# Time-series analysis of population monitoring data

**Analysis of Stochastic Time Series Data using State-Space Models and Kalman Filters**

Marine Mammal Biennial Meeting, October 2009, Quebec City, Quebec

Elizabeth Eli Holmes

Time-series data are commonly collected as part of population monitoring. Variability enters such data through process error (stochasticity in the underlying population dynamics) and through observation error. In many population monitoring studies, the variability due to observation error cannot be independently estimated because it arises from changes in detectability and is some complex (often unknown) function of the environment. State-space modeling provides an established and straight-forward method for analyzing time-series data with both process and observation error. Additionally, state-space models provide a framework for dealing with multiple observation time series and missing observations. Some examples of applications where state-space models are routinely used include development of extinction forecasting models , analysis of animal tracking data, and analysis of multi-site time-series data. This workshop will give students an overview of state-space time-series modeling and give hands-on practice analyzing typical population monitoring data. The morning lectures will introduce autoregressive models and show how familiar univariate and multivariate population models can be written in this form. The introductory lectures will be followed by three hands-on computer labs using R: estimation extinction and viability metrics from noisy count data with missing values, estimation of forecasting models using multiple observation time series, and analysis of the spatial structure with a population using multi-site data. The material will be presented at an introductory level, but students need to have a basic understanding of likelihood inference (e.g. familiarity with the terms likelihood function, likelihood surface, and probability density function). The computer labs will be done in R, but knowledge of R is not necessary. Students must provide laptops.

Instructor:

Eli Holmes is a population analyst for the National Marine Fisheries Service and assists with extinction forecasting for species under the Endangered Species Act. She has published extensively on state-space modeling for analysis of marine mammal and fisheries population monitoring data. She has taught workshops on state-space modeling at the Ecological Society Meeting, National Center for Ecological Analysis and Synthesis, and University of Chicago.

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