Abstract
The purpose of this article is to formulate Bayesian updating from dynamical viewpoint. We prove that Bayesian updating for population mean vectors of multivariate normal distributions can be expressed as an affine symplectic transformation on a phase space with the canonical symplectic structure.
Highlights
The purpose of this article is to formulate Bayesian updating from dynamical viewpoint
We prove that Bayesian updating for population mean vectors of multivariate normal distributions can be expressed as an affine symplectic transformation on a phase space with the canonical symplectic structure
In this paper we prove that Bayesian updating for multivariate normal population mean vector can be expressed by an affine symplectic diffeomorphism
Summary
We review Bayes’ theorem for multivariate normal distributions. Consider a posterior distribution of mean vector for a multivariate normal distribution with covariant matrix. Fix a positive definite symmetric matrix Σ. First we treat the case of covariance matrix Σ is known. Let a prior distribution p (μ ) of μ is distributed N (μ0 , Λ0 ) :. We consider the case of the variance Σ is unknown. If we denote a priori distribution of μ by μ | Σ ~ N ( μ0 , Σ k0 ) , Σ ~ IW (ν 0 , Λ0 ) , the posterior is μ | y, Σ N ( μn , Σ kn ) , Σ | y ~ IW (ν n , Λn ) , where νn
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