Figure 2.

Hierarchical graphical model for the proposed generative process. In our graphical model, variables within the outer plate are replicated for users $i=1,\dots ,I$, variables within the inner plate are replicated for each per-user cycle $c=1,\dots ,C_i$, and variables within the innermost plate are replicated for each skipped cycle $j=0,\dots ,s_{i,c}$. Individual-level parameters ${\mathrm{\lambda }}_i$ (average cycle length without skipping) and ${\mathrm{\pi }}_i$ (probability of skipping a cycle) are drawn from population-level distributions characterized by hyperparameters $u=\left[\mathrm{\kappa },\mathrm{\gamma },\mathrm{\alpha },\mathrm{\beta }\right].\mathrm{ }{s}_{i,c}$ represents number of skipped cycles for user $i$ and cycle number $c$; $d_{i,c}$ represents observed cycle length. We model observed data (cycle lengths $d_{i,c}$) as the sum of true (unobserved) cycle lengths $d_{i,j,c}$ skipped $s_{i,c}$ times (so that an observed cycle length $d_{i,c}$ contains $1+s_{i,c}$ unobserved cycle lengths $d_{i,j,c}$).