Estimating migration proportions from discretely observed continuous diffusion processes

TL;DR

This paper introduces a method to estimate migration proportions from discretely observed continuous diffusion processes by modeling multiple scales and deriving estimators based on observation interval distributions, applied to satellite data.

Contribution

It develops a novel framework for modeling multi-scale diffusion processes with time-dependent coefficients and provides unbiased estimators for migration proportions from discrete observations.

Findings

Derived closed-form expressions for migration proportions.

Provided consistent and unbiased estimators for model parameters.

Applied the model successfully to satellite tag data.

Abstract

We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution cumulants. We use the non - uniform distribution of the observation time intervals to obtain consistent and unbiased estimators for these parameters. Closed form expressions for migration proportions between spatial domains are derived as functions of these parameters. The models are applied to estimate migration patterns from satellite tag data.