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I want to combine two beta distributions to find the the posterior distribution as the precision-weighted combination of the prior and the likelihood distributions. As the prior and likelihood I have two beta distributions. How do i combine them? Want to know about all the theoretical techniques available. Is there any article which may help me in the analysis. Even guiding me with a weblink to any article would also help! Regards, Bik |
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It is unclear exactly what you are asking for. If your prior distribution is $B(\alpha,\beta)$ then the prior density is proportional to $x^{\alpha-1} (1-x)^{\beta-1}$. Your likelihood function is perhaps proportional to $x^{\gamma} (1-x)^{\delta}$. So you multiply these together and your posterior density is proportional to $x^{\alpha+\gamma-1} (1-x)^{\beta+\delta-1}$ which means your posterior distribution is $B(\alpha+\gamma,\beta+\delta)$. |
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