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Sample-based Maximum Likelihood Estimation of the Autologistic Model.

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  • 1Natural Resources Canada, Canadian Forest Service, Victoria, Canada.

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Summary
This summary is machine-generated.

New algorithms enable sample-based maximum likelihood estimation (MLE) for autologistic models. With calibration, these methods provide acceptable parameter estimates for spatial data analysis.

Keywords:
Markov Chain Monte Carlobiascalibrationcluster samplingsample sizesampling variance

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Area of Science:

  • Spatial statistics
  • Statistical modeling
  • Computational statistics

Background:

  • Autologistic models are widely used for analyzing spatial binary data.
  • Estimating parameters for these models, especially on large lattices, is computationally intensive.
  • Maximum likelihood estimation (MLE) has been challenging due to the difficulty in computing the normalizing constant.

Purpose of the Study:

  • To introduce and evaluate new recursive algorithms for fast computation of the normalizing constant in autologistic models.
  • To assess the feasibility and accuracy of sample-based MLE for autologistic parameters.
  • To compare sample-based MLE estimates with benchmark estimates and analyze their properties.

Main Methods:

  • Development of recursive algorithms for normalizing constant computation.
  • Simulation studies using 12 binary lattices (420x420) with varying plot sizes and sample sizes (20-600).
  • Comparison of sample-based MLE estimates with Markov Chain Monte Carlo (MCMC) benchmark estimates.

Main Results:

  • Sample-based MLE is feasible and provides estimates with a systematic bias of 3%-7%, reducible by calibration.
  • Sampling variances of MLE estimates are generally large and conservative.
  • The variance for the spatial association parameter is substantially higher (2-10x) than for the abundance parameter.
  • Estimate distributions were predominantly non-normal.

Conclusions:

  • Sample-based MLE, with appropriate sample size and post-estimation calibration, yields acceptable estimates for autologistic parameters.
  • The developed algorithms significantly improve the computational feasibility of parameter estimation.
  • Equations for predicting expected sampling variance are provided, aiding in study design and interpretation.