= Poisson count change-point model with gamma priors
{c}
{title2=$p(\lambda,\phi,m\mid x)\propto\lambda^{\alpha+S_m-1}e^{-(\beta+m)\lambda}\phi^{\gamma+S_N-S_m-1}e^{-(\delta+N-m)\phi}$}
For independent <Poisson distributions> with rate $\lambda$ up to an unknown index $m$ and rate $\phi$ after it, independent shape-rate <Gamma distribution> priors give the displayed <posterior distribution> when $m$ is uniform on $\{1,\ldots,N\}$ and $S_m=\sum_{i\leq m}x_i$. The model differs from a continuous-time <Poisson change-point posterior>. The endpoint $m=N$ represents no observed change: the second segment is empty and its rate keeps its prior law.
Back to article page
