Subjective priors

A subjective prior (sometimes called an elicited prior) describes the informed opinion of the value of a parameter prior to the collection of data. We discuss in some depth the techniques for eliciting opinions. A subjective prior can be represented as a series of points on a graph:

It is a simple enough exercise to read off a number of points from such graphs and use the height of each point as a substitute for p(q). Sometimes it is possible to reasonably match a subjective opinion like that of the Figure above to a conjugate prior for the likelihood function one is intending to use. Some Monte Carlo software offer a feature that will let an expert draw a distribution of his/her estimate and then fit the required parametric distribution to it. An exact match is not usually important because a) the subjective prior is not usually specified that accurately anyway, and b) the prior has progressively less influence on the posterior the larger the set of data used in calculating the likelihood function. At other times, a single conjugate prior may be inadequate to describe a subjective prior, but a composite of two or more conjugate priors will produce a good representation.

Subjective priors

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