Signal extraction from long-term ecological data using Bayesian and non-Bayesian state-space models

Emerging ecological time series from long-term ecological studies and remote sensing provide excellent opportunities for ecologists to study the dynamic patterns and governing processes of ecological systems. However, signal extraction from long-term time series often requires system learning (e.g., estimation of true system state) to process the large amount of information, to reconstruct system state, to account for measurement error, and to handle missing data. State-space models (SSMs) are a natural choice for these tasks and thus have received increasing attention in ecological and environmental studies. Data-based learning using SSMs that connect ecological processes to the measurement of system state becomes a useful technique in the ecological informatics toolkit. The present study illustrates the use of the Kalman filter (KF), an estimator of SSMs, with case studies of population dynamics. The examples of the SSM applications include the reconstruction of system state using the KF method and Markov chain Monte Carlo methods, estimation of measurement-error variances in the estimates of animal population abundance using basic structural models (BSMs), and estimation of missing values using the KF and Kalman smoother. Estimation of measurement-error variances by BSMs does not require knowledge of the functional form that generates the time series data. Instead, BSMs approximate the trajectory or deterministic skeleton of a system dynamics in a semi-parametric fashion, and provide a robust estimator of measurement-error variances. The present study also compares Bayesian SSMs with non-Bayesian SSMs. The joint use of the KF method or its extensions and Markov chain Monte Carlo (MCMC) methods is a promising approach to the parameter estimation of SSMs.