Learning Bayesian Statistics

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  The Next Step Beyond LLMs: Foundation Models for Inference 22.07.2026 5Min.

  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 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
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  #161 Amortized Inference & Neural Processes, with Luigi Acerbi 16.07.2026 1Std. 32Min.

  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 workTakeaways: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 hereChapters: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
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  Bayesian Statistics vs Epistemology, with Vaden Masrani 29.06.2026 1Std. 40Min.

  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 workTakeaways: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 hereChapters: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
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  Why Bayesian Statistics Is More Computational Than Ever 19.06.2026 4Min.

  Today's clip is from Episode 158 featuring Stefan Radev. In this conversation, Alex Andorra and Stefan break down a core argument from their paper: Bayesian statistics has never been more computational than it is now, and simulation is the thread that ties the whole workflow together.Stefan parcellates the Bayesian workflow into four stages, and this clip covers the first two. Stage one is model specification, where the workflow community has long recommended prior predictive checks. You can do this informally, just running simulations from your model and eyeballing whether the output meets your expectations, or formally, à la Michael Betancourt, by pushing your model's high-dimensional output through a transformation into a low-dimensional, interpretable space and checking it against reality. The punchline: a surprising number of models can be discarded before you've even seen real data, yet Stefan notes these checks remain underused in practice.Stage two is model verification, where the question shifts to whether your inferences are well calibrated. This is the territory of simulation-based calibration and parameter recovery studies, classic tools that have always carried a steep computational price. You simulate thousands of synthetic datasets and run inference on every single one, which is exactly why these checks are so often skipped in papers, even though doing one well can be a contribution in its own right.Here's where amortized simulation-based inference changes the math entirely. Checks that used to take days now take seconds, and instead of laboriously running inference dataset by dataset, you get millions of posterior samples essentially for free. The calibration checks that the field has always known it should be doing finally become cheap enough to actually do.Get the 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
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  Exact GPs vs Approximations: When to Use Each (and Why It Matters) 10.06.2026 4Min.

  Today's clip is from episode 159 featuring Matthijs Hollanders. In this conversation, Alex and Matthijs dig into a deceptively practical question: when you're modeling wildlife across space and time with Gaussian Processes, how do you keep the math from becoming computationally unbearable - and what does good engineering actually look like in the field?Matthijs explains that for most real camera trapping datasets, exact GPs still hold up fine. The reason is less about clever math and more about ecological reality: researchers are usually resource-constrained, so datasets tend to be a few hundred sites, not thousands. And when datasets do get large, they're rarely one giant connected grid - they're clusters of independent regions. That structure is exploitable. Run a separate, smaller GP per region, share the hyperparameters, and you avoid building the massive covariance matrix that makes exact GPs expensive in the first place.But the more interesting thread is where this is heading. Alex introduces Hilbert Space Gaussian Processes (HSGPs) - an approximation that makes compute time nearly linear in dataset size, rather than cubic. The catch, as Matthijs points out, is that approximations aren't always better: if your dataset isn't large enough to be in the regime where the approximation accuracy kicks in, you're better off with the exact GP and its mathematical guarantees. The rule of thumb is simple - if you can use the vanilla GP, just do it.Get the 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
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  #159 Bayesian Occupancy Models, with Matthijs Hollanders 08.06.2026 1Std. 26Min.

