Bayesian Inference via Approximation of Log-likelihood for Priors in Exponential Family

Understand

In this paper, a Bayesian inference technique based on Taylor series approximation of the logarithm of the likelihood function is presented.

• The proposed approximation is devised for the case, where the prior distribution belongs to the exponential family of distributions.
• The logarithm of the likelihood function is linearized with respect to the sufficient statistic of the prior distribution in exponential family such that the posterior obtains the same exponential family form as the prior.
• Similarities between the proposed method and the extended Kalman filter for nonlinear filtering are illustrated.