# A Hierarchical Spatio-Temporal Analog Forecasting Model for Count Data

## TL;DR

This paper introduces a Bayesian hierarchical spatio-temporal analog forecasting model for count data, improving forecast accuracy and uncertainty quantification in ecological applications like waterfowl settling patterns.

## Contribution

It extends previous analog forecasting methods into a formal Bayesian hierarchical framework for count data, demonstrating enhanced accuracy over traditional models.

## Key findings

- Hierarchical analog model outperforms Poisson Bayesian models in forecast accuracy.
- The Bayesian approach allows rigorous uncertainty quantification.
- Application to waterfowl data shows practical utility in ecological forecasting.

## Abstract

1. Analog forecasting has been successful at producing robust forecasts for a variety of ecological and physical processes. Analog forecasting is a mechanism-free nonlinear method that forecasts a system forward in time by examining how past states deemed similar to the current state moved forward. Previous work on analog forecasting has typically been presented in an empirical or heuristic context, as opposed to a formal statistical context. 2. The model presented here extends the model-based analog method of McDermott and Wikle (2016) by placing analog forecasting within a fully hierarchical statistical frame- work. In particular, a Bayesian hierarchical spatial-temporal Poisson analog forecasting model is formulated. 3. In comparison to a Poisson Bayesian hierarchical model with a latent dynamical spatio- temporal process, the hierarchical analog model consistently produced more accurate forecasts. By using a Bayesian approach, the hierarchical analog model is able to quantify rigorously the uncertainty associated with forecasts. 4. Forecasting waterfowl settling patterns in the northwestern United States and Canada is conducted by applying the hierarchical analog model to a breeding population survey dataset. Sea Surface Temperature (SST) in the Pacific ocean is used to help identify potential analogs for the waterfowl settling patterns.