  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 workTakeaways:Q: What is a Bayesian occupancy model and what problem does it solve?A: An occupancy model accounts for the fact that you don't always detect a species when surveying for it, especially when the species is rare. A naive count of where you found it underestimates true occupancy. The model adds a repeated-measures component: you visit each site multiple times, and from the pattern of detections vs. non-detections it estimates a detection probability. Matthijs framed it as a zero-inflation structure where the zero-inflation happens at the site level rather than the observation level -- which keeps the model conceptually simple, just a standard GLM with a Bernoulli “is the species here at all?” stacked on top of a detection-rate process.Q: What are Automated Recording Units and why don't traditional occupancy models handle them well?A: ARUs are camera traps and acoustic monitors that record continuously over deployment periods of days, weeks, or months. The data they produce isn't a sequence of discrete human-led surveys; it's a continuous-time observation stream. Traditional occupancy models were designed for the discrete case -- a human visits a site, records yes or no, goes home. With ARUs, the question becomes how to bin or threshold the continuous data without losing the richer signal it actually contains.Q: When should you not reach for occARU?A: When your dataset is large and your survey interval is fine-grained. The bottleneck is Stan's fitting speed -- years of daily count data across many sites will fit slowly. The workaround is to bin coarser (weekly or monthly), which doesn't hurt occupancy estimation at all and only loses some detection-rate resolution. If you're only interested in occupancy, big grouping windows are fine.Full takeaways hereChapters:00:12:14 What is an occupancy model and what problem does it solve?00:16:16 What are Automated Recording Units and why do they need different models?00:18:45 What is the occARU R package and why does it exist?00:23:55 Why does occARU model counts directly rather than binary detection?00:26:38 What does multi-species hierarchical modeling with Gaussian processes look like?00:32:22 How does occARU implement Gaussian processes efficiently?00:41:01 Why are Gaussian processes such a powerful but tricky modeling tool?00:44:11 What is variance decomposition with global-local shrinkage priors?00:49:02 How does occARU leverage recent Stan features for zero-sum constraints?00:57:37 When does within-chain parallelization actually help?01:01:30 How does Monte Carlo integration reduce high Pareto-k values?01:15:27 When does occARU underperform and what's on the roadmap?Thank you to my Patrons for making this episode possible!Links from the show here.
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  Can AI Learn What Experts Know? Automating Prior Elicitation with Generative Models 02.06.2026 4Min.

  Today's clip is from episode 158 featuring Stefan Radev. In this conversation, Alex and Stefan explore a genuinely fascinating problem: how do you turn an expert's intuition into a mathematically valid prior distribution - and can AI help automate that process?Alex explains that prior elicitation is essentially a translation problem. Experts don't walk around thinking in probability distributions - their knowledge lives in intuitions, rules of thumb, and rough ranges. The challenge is converting that into something a Bayesian model can actually use.The traditional approach? Ask an expert for quantiles or a mean, then parameterize your prior with hyperparameters and simulate until the model-implied quantities match what the expert described. If your pipeline is differentiable end-to-end, you use gradient descent. If not, you fall back to something like Bayesian optimization. Either way, you're iterating toward a prior that genuinely reflects expert knowledge - not just a convenient assumption.But the really exciting part is what came next. In a follow-up paper, they pushed this further: instead of optimizing within a fixed parametric family (say, a Gaussian), they replaced the prior entirely with a normalizing flow - a flexible generative network - and ran the same procedure. No assumed distribution family. Just let the data and the expert's knowledge shape the prior from scratch.The catch? More flexibility means more non-identifiability and stability headaches. But the direction is clear: a fully automated, end-to-end pipeline for building priors from non-probabilistic expert knowledge. And in 2026, that pipeline could theoretically be driven by an agent.Get the 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
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  #158 Bayesian Workflows & Foundation Models, with Stefan Radev 21.05.2026 1Std. 18Min.

  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 workTakeaways:Q: Why are prior predictive checks so underused in practice, and how do simulations help?A: They're underused because researchers don't always think to run them before seeing data -- but also because doing them rigorously (in the style Michael Betancourt advocates, with prior push-forward checks on interpretable summaries) takes effort. Simulations make it cheap to generate thousands of “what-if world” datasets from your model and check whether they look plausible, catching bad priors before you ever touch real data.Q: How can generative AI help with prior elicitation?A: Rather than forcing a domain expert to choose a distributional family and parameterize it, you can use a generative model to translate their qualitative knowledge directly into a prior. The expert describes what realistic data should look like; the generative model produces synthetic datasets matching that description; those datasets are used to fit a prior distribution. It removes the assumption that experts can think in terms of parameters and replaces it with the more natural question: does this look like your data?Q: What would a foundation model for Bayesian inference actually look like?A: Stefan's bet is that it won't be a fine-tuned general LLM. The right analogy is chess: you don't fine-tune GPT to play chess, you teach it when to call Stockfish. For Bayesian inference, you'd want a semantic layer – an LLM that understands the analysis goal – calling specialized numerical engines (MCMC samplers, amortized inference networks) that do the actual computation. Agent skills are already a step in this direction; the longer-term vision is engines that have been trained from scratch to generalize across large families of models and priors.Full takeaways here.Chapters:00:00 How does amortized inference fit into modern Bayesian workflows?06:01 What role do simulations play across the full Bayesian workflow?12:12 How do you elicit priors from a domain expert who doesn't think in distributions?19:01 What would a foundation model for Bayesian inference actually look like?35:32 What is self-consistency in amortized inference and why does it matter?39:22 How does semi-supervised learning improve simulation-based inference?43:16 Why is sensitivity analysis so important yet so underused in Bayesian practice?47:40 What is multiverse analysis and how does it change how we report Bayesian results?51:32 How does amortized inference make sensitivity and multiverse analysis affordable?01:02:47 How do amortized inference and classical MCMC complement each other?01:10:08 What are the next major directions for BayesFlow and amortized inference research?Thank you to my Patrons for making this episode possible!Links from the show here.
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  The Hidden Geometry of Hierarchical Models 13.05.2026 3Min.

