Download 3.1 Subjective determination of the prior density

Chapter 3 Prior Information
3.1 Subjective Determination of the Prior Density
Several useful approach can be used to determine the prior density.
They are
1. the histogram approach
2. the relative likelihood approach
3. matching a given functional form
4. CDF determination
(1) The histogram approach
Divide the parameter space into intervals, determine the subjective
probability of each interval, and then plot a probability histogram.
(2) The relative likelihood approach
Compare the intuitive “likelihoods” of various points in  , and
directly sketching a prior density from these determinations.
(3) Matching a given functional form
Assume that    is of a given functional form, and to then choose
the density of this given form which most closely matches prior
beliefs.
(4) CDF determination
Subjectively determine several  percentiles, plot the points
z ,  , sketch a smooth curve joining them, where
P  z   
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Note:
The histogram and the relative likelihood approaches are the most
useful.
Note:
Untrained or unpredicted people do quite poorly in determining the
probability distributions. Through the study of “Bayesian
robustness”, we can alleviate this problem.
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