1. Bayesian Inference Using JASP
Eric-Jan
Wagenmakers 1

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3. Outline Bayesian inference Bayesian parameter estimation
Bayesian hypothesis testing
The Bayesian t-test
Example: Turning the hands of time 3

4. Bayesian Inference in a Nutshell
In Bayesian inference, uncertainty or degree of belief is quantified by probability.
Prior beliefs are updated by means of the data to yield posterior beliefs. 4

5. Outline Bayesian inference Bayesian parameter estimation
Bayesian hypothesis testing
The Bayesian t-test
Example: Turning the hands of time 5

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16. Outline Bayesian inference Bayesian parameter estimation
Bayesian hypothesis testing
The Bayesian t-test
Example: Turning the hands of time 16

17. Bayesian Hypothesis Test
Suppose we have two models, H0 and H1.
Which model is better supported by the data?
The model that predicted the data best!
The ratio of predictive performance is known as the Bayes factor (Jeffreys, 1961).

18. Bayesian Hypothesis Tests

19. Bayesian Hypothesis Tests

20. Bayesian Hypothesis Tests

21. Bayesian Hypothesis Tests

22. Bayes Factor Inverse

23. Bayes Factor Transitivity

24. Bayes Factor Transitivity

25. Guidelines for Interpretation of the Bayes Factor
BF Evidence
1 – Anecdotal
3 – Moderate
10 – Strong
30 – Very strong
> Extreme 25

26. Visual Interpretation of the Bayes Factor26

27. Visual Interpretation of the Bayes Factor27

28. Visual Interpretation of the Bayes Factor28

29. Advantages of the Bayes Factor
Quantifies evidence instead of forcing an all- or-none decision.
Allows evidence to be monitored as data accumulate.
Able to distinguish between “data support H0” and “data are not diagnostic”.

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31. Disadvantages of the Bayes Factor
Where are the course books for psychologists?
Where is the software?

32. First Annual JASP Workshop A Fresh Way to do Bayesian Statistics
jasp-stats.org
August 6 & August 7, 2015 University of Amsterdam

33. Fifth Annual JAGS and WinBUGS Workshop
Bayesian Modeling for Cognitive Science
August 10 - August 14, 2015 University of Amsterdam

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36. Outline Bayesian inference Bayesian parameter estimation
Bayesian hypothesis testing
The Bayesian t-test
Example: Turning the hands of time 36

37. Bayes Factor for the t Test
Predictive Success for the Null Hypothesis
Predictive Success for the Alternative Hypothesis 37

38. Bayes Factor for the t Test
Prob. of Data Under the Null Hypothesis
Prob. of Data Under the Alternative Hypothesis
H0 states that effect size δ = 0.
But how do we specify H1? 38

39. is the weighted average of the likelihood ratios.
Effect size δ under H1
Likelihood ratio
p(data | H0)
p(data | δ = .1)
The Bayes factor
is the weighted average of the likelihood ratios.
The weights are given by the prior plausibility assigned to the effect sizes.
δ = .1
δ = .3
δ = .5 •
p(data | H0)
p(data | δ = .3)
p(data | H0)
p(data | δ = .5) 39

40. So we need to assign weight to the different values of effect size.
These weigths reflect the relative plausibility of the effect sizes before seeing the data.
For complicated reasons, a popular default choice is to assume a Cauchy distribution (like a Normal, but with fatter tails): 40

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42. Outline Bayesian inference Bayesian parameter estimation
Bayesian hypothesis testing
The Bayesian t-test
Example: Turning the hands of time 42

43. Turning the Wheels of Time
Topolinski and Sparenberg (2012): clockwise movements induce psychological states of temporal progression and an orientation toward the future and novelty.
Concretely: participants who turn kitchen rolls clockwise report more openness to experience.

44. Turning the Wheels of Time

45. Turning the Wheels of Time
Let's demonstrate:
How to run a Bayesian t-test in JASP;
How to interpret the output;
How to conduct a sequential analysis;
How to assess the robustness of the result.

46. Conclusions
Bayesian hypothesis tests have a number of practical advantages;
These advantages are easily available through JASP;
The example discussed here was simple, but JASP handles more complicated analyses as well!