At a glance

  • BDA is about what we should believe given:
    • some observable data, and
    • our model of how this data was generated.
  • Our best friend will be Bayes rule: \[\underbrace{P(\theta \, | \, D)}_{posterior} \propto \underbrace{P(\theta)}_{prior} \times \underbrace{P(D \, | \, \theta)}_{likelihood}\]
  • If \(P(\theta \, | \, D)\) is hard to compute, we resort to magic some clever stuff.

Example: coin flips

  • \(\theta \in [0;1]\) is the bias of a coin:
    • if we throw a coin, the outcome will be heads with probability \(\theta\)
  • we have no clue about \(\theta\) at the outset:
    • a priori we consider every possible value of \(\theta\) equally likely
  • we observe that of 24 flips 7 were heads
  • what shall we believe about \(\theta\) now?

"Classical statistics"

  • null hypothesis significance testing (NHST)
    • e.g., is the coin fair (\(\theta = 0.5\))
  • relies on sampling distributions & p-values
    • standard "tests" can have rigid built-in assumptions
    • implicitly rely on experimenter's intentions
  • looks at point estimates only

Pros & Cons of BDA

Pro

  • well-founded & totally general
  • easily extensible / customizable
  • more informative / insightful

Drawing

Con

  • less ready-made, more hands-on
  • not yet fully digested by community
  • lacks "standard solutions"

Drawing2

3 times Bayes

  1. Bayesian data analysis
    • "classical" analyses Bayes-style (Kruschke 2015)
  2. Bayesian cognitive modeling
    • custom models of the data-generating process (Lee & Wagenmakers 2013)
  3. Bayes in the head
    • model (human) cognition as Bayesian inference

Goals of this course

  • to understand basic ideas of BDA (contrast with NHST)
  • to be able to read current literature on BDA
  • to be able to implement (simple) Bayesian analyses
    • using R (or some other programming language)
    • using JAGS (or some other magic clever stuff)
  • to see how BDA blends seamlessly into cognitive modeling

Resources

Course 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 BDA vs. NHST Wagenmakers (2007)
4 11/4 using R Kruschke 3 hw 1 due
5 11/11 MCMC methods Kruschke 7
6 11/18 using JAGS Kruschke 8 hw 2 due
7 11/25 generative models Kruschke 9
8 12/2 model comparison Kruschke 10 hw 3 due
9 12/9 Bayesian NHST & model criticism Kruschke 11, 12
10 12/16 regression models Kruschke 10 hw 4 due

Credits

for 3 credits you must …

  • hand in all 5 homework sets, and
  • finish with a final project, e.g.:
    • take home exam (enough for a Proseminar Schein)
    • a literature survey (enough for a Proseminar Schein)
    • an analysis of your own data set
    • a replication/extension of some other analysis
    • write a discussion paper (e.g., philosophy of BDA)

grade will be a (non-arbitrary) function of homework grades and final project