  Today's clip is from Episode 157 featuring Stefan Radev. In this conversation, Alex and Stefan dig into one of the hardest open problems in simulation-based inference — hierarchical models.The core idea: when you move from flat to hierarchical models, you're no longer estimating one set of parameters. You have local parameters that vary by location (or subject, or city) and global parameters that capture what's shared across all of them. And you don't just want each separately — you want the full joint posterior, because that's where the Bayesian magic of shrinkage actually lives.Stefan builds the problem from the ground up. Start with the simplest hierarchical case: a two-level model. He uses electoral forecasting in France as the example — cities nested inside departments nested inside the whole country.Now your simulator has to cover all three levels. If that simulator is slow (think: brain emulators, minutes per sample), scaling to hundreds of groups becomes completely intractable. Memory issues, specialized network requirements, the works.The key insight: this problem has structure you can exploit. The joint posterior factorizes in a particularly nice way — each local parameter depends on its own local data and on the global parameters. That means instead of cramming everything into one giant high-dimensional vector and hoping a neural network figures it out, you can decompose the problem. Estimate local parameters conditioned on local data and the globals. Use composition.The takeaway: hierarchical models aren't just "harder flat models" - they have a geometry that demands a different architecture. Respecting that structure is what makes amortized inference scale.Get the 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
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  #157 Amortized Inference & BayesFlow in Practice, with Stefan Radev 06.05.2026 1Std. 18Min.

  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 workTakeaways:Q: What is simulation-based inference and what does "sim-to-real" mean?A: Simulation-based inference (SBI) uses a mechanistic simulator as an epistemic tool: you train a neural network on a large number of labeled simulations and then deploy it on real, unlabeled data. The "sim-to-real" framing captures the key asymmetry -- your network never sees real data during training, only simulations, but it generalizes to real observations at inference time. This is the opposite of the more common "synthetic-for-ML" approach, where fake data is used purely to augment real training data.Q: What is the amortized inference agent skill and what does it do?A: It's an open-source AI agent skill, co-developed by Stefan and Alexandre, that teaches an AI coding agent to run a complete, state-of-the-art amortized inference workflow. Because amortized inference is recent enough that it's underrepresented in LLM training data, vanilla agents tend to get it wrong. The skill injects the right methodology: it guides the agent to set up the simulator, choose the right network architecture, run a pilot, train with appropriate diagnostics, and produce an actionable report -- without the user needing to know the details.Q: What is calibration coverage and why should you never skip it?A: Calibration coverage tells you whether your posterior uncertainty is honest -- whether your credible intervals actually contain the true parameter at the right frequency. A model can show poor parameter recovery yet still be well-calibrated (because it's falling back on the prior), or it can appear to recover parameters while being poorly calibrated. Running calibration diagnostics both in-sample and out-of-sample is especially revealing for hierarchical models, which often appear to underfit in-sample but generalize much better out-of-sample thanks to shrinkage.Full takeaways hereChapters:00:00:00 How does amortized inference fit into the Bayesian workflow?00:12:03 What does "sim-to-real" mean in simulation-based inference?00:15:57 Why is amortized inference particularly suited to psychology and neuroscience?00:21:51 What is the amortized inference agent skill?00:39:00 What is calibration coverage and how do you interpret it?00:41:50 How do you decide what to do next after your first training run?00:44:53 How do actionable insights make Bayesian workflows more usable?00:49:08 What are the unique challenges of hierarchical models in amortized inference?01:00:51 What is the current state of BayesFlow's support for hierarchical models?01:05:00 What are the main failure modes of amortized inference and how do you handle model misspecification?Thank you to my Patrons for making this episode possible!Links from the show
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  How to Design Better Experiments with Expected Information Gain 01.05.2026 5Min.

