This dashboard is powered by a Bayesian hierarchical Negative Binomial model, fit using PyMC via MCMC sampling (NUTS), on the top 20 most-detected species. The outcome is the number of detections for a given species within a given hourly window, including true zeros for hours when nothing was heard. A negative binomial likelihood was chosen over Poisson because detection counts are highly overdispersed — some species (like Carolina Wren and Gray Catbird) call in bursts, producing far more variance than a Poisson model can explain. Temperature, humidity, pressure, and rainfall enter as standardized fixed effects shared across all species. Time of day enters as a quadratic curve, letting each species peak at its own hour rather than sharing one shape — species is treated as a random intercept and random time-of-day slope on the log scale, letting each species have its own baseline calling rate and its own peak timing, with sparse species pulled toward the group average. The model is retrained daily as new detections accumulate, and a new version is only promoted to production if it has a better estimated out-of-sample fit (via LOO cross-validation) than the current one. The current formulation is shown below, where count is assumed to follow a Negative Binomial distribution with mean μ and dispersion α.

What "hierarchical" actually means

Each species' baseline calling rate is pulled toward the group average — pulled hard when a species has little data, barely at all when it has a lot. This is what lets sparse species (like Common Grackle) get a stable, sensible estimate instead of an overfit one, while common species (like Gray Catbird) are trusted almost entirely on their own data.

Coefficients and predictions shown above reflect the current production model version.