an introduction to jasp and bayesian statistics · an introduction to jasp and bayesian statistics...
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An Introduction to JASP and Bayesian StatisticsTim Draws, University of Amsterdam
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Once Upon a Time…
EJ Wagenmakers
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Fast Forward to Today
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3 Key Features of JASP
1. Free: fully open-source
2. Friendly: easy-to-use & intuitive GUI
3. Flexible: allows for classical (frequentist) & Bayesian analyses
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My Goals for Today
• For you to experience the possibilities that JASP has to offer
• For you to grasp the process of Bayesian inference and understand the meaning behind its main concepts
• For you to do statistics and have fun at the same time (it is possible)!
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The Plan
1. Exploring JASP and its possibilities
2. The basic idea of Bayesian statistics
3. Bayesian parameter estimation
4. Bayesian hypothesis testing
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The Plan
1. Exploring JASP and its possibilities
2. The basic idea of Bayesian statistics
3. Bayesian parameter estimation
4. Bayesian hypothesis testing
![Page 8: An Introduction to JASP and Bayesian Statistics · An Introduction to JASP and Bayesian Statistics ... •Bayesian statistics aims to quantifythe uncertainty surrounding our inference](https://reader034.vdocuments.site/reader034/viewer/2022042802/5f3b885dc220337b7b462db3/html5/thumbnails/8.jpg)
The Plan
1. Exploring JASP and its possibilities
2. The basic idea of Bayesian statistics
3. Bayesian parameter estimation
4. Bayesian hypothesis testing
![Page 9: An Introduction to JASP and Bayesian Statistics · An Introduction to JASP and Bayesian Statistics ... •Bayesian statistics aims to quantifythe uncertainty surrounding our inference](https://reader034.vdocuments.site/reader034/viewer/2022042802/5f3b885dc220337b7b462db3/html5/thumbnails/9.jpg)
The Origin of Science
Plato: All knowledge is in our thoughts. We can reason our way towards it.
Aristotle: We have to observe the world in order to find out truths.
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We Still Use Aristotle’s Reasoning
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The Basic Idea of Bayesian Statistics
Basic assumption: Reasoning under uncertainty adheres to the rules of probability theory.
• Bayesian statistics aims to quantify the uncertainty surrounding our inference.
• Prior beliefs are updated by means of the data to yield posterior beliefs.
• Belief updates are governed by predictive success. Does the data confirm or prior knowledge or not?
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Bayesian Inductive Cycle
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The Plan
1. Exploring JASP and its possibilities
2. The basic idea of Bayesian statistics
3. Bayesian parameter estimation
4. Bayesian hypothesis testing
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Parameter Estimation
What‘s the bike situation here?
Amsterdam São Paulo?
! = The true proportion of São Paulo Residents who own a bycicle.
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Frequentist Parameter Estimation
Frequentists consider ! to be a fixed but unknown quantity that can be approximated by using different samples from a population.
Frequentists say: If we were to do this experiment over an over again, in 95% of cases the confidence interval would include the true !.
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Bayesian Parameter Estimation
Bayesians treat parameters as random variables that can be describedwith a probability distribution.
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Bayesian Parameter Estimation
• When estimating parameters, our prior beliefs are reflected in theprior distribu*on.
• Beliefs are then updated by the predictive updating factor.• The update yields the posterior distribution.
! " #$%$ = ! #$%$ "! #$%$ ∗ ! "
(posterior = predictive updating factor * prior)
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Bayesian Parameter Estimation
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Bayesian Parameter Estimation
Let‘s estimate the proportion of São Paulo Residents who own a bike!
Amsterdam São Paulo?
Go to resource (2): A First Lesson in Bayesian Inference(https://tellmi.psy.lmu.de/felix/BayesLessons/BayesianLesson1.Rmd)
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The Plan
1. Exploring JASP and its possibilities
2. The basic idea of Bayesian statistics
3. Bayesian parameter estimation
4. Bayesian hypothesis testing
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Frequentist Hypothesis Testing1. Formulate hypotheses (e.g., H0 and H1)2. Collect data3. Calculate the p-value 4. If p < 0.05: We have found an effect!
If p > 0.05: We have not found an effect.
Problem: The p-value is the probability of obtaining the observed data, or something more extreme, given that H0 is true.
The p-value does not tell us anything about how likely it is that a hypothesis is true. (However, this is mostly what we are interested in.)
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Bayesian Hypothesis TestingThe central question in Bayesian Hypothesis Testing: Which of the hypotheses is better supported by the data?
Answer: The model that predicted the data best!
The ratio of predictive performance is known as the Bayes factor.
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Bayesian Hypothesis Testing! "1 #$%$! "0 #$%$
= ! #$%$ "1! #$%$ "0
∗ P H1P H0
posterior model odds = Bayes factor * prior model odds
Example:
41 =
41 ∗
11
BF10 = 4(The data are 4 times more likely to occur under H1
than under H0.)
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Bayesian Hypothesis TestingWe can flip the Bayes factor fraction in order to quantify evidence in favor of H0:
! "#$# %1! "#$# %0
= '( BF10 = 4
! "#$# %0! "#$# %1
= (' BF01 = ('
Both of these Bayes factors convey the exact same thing: The data are 4 times more likely to occur under H1 than under H0.
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Bayesian Hypothesis TestingInterpreting strength of evidence: What does the Bayes factor tell us?
BF Evidence
1-3 Anecdotal3-10 Moderate10-30 Strong30-100 Very strong100+ Extreme
Harold Jeffreys
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Bayesian Hypothesis TestingInterpreting strength of evidence: What does the Bayes factor tell us?
BF10 = 4 (Odds of 4:1 in favor of H1)BF01 = ¼ (Odds of 1:4 in favor of H0)
Spin the wheel! How surprised are you when the arrow lands on the smaller part?
" #$%$ &1
" #$%$ &0
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Bayesian Hypothesis TestingInterpreting strength of evidence: What does the Bayes factor tell us?
BF10 = 32 (Odds of 32:1 in favor of H1)BF01 = !"# (Odds of 1:32 in favor of H0)
$ %&'& (1
$ %&'& (0
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Bayesian Hypothesis TestingBack to our previous example: Which of the hypotheses is better supported by the data?
In Germany, 75% of people own a bike. Is it the same in Brazil?
H0: 75% of Brazilians have a bike. (! = 0.75)H1: A different proportion of Brazilians have a bike. (! ≠ 0.75)
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Any Questions?
You can find all workshop materials at https://jasp-stats.org/usp-workshop