  Today's clip is from Episode 156 featuring Adam Foster. In this conversation, Adam explains Expected Information Gain (EIG) -the scoring function at the heart of optimal Bayesian experimental design.The core idea: when designing an experiment, you need a way to compare possible designs and pick the best one. EIG is that score - it tells you how much information you expect to gain about your model parameters from a given design. The higher the EIG, the better the design.Adam builds intuition for EIG from two directions that sound completely different but lead to the same place. First, the Bayesian angle: simulate datasets from your prior predictive distribution, run inference on each, measure how much uncertainty dropped, and average across datasets. Second, a classic puzzle - the 12 prisoners balance scale problem - where the best weighing strategy turns out to be the one that makes all three outcomes (tip left, tip right, balance) equally likely. This maximizes outcome entropy, which is exactly what EIG does: it steers you toward designs where every possible result narrows down your hypotheses as fast as possible.The takeaway: good experimental design isn't about intuition or convention - it's about making your data work as hard as possible, and EIG gives you a rigorous way to do that.Get the 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
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  #156 Bayesian Experimental Design & Active Learning, with Adam Foster 25.04.2026 1Std. 16Min.

  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 workTakeawaysQ: What is Bayesian experimental design and what problem does it solve?A: It's the practice of using a Bayesian model to decide how to collect data before you collect it. Most statistical thinking starts with a fixed dataset. Bayesian experimental design sits upstream -- you have control over experimental parameters (which questions to ask, which reagents to mix, which conditions to test) and you want to choose them optimally. The Bayesian angle is to ask: what new data would most reduce my current uncertainty?Q: When should you actually use Bayesian experimental design?A: When two conditions hold: you have active control over how data is collected (not just passive observation), and you have a Bayesian model whose prior predictive distribution gives a reasonable picture of what typical data might look like. It's especially valuable when data collection is expensive or irreversible -- when the "committal step" of running an experiment has real cost, it's worth doing the analysis first.Q: What is expected information gain (EIG) and why is it central to Bayesian experimental design?A: EIG is the score you assign to a candidate experimental design -- the amount of information you expect to gain about your model parameters by running an experiment with that design. You compute it by simulating datasets from your prior predictive, doing Bayesian inference on each, and averaging how much the uncertainty decreased. What's remarkable is that you can derive the same quantity from two completely different starting points -- reducing parameter uncertainty, or maximizing outcome uncertainty while correcting for noise - and arrive at the same formula. That convergence is why EIG keeps being re-discovered independently across fields.Full takeaways hereChapters:00:00 What is Bayesian experimental design and why does it matter?00:06:02 What problem does Bayesian experimental design actually solve?00:08:54 When should practitioners use Bayesian experimental design?00:12:00 Is Bayesian experimental design changing how scientists work in practice?00:15:04 What are the limitations of Bayesian experimental design?00:17:55 What is expected information gain (EIG) and how does it work?00:21:05 How do you compute expected information gain in practice?00:23:48 What is active learning and how does it connect to Bayesian experimental design?00:41:02 What is active learning by disagreement?00:48:57 What is deep adaptive design and when should you00: use it?00:56:02 How is Bayesian experimental design applied in protein dynamics and quantum chemistry?01:01:58 What does a practical Bayesian experimental design workflow look like?Thank you to my Patrons for making this episode possible!Links from the show
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  Pricing Under Uncertainty: A Bayesian Workflow 16.04.2026 5Min.

