The Model

Process	Observations	Kernel

The Integro-Difference Equation model, sometimes abbreviated to IDE or, to avoid confusion with integrated development environments, IDEM, is a hierarchical dynamic spatio-temporal model, which can be written

Here, Y, the process, defined over the space D_s and discrete time t = 1, …, T evolves dynamically with respect to discrete time, according to a weighted integral of its previous state. There is also a non-dynamical component η_t(s) and measurement error/noise process for the data, ϵ_t(s), all of which are assumed mutually independent in time.

The package is written to go along with the paper, available at arxiv Efficient Bayesian Filtering and Inference for Integro-Difference Equation Models.

For further reading, you can start with the books Statistics for Spatio-Temporal Data, Spatio-Temporal Statistics with R , and the articles Data-Driven Spatio-Temporal Modeling Using the Integro-Difference Equation, Deep integro-difference equation models for spatio-temporal forecasting, and Bayesian non-parametric modeling for integro-difference equations

This project could also be understood as a re-implementation and continuation of Andrew Zammit Mangion's R package IDE, though the hope is that the functionality and speed will surpass that implementation.

For more information, see the gitlab pages.

Installation

If you want to run on the GPU, be sure to install JAX with support for your GPU; check out their installation guide.

Install with pip:

pip install jaxidem

Or install the latest commit from git:

pip install git+https://gitlab.com/tatephughes/JAX-IDEM.git

Also available as a wheel in releases.

Requires Python 3.11 or later.