Welcome to OccuSpytial’s documentation!

OccuSpytial is a library for performing bayesian inference of single-season site occupancy models. A species occupancy model is used to account for imperfect detection of a species in surveys and to determine the probability of occupancy \((\psi_i)\) at each site. This is done by quantifying the conditional detection probability \((d_{ij})\) of a species at a site based off of data. This library specifically implements models that take into account the spatial autocorrelation between between neighboring sites for the occupancy covariates.

The basic formulation of the model as shown by Rorazio and Royle (2008) is:

\[\begin{split}\begin{align} \begin{split} z_i|\psi_i \sim& \text{ Bernoulli}(\psi_i)\\ y_{ij}|z_i, d_{ij} \sim& \text{ Bernoulli}(z_id_{ij}). \end{split} \end{align}\end{split}\]

The probabilities \(\psi_i\) and \(d_{ij}\) are linked to vectors \(\mathbf{\alpha}\) and \(\mathbf{\beta}\) via a suitable link function \(f(.)\) such that \(\psi_i = f(\mathbf{x}_i^T\mathbf{\beta} + \eta_i)\) and \(d_{ij} = f(\mathbf{w}_{ij}^T\mathbf{\alpha})\); where \(\eta_i\) is the spatial random effect used to model the effect that the site neighbourhood structure has on the species occurrence probabilities, \(\mathbf{x}_i\) is site \(i\)’s covariance, \(\mathbf{w}_{ij}\) is the detection covariate of site \(i\) at the \(j\)’th visit, \(\mathbf{\alpha}\) and \(\mathbf{\beta}\) are detection and occupancy regression effects. Currently, the spatial random effects are modelled using an Intrinsic Conditional Autoregressive (ICAR) model.

For more information about the currently implemented methods, see Gibbs Samplers and User Guide for examples of how to use each. All implemented samplers are fast and use C code (via Cython) for computationally intensive parts of each algorithm.

Todo

• Implement a Hamiltonian Monte Carlo sampler variant.

Installation

• Installation
  • Using pip
  • From source
  • Testing

User Guide

• Input format
• Sampling example
  • Gibbs sampling
• Visualizing posterior samples

API Reference

• Gibbs Samplers
  • Base Sampler
  • Logit link based
  • Probit link based
• Utility Functions & Classes
  • Datasets
  • Development Utils

License

Copyright (c) 2018-2020, Zolisa Bleki and contributors.

OccuSpytial is free software made available under the BSD License. For details see the LICENSE file.