  Today's clip is from Episode 152 of the podcast, featuring Daniel Saunders. In this conversation, Daniel explores how Bayesian decision theory handles real-world risk aversion beyond the textbook maximum expected utility framework.The key insight: classical Bayesian decision theory assumes risk neutrality, but in practice, people and businesses are risk-averse. Using a pricing optimization example, Daniel shows how uncertainty varies dramatically across price points—lower prices have predictable demand, while higher prices create wide uncertainty in profits. This asymmetry matters when you want safer decisions.Daniel introduces exponential utility functions—a technique from economics that models diminishing returns on money. By adjusting a risk-aversion parameter, you can see how increasing risk aversion shifts optimal decisions away from high-uncertainty, high-profit scenarios toward more predictable outcomes.The broader lesson: optimal decision-making requires separating the modeling process from the decision process, allowing you to build in constraints and risk adjustments that pure expected utility maximization would miss.Get the full discussion hereSupport & Resources→ Support the show on Patreon: https://www.patreon.com/c/learnbayesstats→ Bayesian Modeling Course (first 2 lessons free): https://topmate.io/alex_andorra/1011122Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at https://bababrinkman.com/ !
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  #155 Probabilistic Programming for the Real World, with Andreas Munk 08.04.2026 1Std. 54Min.

  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 is bridging deep learning and probabilistic programming so important?A: Deep learning is extraordinarily good at fitting complex functions, but it throws away uncertainty. Probabilistic programming keeps uncertainty explicit throughout. Combining the two – as in inference compilation – lets you get the expressiveness of neural networks while still doing proper Bayesian inference.Q: What is inference compilation and how does it relate to amortized inference?A: Amortized inference is the general idea of training a model upfront so you don't have to run expensive inference from scratch every single time. Inference compilation is a specific form of amortized inference where a neural network is trained to propose good posterior samples for a given probabilistic program – essentially learning to do inference rather than computing it fresh each query.Q: What is PyProb and what problems does it solve?A: PyProb is a probabilistic programming library designed specifically to support amortized inference workflows. It lets you write probabilistic models in Python and then train inference networks on top of them, making methods like inference compilation practical for real-world simulators and scientific models.Full takeaways here.Chapters:00:00:00 Introduction to Bayesian Inference and Its Barriers00:03:51 Andreas Munch's Journey into Statistics00:10:09 Bridging the Gap: Bayesian Inference in Real-World Applications00:15:56 Deep Learning Meets Probabilistic Programming00:22:05 Understanding Inference Compilation and Amortized Inference00:28:14 Exploring PyProb: A Tool for Amortized Inference00:33:55 Probabilistic Surrogate Networks and Their Applications00:38:10 Building Surrogate Models for Probabilistic Programming00:45:44 The Challenge of Bayesian Inference in Enterprises00:52:57 Communicating Uncertainty to Stakeholders01:01:09 Democratizing Bayesian Inference with Evara01:06:27 Insurance Pricing and Latent Variables01:16:41 Modeling Uncertainty in Predictions01:20:29 Dynamic Inference and Decision-Making01:23:17 Updating Models with Actual Data01:26:11 The Future of Bayesian Sampling in Excel01:31:54 Navigating Business Challenges and Growth01:36:40 Exploring Language Models and Their Applications01:38:35 The Quest for Better Inference Algorithms01:41:01 Dinner with Great Minds: A Thought ExperimentThank you to my Patrons for making this episode possible!Links from the show here.
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  Bitesize | "What Would Have Happened?" - Bayesian Synthetic Control Explained 02.04.2026 5Min.

  Today's clip is from Episode 154 of the podcast, with Thomas Pinder.In this conversation, Thomas Pinder explains how Bayesian methods naturally lend themselves to causal modeling, and why that matters for real-world business decisions. The key insight is that causal questions in industry are rarely black and white: instead of a single treatment effect, you get a full posterior distribution, credible intervals, and the ability to communicate the probability that an effect is positive, which is far more useful to stakeholders than a p-value.Thomas then dives into Bayesian Synthetic Control, a reframing of the classic synthetic control method from a constrained optimization problem into a Bayesian regression problem. Rather than optimizing weights on a simplex, you place a Dirichlet prior on the regression coefficients, which turns out to be not just mathematically elegant but practically richer: you can express prior beliefs about how many control units are informative, set the concentration parameter accordingly, or let a gamma hyperprior on that parameter let the data decide. The result is a more flexible, less fragile counterfactual, implemented cleanly in PyMC or NumPyro.Get the full discussion here Support & Resources→ Support the show on Patreon: https://www.patreon.com/c/learnbayesstats→ Bayesian Modeling Course (first 2 lessons free): https://topmate.io/alex_andorra/1011122Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at https://bababrinkman.com/ !
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  #154 Bayesian Causal Inference at Scale, with Thomas Pinder 25.03.2026 1Std. 26Min.

