Binomial model
Description
The binomial model is a model of counts of binary outcomes in sets of trials.
Definition
For counts of successes \(y\), number of trials \(N\) and predictors \(x\), the model is:
\[ \begin{align} y_i \sim \text{Binomial}(N_i, \exp{(\eta_i)}) \\ \eta_i = \alpha + \beta \cdot x_i \end{align} \]
Where \(y_i\) is the number of successes and \(N_i\) is the number of trials for observation \(i\).
Parameters needing priors
- \(\alpha\) (intercept)
- \(\beta\) (predictor weights)