Posterior distribution of Bernoulli distribution

by Aditi Akolkar   Last Updated September 12, 2019 02:19 AM

The pdf of X | $\theta$ is given by $\theta^x (1- \theta)^{1-x}$

and its prior distribution is given by $p(\theta) \frac {1} {B(\alpha, \beta)} \theta^{\alpha - 1} (1 - \theta)^{\beta - 1}$

where $B(\alpha, \beta) = \int_0^1 x^{\alpha - 1} (1-x)^{\beta -1} dx$

Can someone help me determine posterior distribution of $\theta$ and to show that its a weighted average between the MLE and the prior estimate of $\theta$ under the beta prior?

Related Questions

The posterior distribution of Bt is Bernoulli

Updated June 10, 2019 21:19 PM

MAP estimation as regularisation of MLE

Updated September 18, 2018 17:19 PM

A simple question about MAP and MLE

Updated June 23, 2015 03:08 AM