Integration in Bayesian Data Analysis
The aim of this chapter is to demonstrate usage of the numerical methods developed in chapters 3 and 4 for the Bayesian analysis of data. The chapter begins with an example for which the Bayesian evidence (or rather the integrated likelihood) and marginal densities may be computed in closed form. These numerical techniques are then applied to a difficult problem in data analysis; namely, inferring the number of decaying exponentials and the values of the decays in real experimental data. The chapter concludes with examples of model selection by determining the appropriate noise model and signal model to use in a given data set.
KeywordsGibbs Sampler Importance Sampling Gaussian Approximation Conditional Density Decay Model
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