Prob Expert: conjugate prior

Table of conjugate distributions

normal with known mean μ	variance σ²	scaled inverse-chi-square	$\nu,\ \sigma^2\!$	$\nu+n,\frac{\nu\sigma^2+\sum_{i=1}^n (x_i-\mu)^2}{\nu+n}\!$
normal with known variance σ²	mean μ	normal	$\mu_0, \sigma_0^2\!$	$(\frac{\mu_0}{\sigma_0^2} + \frac{\sum_{i=1}^n x_i}{\sigma^2})/(\frac{1}{\sigma_0^2} + \frac{n}{\sigma^2}), (\frac{1}{\sigma_0^2} + \frac{n}{\sigma^2})^{-1}$
Pareto	shape k	Gamma	$\alpha,\ \beta\!$	$\alpha+n,\ \beta+\sum_{i=1}^n \ln\frac{x_i}{x_{\mathrm{m}}}\!$
Pareto	location x_m	Pareto
Poisson	rate λ	Gamma	$\alpha,\ \beta\!$	$\alpha + \sum_{i=1}^n x_i,\ \beta + n\!$