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! Get in touch at alex.andorra@pymc-labs.com

• 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/ !

• Support & get perks!

• Proudly sponsored by PyMC Labs! Get in touch at alex.andorra@pymc-labs.com

• 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 Exploring Generative AI and Scientific Modeling
10:27 Understanding Simulation-Based Inference (SBI) and Its Applications
15:59 Diffusion Models in Simulation-Based Inference
19:22 Live Coding Session: Implementing Baseflow for SBI
34:39 Analyzing Results and Diagnostics in Simulation-Based Inference
46:18 Hierarchical Models and Amortized Bayesian Inference
48:14 Understanding Simulation-Based Inference (SBI) and Its Importance
49:14 Diving into Diffusion Models: Basics and Mechanisms
50:38 Forward and Backward Processes in Diffusion Models
53:03 Learning the Score: Training Diffusion Models
54:57 Inference with Diffusion Models: The Reverse Process
57:36 Exploring Variants: Flow Matching and Consistency Models
01:01:43 Benchmarking Different Models for Simulation-Based Inference
01:06:41 Hierarchical Models and Their Applications in Inference
01:14:25 Intervening in the Inference Process: Adding Constraints
01:25:35 Summary of Key Concepts and Future Directions

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!
- Jonas's Diffusion for SBI Tutorial & Review (Paper & Code)
- The BayesFlow Library
- Jonas on LinkedIn
- Jonas on GitHub
- Further reading for more mathematical details: Holderrieth & Erives
- 150 Fast Bayesian Deep Learning, with David Rügamer, Emanuel Sommer & Jakob Robnik
- 107 Amortized Bayesian Inference with Deep Neural Networks, with Marvin Schmitt

• Support & get perks!

• Proudly sponsored by PyMC Labs! Get in touch at alex.andorra@pymc-labs.com

• 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 Scaling Bayesian Neural Networks
04:26 Origin Stories of the Researchers
09:46 Research Themes in Bayesian Neural Networks
12:05 Making Bayesian Neural Networks Fast
16:19 Microcanonical Langevin Sampler Explained
22:57 Bottlenecks in Scaling Bayesian Neural Networks
29:09 Practical Tools for Bayesian Neural Networks
36:48 Trade-offs in Computational Efficiency and Posterior Fidelity
40:13 Exploring High Dimensional Gaussians
43:03 Practical Applications of Bayesian Deep Ensembles
45:20 Comparing Bayesian Neural Networks with Standard Approaches
50:03 Identifying Real-World Applications for Bayesian Methods
57:44 Future of Bayesian Deep Learning at Scale
01:05:56 The Evolution of Bayesian Inference Packages
01:10:39 Vision for the Future of Bayesian Statistics

Thank you to my Patrons for making this episode possible!

Come meet Alex at the Field of Play Conference in Manchester, UK, March 27, 2026!

Links from the show:

David Rügamer:
* Website
* Google Scholar
* GitHub

Emanuel Sommer:
* Website
* GitHub
* Google Scholar

Jakob Robnik:
* Google Scholar
* GitHub
* Microcanonical Langevin paper
* LinkedIn