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Example
27
Bayesian Estimation Using a
Non-Diffuse Prior Distribution
Introduction
This example demonstrates using a non-diffuse prior distribution.
About the Example
Example 26 showed how to perform Bayesian estimation for a simple model with the
uniform prior distribution that Amos uses by default. In the present example, we
consider a more complex model and make use of a non-diffuse prior distribution. In
particular, the example shows how to specify a prior distribution so that we avoid
negative variance estimates and other improper estimates.
More about Bayesian Estimation
In the discussion of the previous example, we noted that Bayesian estimation depends
on information supplied by the analyst in conjunction with data. Whereas maximum
likelihood estimation maximizes the likelihood of an unknown parameter θ when
given the observed data y through the relationship L(θ|y) ∝ p(y|θ), Bayesian
estimation approximates the posterior density of y, p(θ|y) ∝ p(θ)L(θ|y), where p(θ) is
the prior distribution of θ, and p(θ|y) is the posterior density of θ given y.
Conceptually, this means that the posterior density of y given θ is the product of the
prior distribution of θ and the likelihood of the observed data (Jackman, 2000, p. 377).