ABSTRACT
This chapter is devoted to state-space models, i.e., models with dynamic state transition in the latent layer of the hierarchical structure. Conversely to the examples presented in the previous chapters, unknown quantities of interest (e.g., the number of fish, the biomass of a fish stock) evolve with time while observables only give a noisy piece of information about these latent variables. From a graphical modeling perspective, state-space modeling consists of adding arrows between variables within the hidden layer of a DAG so as to create the temporal link between these variables. To go one step further, state-space modeling consists of defining two key equations: the process equation with process noise that captures the stochastic dynamics of the hidden state variables, and the observation equation that relates the data at hand to the state variables, which may involve some observation noise. Surprisingly enough, statistical estimation under the Bayesian setting of (even complex) state-space models remains easily tractable. The flexibility of Bayesian analysis of state-space models is exemplified through two examples of growing complexities; both present educational qualities for illustrating the strengths and limits of the Bayesian analysis of state-space models. The first example sketches the dynamics of the biomass of a fish stock under fishing pressure. The model is used to derive estimates of key management parameters and to forecast changes in biomass under different management scenarios. The second example is an aged-structured population model for A. salmon. The model mimics the salmon life cycle with all its development stages, represented through a multidimensional state-space model.
