A key player in Bayesian statistics is the integrated likelihood function of a model for given data. The integral, also known as the marginal likelihood, is taken over the model’s parameter space with respect to a probability measure that quantifies prior belief. While Chapter 2 was concerned with maximizing the likelihood function, we now seek to integrate that same function. This chapter aims to show how algebraic methods can be applied to various aspects of this problem. Section 5.1 discusses asymptotics of Bayesian integrals for large sample size, while Section 5.2 concerns exact evaluation of integrals for small sample size.
KeywordsBayesian Information Criterion Marginal Likelihood Prior Density Independence Model Exact Integration
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