Transcript How to Write and Present Class 6: Results

Welcome to Amsterdam!
Welcome to Amsterdam!
Bayesian Modeling for Cognitive
Science: A WinBUGS Workshop
Contributors
Michael Lee
http://www.socsci.uci.edu/~mdlee/
Contributors
Dora Matzke
http://dora.erbe-matzke.com/
Contributors
Ruud Wetzels
http://www.ruudwetzels.com/
Contributors
EJ Wagenmakers
http://www.ejwagenmakers.com/
Assistants
Don van Ravenzwaaij
http://www.donvanravenzwaaij.com
Assistants
Gilles Dutilh
http://gillesdutilh.com/
Assistants
Helen Steingröver
Why We Like
Bayesian Modeling
 It is fun.
 It is cool.
 It is easy.
 It is principled.
 It is superior.
 It is useful.
 It is flexible.
Our Goals
This Week Are…
 For you to experience some of the
possibilities that WinBUGS has to offer.
 For you to get some hands-on training by
trying out some programs.
 For you to work at your own pace.
 For you to get answers to questions when you
get stuck.
Our Goals This Week
Are NOT…
 For you to become a Bayesian graphical
modeling expert in one week.
 For you to gain deep insight in the statistical
foundations of Bayesian inference.
 For you to get frustrated when the programs
do not work or you do not understand the
materials (please ask questions).
Logistics
 You should now have the course book,
information on how to get wireless access,
and a USB stick. The stick contains a pdf of
the book and the computer programs.
Logistics
 Brief plenary lectures are at 09:30 and 14:00.
 All plenary lectures are in this room.
 All practicals are in the computer rooms on
the next floor.
 Coffee and tea are available in the small
opposite the computer rooms.
What is Bayesian Inference?
Why be Bayesian?
What is Bayesian
Inference?
What is Bayesian Inference?
“Common sense expressed in numbers”
What is Bayesian Inference?
“The only statistical procedure that is
coherent, meaning that it avoids statements
that are internally inconsistent.”
What is Bayesian Inference?
“The only good statistics”
Outline
 Bayes in a Nutshell
 The Bayesian Revolution
 This Course
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.
Bayesian Parameter
Estimation: Example
 We prepare for you a series of 10 factual
questions of equal difficulty.
 You answer 9 out of 10 questions correctly.
 What is your latent probability θ of
answering any one question correctly?
Bayesian Parameter
Estimation: Example
 We start with a prior distribution for θ. This
reflect all we know about θ prior to the
experiment. Here we make a standard choice
and assume that all values of θ are equally
likely a priori.
Bayesian Parameter
Estimation: Example
 We then update the prior distribution by means
of the data (technically, the likelihood) to
arrive at a posterior distribution.
 The posterior distribution is a compromise
between what we knew before the experiment
and what we have learned from the
experiment. The posterior distribution reflects
all that we know about θ.
Mode = 0.9
95% confidence
interval: (0.59, 0.98)
Outline
 Bayes in a Nutshell
 The Bayesian Revolution
 This Course
The Bayesian Revolution
 Until about 1990, Bayesian statistics could
only be applied to a select subset of very
simple models.
 Only recently, Bayesian statistics has
undergone a transformation; With current
numerical techniques, Bayesian models are
“limited only by the user’s imagination.”
The Bayesian Revolution
in Statistics
The Bayesian Revolution
in Statistics
Why Bayes is Now Popular
Markov chain Monte Carlo!
Markov Chain
Monte Carlo
 Instead of calculating the posterior
analytically, numerical techniques such as
MCMC approximate the posterior by
drawing samples from it.
 Consider again our earlier example…
Mode = 0.89
95% confidence
interval: (0.59, 0.98)
With 9000 samples,
almost identical to
analytical result.
Want to Know More
About MCMC?
MCMC
 With MCMC, the models you can build and
estimate are said to be “limited only by the
user’s imagination”.
 But how do you get MCMC to work?


Option 1: write the code it yourself.
Option 2: use WinBUGS!
Outline
 Bayes in a Nutshell
 The Bayesian Revolution
 This Course
Bayesian Cognitive Modeling:
A Practical Course
 …is a course book under development, used
at several universities.
 …is still regularly updated.
 …will eventually be published by Cambridge
University Press.
 …greatly benefits from your suggestions for
improvement! [e.g., typos, awkward
sentences, new exercises, new applications,
etc.]
Bayesian Cognitive Modeling:
A Practical Course
 …requires you to run computer code. Do not
mindlessly copy-paste the code, but study it
first, and try to discover why it does its job.
 …did not print very well (i.e., the quality of
some of the pictures is below par). You will
receive a better version tomorrow!
WinBUGS
Bayesian inference
Using
Gibbs Sampling
You want to have this
installed (plus the
registration key)
WinBUGS
 Knows many probability distributions
(likelihoods);
 Allows you to specify a model;
 Allows you to specify priors;
 Will then automatically run the MCMC
sampling routines and produce output.
WinBUGS knows many statistical
distributions (e.g., the binomial distribution,
the Gaussian distribution, the Poisson
distribution). These distributions form the
elementary building blocks from which you
may construct infinitely many models.
WinBUGS & R
 WinBUGS produces MCMC samples.
 We want to analyze the output in a nice
program, such as R or Matlab.
 This can be accomplished using the R
package “R2WinBUGS”, or the Matlab
function “matbugs”.
R: “Here are the data and a
bunch of commands”
WinBUGS: “OK, I did
what you wanted, here’s
the samples you asked for”
Matlab: “Here are the data and a
bunch of commands”
WinBUGS: “OK, I did
what you wanted, here’s
the samples you asked for”
Getting Started
 Work through some of the exercises of the
book.
 Most of you will want to get started with the
chapter “getting started”.
 For those of you who have worked with the
book before, you can start wherever you
want. Note that most early chapters have
been restructured (and new content was
added).
Running the R programs
 The R scripts have extension .R. You can use
“File” -> “Open Script” to read these.
 You can run these scripts by copying-andpasting the scripts in the R console.
Saving Your Work
 If you want to save your work, please do this
on the USB stick!
WARNING
 The first chapters are mostly about simple
statistical models. This lays the groundwork
for the later chapters on more complicated
cognitive modeling.
 The idea is that you have to walk before you
can run.
Questions?
 Feel free to ask questions when you are
stuck.
 Answers to the exercises for the first few
chapters can be found at the end of the book!!
Inside every Non-Bayesian,
there is a Bayesian
struggling to get out
Dennis Lindley