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Bayesian Inference for Stochastic Processes (303506)

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Keywords: Bayesian, inference, stochastic process, DNA evolution, and pricing an option

Bayesian Inference for stochastic processes is an important part of statistical analysis and has many applications to real world problems. This presentation will consist of four components: (1) A brief review of stochastic processes, (2) a concise examination of Bayesian inference, (3) The use of R and WinBUGS for implementing Bayesian inferences, and (4) Bayesian inferences for stochastic processes with applications to biology and finance. With regard to the first component of the presentation, the definition of a stochastic process is provided, followed by an explanation of the following four types: (a) discrete time and discrete state space, (b) continuous time and discrete space, (c) discrete time and continuous state space, and (d) continuous time and continuous state. By Bayesian inference is meant estimation of parameters, tests of hypotheses about the parameters, and prediction of future observations. All such inferences are based on the posterior distribution of the unknown parameters which is a result of Bayes theorem, which in turn depends on sample information (via the likelihood function) and prior information (using the prior distribution).