Bayesian Statistics: Computation

Charles A. Rohde
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Charles A. Rohde: Johns Hopkins University, Bloomberg School of Health

Chapter Chapter 15 in Introductory Statistical Inference with the Likelihood Function, 2014, pp 181-185 from Springer

Abstract: Abstract By Bayes theorem the posterior density of θ is given by p ( θ | x ) = f ( x ; θ ) p ( θ ) f ( x ) $$\displaystyle{p(\theta \vert x) = \frac{f(x;\theta )p(\theta )} {f(x)} }$$ where f ( x ) = ∫ Θ f ( x ; θ ) p ( θ ) d m ( θ ) $$\displaystyle{f(x) =\int _{\Theta }f(x;\theta )p(\theta )dm(\theta )}$$ The calculation of the posterior thus requires calculation of an integral of the likelihood weighted by the prior. Usually this integral can only be determined in closed form for conjugate priors.

Keywords: Markov Chain; Markov Chain Monte Carlo; Bayesian Analysis; Gibbs Sampler; Importance Sampling (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-10461-4_15

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DOI: 10.1007/978-3-319-10461-4_15

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