  • Support & get perks!• 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 was GPJax created and how does it benefit researchers?A: GPJax was developed to provide a high-performance, flexible framework for Gaussian processes (GPs) within the JAX ecosystem. It allows researchers to move beyond black-box implementations and easily experiment with custom kernels and model structures while leveraging JAX’s automatic differentiation and GPU acceleration.Q: What are the primary advantages of using Gaussian processes for data modeling?A: Gaussian processes are highly effective at modeling complex, nonlinear relationships in data. Unlike many machine learning methods that only provide a point estimate, GPs offer built-in uncertainty quantification, which is essential for understanding the reliability of predictions in research and industry.Q: How does the GPJax and NumPyro integration enhance probabilistic modeling?A: The integration allows users to treat GPJax models as components within a larger NumPyro probabilistic program. This combination enables the use of advanced sampling techniques like NUTS (No-U-Turn Sampler), making it easier to build and fit complex hierarchical models that include Gaussian processes.Q: What are the main challenges when applying Gaussian processes to high-dimensional data?A: High-dimensional data significantly complicates GP modeling due to the curse of dimensionality and the cubic scaling of computational costs. In high dimensions, defining meaningful distance metrics for kernels becomes harder, often requiring specialized techniques like sparse GPs or dimensionality reduction to remain tractable.Full takeaways here!Chapters:11:40 What is GPJax and how does it simplify Gaussian Process modeling?15:48 How are Bayesian methods used for experimentation and causal inference in industry?18:40 How do you implement Bayesian Synthetic Control?32:17 What is Bayesian Synthetic Difference-in-Differences?39:44 What are the research applications and supported methods for the GPJax library?45:47 What are the primary software and computational bottlenecks when scaling Gaussian Processes?49:02 What are the real-world industrial applications of Gaussian Process models?54:36 How is Bayesian modeling applied to soccer and sports analytics?58:43 What is the future development roadmap for the GPJax ecosystem?01:05:37 What is Impulso and how does it integrate into a Bayesian modeling workflow?01:13:42 How do you balance Bayesian computational overhead with industrial latency requirements?01:20:26 Why is there optimism that scalable Bayesian methods for causal inference are now within reach?Thank you to my Patrons for making this episode possible!Links from the show here!
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  #153 The Neuroscience of Philanthropy, with Cherian Koshy 11.03.2026 1Std. 9Min.

  • Support & get perks!• 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: Is generosity a natural human trait?A: Yes, generosity is hardwired in our brains and is essential for social interaction.Q: Why do people say they care about causes but not act on it?A: There is often a disconnect between stated care for causes and actual action. Understanding the conditions under which generosity aligns with a person's identity is crucial for bridging this gap.Q: How should fundraising efforts be approached?A: Fundraising should primarily focus on belief updating rather than mere persuasion.Q: What are the benefits of being generous?A: Generosity has significant mental and physical health benefits, as the brain's reward systems activate when we give, making us feel good.Q: How do our beliefs relate to our actions?A: Our beliefs about ourselves strongly influence our actions and decisions, including our decision to be generous.Q: Can generosity impact a community?A: Yes, generosity can be a powerful tool for improving community dynamics.Q: How can technology like AI assist institutions with donors?A: AI could help institutions remember donors better, improving the donor-institution relationship.Chapters:00:00 What's the role of Behavioral Science inPhilanthropy19:57 What is The Neuroscience of Generosity?24:40 How can we best understand Donor Decision-Making?32:14 How can we achieve reframe Beliefs and Actions?35:39 What is the role of Identity in Habit Formation?38:06 What is the Generosity Gap in Philanthropy?45:06 How can we reduce Friction in Donation Processes?48:27 What is the role of AI and Trust in Nonprofits?52:11 How can we build Predictive Models for Donor Behavior?55:41 What is the role of Empathy in Sales and Stakeholder Engagement?01:00:46 How can we best align ideas with Stakeholder Beliefs?01:02:06 How can we explore Generosity and Memory?Thank you to my Patrons for making this episode possible!Links from the show:Come meet Alex at the Field of Play Conference in Manchester, UK, March 27, 2026! https://www.fieldofplay.co.uk/Bayesian workflow agent skillNeurogiving, The Science of Donor Decision-MakingCherian's websiteCherian's press kitLBS #89 Unlocking the Science of Exercise, Nutrition & Weight Management, with Eric Trexler
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  Bitesize | How To Model Risk Aversion In Pricing? 04.03.2026 3Min.

