An ecological example of such a time-series would be a series of yearly population size estimates. Where are observed at regular time intervals for a time-series of length n and are the true unobserved states, with x 0 representing the initial state. An example of a simple univariate linear Gaussian SSM is the one we will use to demonstrate parameter-estimability problems: While the SSM framework is flexible, much of its theoretical foundation is based on simple linear Gaussian SSMs (sometimes referred as normal dynamic linear models, see Newman et al. The flexibility of the SSM approach allows ecologists to build complex models that describe the biological and measurement processes with levels of detail that were previously unattainable. SSMs can be used to model a variety of linear and nonlinear processes and can represent stochasticity with diverse statistical distributions (e.g. The SSM framework is flexible, especially when fitted with Monte Carlo methods such as particle filters or Markov Chain Monte Carlo (MCMC). SSMs are a type of hierarchical model, in which one level treats the underlying unobserved states as an autocorrelated process, while another level accounts for measurement error 11. 4), yet, we show that it suffers from parameter- and state-estimation problems. The model we chose is often used to explain how SSMs can account for two levels of stochasticity (e.g. Here, we demonstrate that even simple SSMs can be problematic. The SSM framework has since become a general approach to account for multiple levels of stochasticity when modelling time-series, making them increasingly popular in the terrestrial literature (e.g. Because marine observations are often associated with large measurement errors that can mask biological signals, much of the early development of SSMs in ecology was by marine ecologists and fisheries scientists (e.g. SSMs are desirable because they are structured so as to differentiate between two distinct sources of variability: the biological or process variation (e.g., demographic stochasticity) and the measurement error associated with the sampling method 2, 4. State-space models (SSMs) are increasingly used in ecology and are becoming the favoured statistical framework for modelling animal movement and population dynamics 1, 2, 3, 4. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results. We suggest potential solutions, but show that it often remains difficult to estimate parameters. Biased parameter estimates of a SSM describing the movement of polar bears ( Ursus maritimus) result in overestimating their energy expenditure. Using an animal movement example, we show how these estimation problems can affect ecological inference. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. Recent ecological SSMs are often complex, with a large number of parameters to estimate. They can model linear and nonlinear processes using a variety of statistical distributions. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics.
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