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)

See also