  Today's clip is from Episode 152 of the podcast, with Daniel Saunders. In this conversation, Daniel Saunders explains how to incorporate risk aversion into Bayesian price optimization. The key insight is that uncertainty around expected profit is asymmetric across price points, low prices yield more predictable (if modest) returns, while high prices introduce much wider uncertainty. Rather than simply maximizing expected profit, you can pass profit through an exponential utility function that models diminishing returns, a well-established idea from economics. This adds an adjustable risk aversion parameter to the optimization: as risk aversion increases, the model shifts toward more conservative price recommendations, trading off potentially large but uncertain gains for outcomes with tighter, more reliable distributions.Get the full discussion here• Join this channel to get access to perks:https://www.patreon.com/c/learnbayesstats• Intro to Bayes Course (first 2 lessons free): https://topmate.io/alex_andorra/503302• Advanced Regression Course (first 2 lessons free): https://topmate.io/alex_andorra/1011122Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at https://bababrinkman.com/ !
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  #152 A Bayesian decision theory workflow, with Daniel Saunders 26.02.2026 1Std. 19Min.

  • Support & get perks!• Proudly sponsored by PyMC Labs!• Intro to Bayes and Advanced Regression courses (first 2 lessons free)Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work !Chapters:00:00 The Importance of Decision-Making in Data Science06:41 From Philosophy to Bayesian Statistics14:57 The Role of Soft Skills in Data Science18:19 Understanding Decision Theory Workflows22:43 Shifting Focus from Accuracy to Business Value26:23 Leveraging PyTensor for Optimization34:27 Applying Optimal Decision-Making in Industry40:06 Understanding Utility Functions in Regulation41:35 Introduction to Obeisance Decision Theory Workflow42:33 Exploring Price Elasticity and Demand45:54 Optimizing Profit through Bayesian Models51:12 Risk Aversion and Utility Functions57:18 Advanced Risk Management Techniques01:01:08 Practical Applications of Bayesian Decision-Making01:06:54 Future Directions in Bayesian Inference01:10:16 The Quest for Better Inference Algorithms01:15:01 Dinner with a Polymath: Herbert SimonThank you to my Patrons for making this episode possible!Links from the show:Come meet Alex at the Field of Play Conference in Manchester, UK, March 27, 2026! https://www.fieldofplay.co.uk/A Bayesian decision theory workflowDaniel's website, LinkedIn and GitHubLBS #124 State Space Models & Structural Time Series, with Jesse GrabowskiLBS #123 BART & The Future of Bayesian Tools, with Osvaldo MartinLBS #74 Optimizing NUTS and Developing the ZeroSumNormal Distribution, with Adrian SeyboldtLBS #76 The Past, Present & Future of Stan, with Bob Carpenter
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  BITESIZE | How Do Diffusion Models Work? 19.02.2026 3Min.

  Today's clip is from Episode 151 of the podcast, with Jonas ArrudaIn this conversation, Jonas Arruda explains how diffusion models generate data by learning to reverse a noise process. The idea is to start from a simple distribution like Gaussian noise and gradually remove noise until the target distribution emerges. This is done through a forward process that adds noise to clean parameters and a backward process that learns how to undo that corruption. A noise schedule controls how much noise is added or removed at each step, guiding the transformation from pure randomness back to meaningful structure.Get the full discussion here• Join this channel to get access to perks:https://www.patreon.com/c/learnbayesstats• Intro to Bayes Course (first 2 lessons free): https://topmate.io/alex_andorra/503302• Advanced Regression Course (first 2 lessons free): https://topmate.io/alex_andorra/1011122Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at https://bababrinkman.com/ !