Learning Bayesian Statistics

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.

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.

Chapters
0:00 - Intro
01:25 - About Learning Bayesian Statistics Podcast
05:35 - What Bayesian Statistics Is
08:44 - The Main Thing That Worked
11:03 - Building Network & Community
13:23 - Monetizing The Show
16:17 - Main Lessons from Alex

Hope you like it, my dear Bayesians! As usual, you can support the show on Patreon, and reach out to me with fun ideas 🖖

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 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!

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!

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 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!