Decisions Under Uncertainty: A Hands‑On Guide to Bayesian Decision Theory

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TipLecture Overview

We often must make decisions under uncertainty—should you carry an umbrella if there’s a 30 % chance of rain? Bayesian decision theory provides a principled, probabilistic framework to answer such questions by combining beliefs (probabilities), utilities (what matters to us), and actions to maximize expected gain.

This talk:

• Introduces key decision‑theoretic concepts in intuitive terms.
• Uses a toy umbrella example to ground ideas in relatable context.
• Demonstrates applications in Bayesian optimization (PoI/EI) and Bayesian experimental design.
• Is hands‑on—with Python code and practical tools—so participants leave ready to apply these ideas to real‑world problems.

TipWhat You’ll Learn:

• This talk bridges everyday decision-making (umbrella example) with advanced techniques like
• Bayesian optimization and
• Experimental design, and equips attendees with conceptual clarity and immediate code they can adapt to their data-driven workflows.

TipAudience:

Primarily data scientists, ML practitioners, and statisticians who:

• Have applied Bayesian models but want a broader decision-theory perspective.
• Want actionable insight into uncertainty-aware decision frameworks.
• Seek practical demos in Python.

ImportantTools and Frameworks:

• GPyTorch for Gaussian processes
• OptBayesExpt for Bayesian experimental design

workshop repo

TipSpeakers:

Quan Nguyen

Post doc researcher at Bayesian machine learning, decision making under uncertainty.

Author of books - Bayesian optimization - Grokking Bayes

• website: https://krisnguyen.github.io/
• twitter: https://twitter.com/the_subtrahend
• talks repo: github.com/KrisNguen135/Talks

Outline

Motivation & Core Concepts (5 min)

• Frame real-world decision problems: rain or shine, clinical trials, A/B testing.
• Introduce Bayesian decision theory: beliefs \times utilities \to action via expected utility maximization.

Toy Example: Should I Bring an Umbrella? (8 min)

• Define: Probability p of rain; utility/loss matrix

Action	Rain	No Rain
Umbrella	–1 (weight)	–1 (inconvenience)
No Umbrella	–10 (soaked)	0

• Derive expected utility:

EU_umbrella = -1 EU_no_umbrella = -10p

So bring umbrella if p > 0.1

• Interactive Python demo: explore how p and utility values shift the decision point.

Bayesian Optimization: PoI & EI (8 min)

• Introduce Gaussian-process-based optimization and the need to trade off exploration vs. exploitation.
• Define Probability of Improvement (PoI) and Expected Improvement (EI)
• Show how they’re derived from decision theory: choosing the next point to maximize expected gain.

• Python demo using GPyTorch: fit GP, compute PoI/EI acquisition functions, visualize decision boundary—why one chooses a high-uncertainty point vs. one near known good values.

Bayesian Experimental Design (BED): Minimizing Uncertainty (8 min)

• Motivation: cost-sensitive data collection (labeling, surveys, medical tests).
• Define an information-based utility (e.g., expected reduction in entropy).
• Show how decision theory prescribes choosing the next experiment to maximize this expected utility.

• Python demo using OptBayesExpt.

Summary & Takeaways (1 min)

• Reiterate the decision-theoretic arc: belief → utility → action.
• Emphasize the unifying framework across umbrella example, optimization, and experimental design.
• Share resources & practical tips: GPyTorch / scikit-optimize, OptBayesExpt

Takeaway

What can go wrong

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