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book/models/change_of_variable_hmc.md

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# Change of Variable in HMC
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**Rat tumor problem:** We have J certain kinds of rat tumor diseases. For each kind of tumor, we test $N_{j}$ people/animals and among those $y_{j}$ tested positive. Here we assume that $y_{j}$ is distrubuted with **Binom**($N_{i}$, $\theta_{i}$). Our objective is to approximate $\theta_{j}$ for each type of tumor.
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**Rat tumor problem:** We have J certain kinds of rat tumor diseases. For each kind of tumor, we test $N_{j}$ people/animals and among those $y_{j}$ tested positive. Here we assume that $y_{j}$ is distrubuted with **Binom**($N_{j}$, $\theta_{j}$). Our objective is to approximate $\theta_{j}$ for each type of tumor.
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In particular we use following binomial hierarchical model where $y_{j}$ and $N_{j}$ are observed variables.
2020

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