Introduction
Eliciting prior information
Elicitation of prior information in Bayesian
statistics
Kevin Wilson
Newcastle University
Supervised by Dr Malcolm Farrow and Dr Tom Nye
November 3, 2009
Kevin Wilson
Bayes linear
Introduction
Eliciting prior information
1
Introduction
Bayesian statistics
What is a prior?
2
Eliciting prior information
What is elicitation?
Why is elicitation necessary?
Human errors and biases
Kevin Wilson
Bayes linear
Introduction
Eliciting prior information
Bayesian statistics
What is a prior?
In a full Bayesian analysis we use the continuous form of Bayes
Theorem
π(θ)L(θ | x)
π(θ | x) =
,
f (x)
where
f (x) =
π(θ)L(θ | x)dθ, for continuous θ,
θ∈Θ π(θ)L(θ | x), for discrete θ.
θ∈Θ
This can also be expressed as
posterior ∝ prior × likelihood.
Kevin Wilson
Bayes linear
Introduction
Eliciting prior information
Bayesian statistics
What is a prior?
The prior is a probability distribution which represents our
beliefs before we collect any data.
A full joint prior distribution must be specified for all of the
unknowns in the analysis.
The prior distribution should accurately and honestly reflect
out prior beliefs.
In a Bayesian analysis beliefs are updated as a result of
observing data.
Kevin Wilson
Bayes linear
Introduction
Eliciting prior information
What is elicitation?
Why is elicitation necessary?
Human errors and biases
Elicitation is the process of turning an expert’s prior beliefs
about one or more uncertain quantities into a probability
distribution for those quantities.
The term expert simply refers to somebody within the field in
which the experiment/analysis is to take place.
A successful elicitation process will lead to a prior distribution
which accurately reflects the expert’s beliefs.
An elicitation is accurate even if the expert’s prior judgements
turn out to be completely incorrect!
Kevin Wilson
Bayes linear
Introduction
Eliciting prior information
Setup
Elicit
Kevin Wilson
What is elicitation?
Why is elicitation necessary?
Human errors and biases
Fit
Bayes linear
Adequate?
Introduction
Eliciting prior information
What is elicitation?
Why is elicitation necessary?
Human errors and biases
Expertise in a subject area is not the same as expertise in
statistics and probability.
Although an expert may have substantial subject specific
knowledge they may find it difficult to transfer that to
probability distributions for parameters.
The elicitation process is that of a facilitator helping the
expert to express their knowledge in probabilistic form.
Questions should only be asked in terms of observable
quantities.
It is upto the facilitator to choose which and how many
quantities to elicit.
Kevin Wilson
Bayes linear
Introduction
Eliciting prior information
What is elicitation?
Why is elicitation necessary?
Human errors and biases
Example: Mr X
Evaluate the probabilities that Mr X, who is described as
‘meticulous, introverted, meek and solemn’ is engaged in the
following occupations;
farmer
salesman
pilot
librarian
physician
Kevin Wilson
Bayes linear
Introduction
Eliciting prior information
Kevin Wilson
What is elicitation?
Why is elicitation necessary?
Human errors and biases
Bayes linear