Course introduction

BADT

Author

Sahlin

Why this course

A PhD course in Bayesian analysis for participants that are not from maths

A PhD course that brings up the link between Bayesian inference and Decision theory

A possibility to discuss, praise and challenge Bayesian thinking

An introduction to Bayesian analysis to get started or get more experience

  • Bayesian analysis: Bayesian statistics, Bayesian inference, Bayesian data analysis, Bayesian modelling, Bayesian computation, Bayesian networks, Bayesian emulation, Bayesian evidence synthesis

  • Decision theory: Bayesian decision theory, Bayesian hypothesis testing, Bayesian learning, decision making under uncertainty, evidence-based decision making, communicating uncertainty, uncertainty analysis in assessments, weight of evidence approaches

Summer school 2015, PhD course spring 2018, PhD course online spring 2022, PhD course physical 2026

Bayes@Lund web page

Bayes@Lund Youtube Channel

Goals

Content:

Bayesian analysis, Discrete Bayesian Belief Networks, Hierarchical modelling, Continuous Bayesian Belief Networks

Probabilistic uncertainty analysis, Non-probabilistic methods for uncertainty analysis, Scientific principles to quantify uncertainty

Bayesian Decision Theory, Principles of cautious decision making

Material and content

Two books

BR - Alicia A. Johnson, Miles Ott, Mine Dogucu Bayes Rules

DBDA - John K. Kruschke Doing Bayesian Data Analysis

Additional material: lecture notes and exercises available and updated during the course on this git web page

Assessment

Assessment is based on student activities in practical exercises and seminars, and on the written project report.

  • Presence at the two physical meetings (let us know if you cannot attend in advance)

  • Active participation in literature seminars

  • Completed individual report

Literature seminar

Learning goals

  • Digest a Bayesian decision analysis for a concrete problem

  • Practice to identify sources of uncertainty in an assessment

  • Be able to give examples of principles to quantify and treat uncertainty in a Bayesian analysis

  • Be able to give an account of science theoretic arguments behind principles to quantify and treat uncertainty in knowledge production and decision making

  • Reflect on the limitations and justification of Bayesian principles and subjective probability to produce scientific advice or decision support

  • Practice collaboration and presentation in an interdisciplinary context

Instructions

The literature seminar is constructed around three themes.

  • Before the seminar

Download the literature. You have been placed in a group (A-C). You are to read the three papers assigned to your group. Skim through the other papers. Look at the questions for your group.

  • During the seminar

Together with your group, prepare and give a presentation of the three papers (try to keep it short < 8 min per paper). Structure the presentation around the answers to the questions under that theme.

Theme 1: The Bayesian analysis combined with decision making

Group A. Augustynczik, A. L. et al. Productivity of Fagus sylvatica under climate change–A Bayesian analysis of risk and uncertainty using the model 3-PG. Forest Ecology and Management 401, 192–206 (2017). link to paper

Group B. Spiegelhalter, D. J. & Best, N. G. Bayesian approaches to multiple sources of evidence and uncertainty in complex cost-effectiveness modelling. Statist. Med. 22, 3687–3709 (2003). link to paper

Group C. Theobald, C. M. & Talbot, M. The Bayesian choice of crop variety and fertilizer dose. Journal of the Royal Statistical Society: Series C (Applied Statistics) 51, 23–36 (2002). link to paper

Questions

  • Describe the decision problem! Who is the decision-maker? What are the decision alternatives? How are values/preferences defined and used? What qualifies as a good decision?

  • Describe the model to inform the decision problem. What is the quantify of interest? What type of data was used? How were priors specified?

  • List sources of uncertainty for this assessment!

  • Describe strengths and weaknesses of the methods and principles underlying the paper as a method in research and as a method to produce scientific advice (decision-support).

Theme 2: Uncertainty and subjective probability

Group A. Meder, B., Le Lec, F. & Osman, M. Decision making in uncertain times: what can cognitive and decision sciences say about or learn from economic crises? Trends in Cognitive Sciences 17, 257–260 (2013). link to paper

Group B. Paté-Cornell, E. On “Black Swans” and “Perfect Storms”: Risk Analysis and Management When Statistics Are Not Enough: On Black Swans and Perfect Storms. Risk Analysis 32, 1823–1833 (2012). link to paper

Group C. Parker, W. S. Whose probabilities? Predicting climate change with ensembles of models. Philosophy of Science 77, 985–997 (2010). link to paper

Questions

  • What type of assessment or decision problem is used as context for the paper?

  • How is uncertainty presented or defined by the authors?

  • What use of subjective probability is described and are there any requirements or justifications for this use?

  • Do the authors suggest any limitations with subjective probability as a measure to quantify uncertainty in research and in processes that produce scientific advice? If so, which?

Theme 3: Beyond the Bayesian paradigm

Group A. French, S. Axiomatizing the Bayesian Paradigm in Parallel Small Worlds. Operations Research (2020). link to paper

Group B. O’Hagan, A. & Oakley, J. E. Probability is perfect, but we can’t elicit it perfectly. Reliability Engineering & System Safety 85, 239–248 (2004). link to paper

Group C. Gärdenfors, Peter. & Sahlin, Nils. E. Unreliable probabilities, risk taking, and decision making. Synthese 53, 361–386 (1982). link to paper

Questions

  • What challenges with the Bayesian paradigm are raised by the authors?

  • What is their solution?

  • Describe strengths and weaknesses of the methods and principles proposed in the paper relevant and useful in research and in processes that produce scientific advice (decision-support).

Individual project

The purpose of the individual project is to allow you to implement Bayesian analysis on a problem that you specify yourself. This can be something that is related to your research (but it doesn’t have to be). Select a problem making sure that the amount of work should not exceed more than a week.

The problem should be either a Bayesian analysis with an informed and justified prior or a Decision analysis supported by a Bayesian analysis

  1. Share your project idea

  2. Get early feedback from Ullrika/Zheng

  3. Perform the project

  4. Produce a minimal report (project description, what you did, result)

  5. Get feedback from Ullrika/Zheng

  6. The project should preferably be finalised within a month after the last course day. Instructions to submit will follow

If you are new to Bayesian stuff - MAKE IT SIMPLE!

If you feel advanced - take the opportunity to try something new

Practical things

LADOK - contact your ladok-administrator with a request to be admitted to the course with identity 6FNAM001.

We will issue certificates upon a completed course.

PUB after the course today