Bayesian data analysis & cognitive modeling 2015

overview

session	date	topic	reading (main)	homework
1	10/14	course overview & probability primer	Kruschke 4 & 5.1
2	10/21	basics of BDA	Krushke 5 & 6
3	10/28	Classical and Bayesian statistics (with shiny)	Wagenmakers (2007)
4	11/4	Regression modeling in R	Kruschke 3	hw 1 solutions
5	11/11	MCMC methods	Kruschke 7
6	11/18	using JAGS	Kruschke 8	hw 2 solutions
7	11/25	generative models	Kruschke 9
8	12/2	model comparison	Vandekerckhove et al. (2015)	hw 3 solutions
9	12/9	estimation, comparison & criticism	Kruschke 11, 12
10	12/16	Stan, JASP, GLMs, projects	Kruschke 10	hw 4 solutions
11	13/01	task types & link functions	Franke (2016)
12	20/01	Q&A session
13	27/01	estimating subjective beliefs	tba	hw 5
14	03/02	nonparametric Bayesian methods	see below
15	10/02	project presentations

some project ideas are here

day by day

1. course overview & probability primer, October 14

• course overview
• student survey
• probability primer
  • subjective vs. objective
  • mass vs. density
  • cumulative distributions
  • conditional probability
  • Bayes rule
  • joint distributions
  • marginalization
• required reading
  • Kruschke 2015, chapters 4 & 5.1

2. basics of BDA, October 21

• towards BDA (Kruschke 5, 6)
  • models, parameters, data, likelihood, priors
  • x% credible interval
  • coin bias example
  • credible intervals
• required reading
  • Kruschke 2015, chapters 5 & 6
• optional reading
  • Understanding Bayes

3. Classical and Bayesian statistics, October 28

• recap classical statistics
  • motivating binomial example
  • maximum likelihood, sufficiency, consistency, bias
  • sampling distribution, the bootstrap
  • p values, confidence intervals
  • problems with p values and confidence intervals
• Bayes factor and (Markov Chain) Monte carlo methods
• t-test
  • classical versus Bayesian
• required reading
  • Wagenmakers (2007) “A practical solution to the pervasive problem of p values”
• optional reading
  • Bayesian Benefits for the Pragmatic Researcher
  • A Tutorial on Fisher Information
  • Statistical Evidence in Experimental Psychology

4. Regression modeling in R, November 4

• recap of session 3
• introduction to regression modeling
  • loss function, least squares, maximum likelihood
  • problems, pitfalls, and assumptions; regularization
• R
  • how to run a regression
  • how to implement own regression function
  • cool tools: rmarkdown, shiny, RStudio

• Bayesian regression

• optional reading
  • A (very) short introduction to R
  • Chapter 6, Analyzing Linguistic Data

5. MCMC sampling, November 11

• MCMC sampling (importance, theory)

• convergence checks (theory)

• required reading
  • Kruschke 2015, chapter 7

6. JAGS, November 18

• why and how to use JAGS
  • syntax
  • calls from R
  • good practices & debugging

• MCMC convergence checks in practice

• required reading
  • Kruschke 2015, chapter 8

7. generative models, November 25

• generative models, graphical Bayes nets
• notation from Lee & Wagenmakers

• limitations; pointers to Church / WebPPL

• required reading
  • Kruschke 2015, chapter 9
• optional reading
  • Lee (2011)
  • Lee (2008)

8. model comparison, December 2

• model comparison by Bayes factor
• philosophy of Bayes factors
  • comparison with AIC, BIC, MDL…
• methods for computing Bayes factors:
  • grid approximation
  • trans-dimensional MCMC
  • importance sampling
  • Savage-Dickey
• required reading
  • Kruschke 2015, chapter 10
• optional reading
  • Vandekerckhove et al. (2015)
  • Wagenmakers et al. (2010)

9. estimation, comparison, & criticism, December 9

• answer different questions

• optional reading
  • Jeffreys’ Default Bayes factors
  • Special Issue: Philosophy of Bayesian statistics
  • The new Bayesian statistics

10. Stan, JASP, possible projects: December 16

• Stan

• JASP

• optional reading
  • JASP interview
  • Stan examples

11. Task types & link functions: January 13

• theoretical & experimental pragmatics
  • natural language quantifiers
  • scalar implicatures
  • typicality of quantifier \(\textit{some}\)
• generalized linear model
  • types of dependent variables
  • predictors & link functions
• probabilistic model
  • gradient salience of alternative expressions
  • one predictor feeds two link functions
• main reading:
  • Franke (2016)
• optional reading:
  • Degen & Tanenhaus (2015)
  • van Tiel & Geurts (2014)
• model code:
  • here

12. Q&A session: January 20

• ramblings by Fabian
• Here is his talk from the day before (might help for homework 5)

13. estimating subjective beliefs: January 27

• models with subjects doing Bayesian inference
• need for subjective belief estimates
• hierarchical model for estimating population-level average beliefs
• reading to be added soon

14. non-parametric Bayesian methods: February 3

• motivation and misnomers
• Bayesian linear regression on EEG data (recap)
• Gaussian process regression
  • the kernel trick
  • infinite dimensional multivariate normal distribution
• Finite mixture models (recap)
• Dirichlet process mixture
  • Modeling significant \(p\) values
• optional reading:
  • Gronau et al. (submitted)
  • Gershman & Blei (2012)
  • Rasmussen & Williams (2006; Ch. 1 & 2)
• optional listening:
  • The Talking Machines (Season 2, Episode 2)

15. project presentations: February 10

• short presentations of projects
• final remarks, reflection, discussion