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 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/1011122

Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at https://bababrinkman.com/ !

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 Barriers
00:03:51 Andreas Munch's Journey into Statistics
00:10:09 Bridging the Gap: Bayesian Inference in Real-World Applications
00:15:56 Deep Learning Meets Probabilistic Programming
00:22:05 Understanding Inference Compilation and Amortized Inference
00:28:14 Exploring PyProb: A Tool for Amortized Inference
00:33:55 Probabilistic Surrogate Networks and Their Applications
00:38:10 Building Surrogate Models for Probabilistic Programming
00:45:44 The Challenge of Bayesian Inference in Enterprises
00:52:57 Communicating Uncertainty to Stakeholders
01:01:09 Democratizing Bayesian Inference with Evara
01:06:27 Insurance Pricing and Latent Variables
01:16:41 Modeling Uncertainty in Predictions
01:20:29 Dynamic Inference and Decision-Making
01:23:17 Updating Models with Actual Data
01:26:11 The Future of Bayesian Sampling in Excel
01:31:54 Navigating Business Challenges and Growth
01:36:40 Exploring Language Models and Their Applications
01:38:35 The Quest for Better Inference Algorithms
01:41:01 Dinner with Great Minds: A Thought Experiment

Thank you to my Patrons for making this episode possible!

Links from the show here.

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/1011122

Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at https://bababrinkman.com/ !

• 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!

• 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 inPhilanthropy
19:57 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 skill
• Neurogiving, The Science of Donor Decision-Making
• Cherian's website
• Cherian's press kit
• LBS #89 Unlocking the Science of Exercise, Nutrition & Weight Management, with Eric Trexler

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/1011122

Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at https://bababrinkman.com/ !

• 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 Science

06:41 From Philosophy to Bayesian Statistics

14:57 The Role of Soft Skills in Data Science

18:19 Understanding Decision Theory Workflows

22:43 Shifting Focus from Accuracy to Business Value

26:23 Leveraging PyTensor for Optimization

34:27 Applying Optimal Decision-Making in Industry

40:06 Understanding Utility Functions in Regulation

41:35 Introduction to Obeisance Decision Theory Workflow

42:33 Exploring Price Elasticity and Demand

45:54 Optimizing Profit through Bayesian Models

51:12 Risk Aversion and Utility Functions

57:18 Advanced Risk Management Techniques

01:01:08 Practical Applications of Bayesian Decision-Making

01:06:54 Future Directions in Bayesian Inference

01:10:16 The Quest for Better Inference Algorithms

01:15:01 Dinner with a Polymath: Herbert Simon

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/
• A Bayesian decision theory workflow
• Daniel's website, LinkedIn and GitHub
• LBS #124 State Space Models & Structural Time Series, with Jesse Grabowski
• LBS #123 BART & The Future of Bayesian Tools, with Osvaldo Martin
• LBS #74 Optimizing NUTS and Developing the ZeroSumNormal Distribution, with Adrian Seyboldt
• LBS #76 The Past, Present & Future of Stan, with Bob Carpenter

Today's clip is from Episode 151 of the podcast, with Jonas Arruda

In 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/1011122

Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at https://bababrinkman.com/ !