ne">\(x\in \mathbb{R}^{n\cdot m}, \alpha \in \mathbb{R}^n, \beta\in \mathbb{R}^m\)</span>, then for <span class="math inline">\(y \in \mathbb{N}^n\)</span>, <span class="math display">\[
\text{PoisonLogGLM}(y|x, \alpha, \beta) = \prod_{1\leq i \leq
n}\text{Poisson}(y_i|\exp(\alpha_i + x_i\cdot \beta)). \]</span></p>
</div>
<div id="sampling-statement-19" class="section level3">
<h3><span class="header-section-number">13.7.2</span> Sampling Statement</h3>
<p><code>y ~</code> <strong><code>poisson_log_glm</co