Density Estimation – Bayesian
Andrew R. Webb, Keith D. Copsey · 2011
Class-conditional density functions can be used within Bayes’ rule to produce a discrimination rule. Bayesian approaches to parametric density estimation can be used to take into account parameter uncertainty due to the training data sampling. This chapter considers analytic, sampling and variational procedures for Bayesian estimation. It first discusses analytic approaches to Bayesian inference and introduces sampling approaches to Bayesian inference. The chapter then explains Markov chain Monte Carlo (MCMC) sampling algorithms. It also provides a worked discrimination example. Further, the chapter introduces the advanced topic of Sequential Monte Carlo (SMC) Samplers, another sampling approach to Bayesian inference. It considers Variational Bayes approximations, which provide an alternative means of approximating full Bayesian inference than sampling methods. Finally, the chapter describes Approximate Bayesian Computation, a recent development for use in problems where the likelihood function cannot be evaluated analytically. Controlled Vocabulary Terms approximate bayesian computation; Bayes estimator; Bayesian inference; Kernel density estimation; Markov chain Monte Carlo estimation; particle filter