Today's clip is from Episode 166, featuring Bill Engels & Jesse Grabowski. In this conversation, Bill explains what a kernel means in a Gaussian process and how it defines the idea of similarity between data points. He then breaks down the role of the length scale, showing how it controls how quickly the relationship between two points changes, and how amplitude controls the overall scale of the functions a GP can represent. The discussion also connects these ideas to the practical use of Gaussian processes for modeling unknown nonlinear relationships, and why kernels provide an interpretable way to describe how inputs are related.Full discussion hereSupport & 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!
- Oct 1, 20261h 58m
#166 PTGP: A New Gaussian Process Library, with Bill Engels & Jesse Grabowski
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 PTGP and why did Bill and Jesse build it?A: PTGP is a new Gaussian process library built on PyTensor and PyMC, aimed squarely at practitioners rather than researchers assembling their own GP methods from papers. Bill Engels, who wrote PyMC's original GP submodule during a Google Summer of Code, built it because most GP libraries implement one method well but give little guidance on when to use it or how to fix it when it breaks. PTGP is opinionated by design: it picks battle-tested algorithms, tells you which one fits your data size, and ships the debugging knowledge alongside the code.Q: Why are Gaussian processes described as sitting at the intersection of statistics and machine learning?A: A Gaussian process starts from a simple idea: things that are close in the input space should be close in the output space, and the kernel function defines exactly what "close" means for your problem. That makes GPs look like machine learning (let the data speak through a flexible function) while staying fully interpretable once you've chosen a kernel, since observing data collapses the process into an ordinary multivariate normal.Full takeaways here!Chapters:05:51 Where do Gaussian processes actually get used in practice?09:07 What do a kernel's length scale and amplitude actually control?11:58 What is HSGP and how does it combine with hierarchical models?14:51 Where does PTGP fit in a modern data science workflow?21:01 Are Gaussian processes interpretable, or are they a black box?27:49 Why aren't Gaussian processes used everywhere already?32:44 What does a kernel function actually tell you about your data?46:33 What is PyTensor and what does it give you over other backends?50:54 How do you build a Gaussian process model in PyTensor?52:09 Why is fitting a Gaussian process so computationally expensive?56:00 How does PyTensor's rewrite system speed up GP math for you?59:54 How did an eight-line rewrite replace a matrix inverse in PTGP?01:01:10 Which backends can PyTensor compile your Gaussian process to?01:11:27 What are inducing points and when should you use them?01:22:09 What goes wrong when you fit a VFE approximation, and how do you fix it?01:23:18 How do you use an AI agent inside a Jupyter notebook?01:36:06 What are PTGP's skill files and which failures do they catch?01:42:20 How do you balance learning something against shipping it with an LLM?01:44:28 How do you tell a useful LLM answer from a convincing wrong one?01:48:37 Why does a good-looking AI output create an illusion of learning?Thank you to my Patrons for making this episode possible!Full links from the show here!
- Sep 28, 20264 min
How AI Can Evaluate Bayesian Workflows with Bayesify
Today's clip is from Episode 165, featuring Alex Fengler. In this conversation, Alex introduces Bayesify , a tool that uses AI to analyze research papers and assess how well they follow a Bayesian workflow.He explains how the tool breaks an analysis down step by step, identifies strengths and weaknesses, and provides suggestions for improving the paper. They also discuss how BasiFi can be used as an educational resource, a review engine for researchers, and potentially as a way to study how the quality of Bayesian analyses has changed over time.Alex also explains why the team is building a human-rated "gold set" of papers to evaluate how well the tool's scoring aligns with expert judgment. It's an interesting example of how AI can be used not just to generate research, but to help verify and evaluate statistical workflows.Full discussion hereSupport & 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!
- Sep 18, 20261h 47m
#165 Hierarchical Sequential Sampling Modeling, with Alex Fengler
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 HSSM and how does it relate to HDDM?A: HSSM stands for hierarchical sequential sampling models, a generalization of HDDM (hierarchical drift diffusion models), the older toolbox for the same class of decision-making models, but HSSM is built from the ground up on simulation-based inference. That's what lets it handle any variation of the underlying process model, not just the ones with a tractable closed-form likelihood.Q: What is the drift diffusion model and why has cognitive science relied on it so heavily?A: The drift diffusion model treats a decision as a random walk that accumulates evidence until it crosses one of two boundaries, with parameters controlling boundary separation, starting bias, and drift rate. It's been used in thousands of published papers largely because it has a closed-form likelihood, which makes standard Bayesian and maximum-likelihood inference fast. Small variations on the model are often just as scientifically motivated, but if their likelihoods aren't analytically convenient, the literature using them stays sparse.Q: What is a likelihood approximation network (LAN) and what does it actually learn?A: A LAN is a neural network trained to take in a process's parameters and a trial's outcome and output how likely that outcome was, learned purely from repeated simulation rather than derived analytically. Once trained, it functions as a fast, reusable likelihood you plug directly into Bayes' rule, in place of a closed-form solution that may not exist for the model you actually want to fit.Q: What's the difference between amortizing the likelihood and amortizing the posterior?A: Amortizing the likelihood, HSSM's approach, means training a network once to approximate the likelihood, then reusing that same network across arbitrarily many downstream models: different priors, hierarchical structures, or regression backends, with no retraining. Amortizing the posterior directly, the approach tools like BayesFlow take, gives near-instant inference once trained, but locks the network into the specific scenario it was trained for.Chapters:00:00:00 What is HSSM and how does it fit into the Bayesian inference landscape?00:12:09 How did HSSM evolve from HDDM, and what does it apply to?00:30:25 How do neural networks learn likelihoods for Bayesian inference?00:37:01 What makes amortized Bayesian inference so flexible?00:41:04 What are the real computational costs of amortized inference?00:55:16 How does HSSM integrate with libraries like BayesFlow?00:58:57 What does a live demo of HSSM and BayesFlow look like?01:18:33 What is Bayesify and how does it score a paper's Bayesian workflow?01:23:12 What new model classes are coming to the HSSM ecosystem?01:30:12 How is AI reshaping development in the HSSM ecosystem?01:38:42 How should society incentivize keeping hard cognitive skills alive?Thank you to my Patrons for making this episode possible!Links from the show.
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About Learning Bayesian Statistics
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
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