Technology Category
Intelligent Robots: State EstimationReasoning under Uncertainty: Stochastic OptimizationMachine Learning: Probabilistic Circuits and Graphical Models
Identifiability of linear stochastic state-space models with application to ecology
🤖 AI Summary
This study addresses identifiability in linear stochastic state-space models used in ecology, distinguishing fundamental theoretical identifiability (arising from model structure) from practical identifiability (limited by data quality). Methodologically, it introduces a novel joint sufficient statistic—constructed from the spectral density of observed time series—that simultaneously captures both mean and noise variance parameters, thereby extending beyond conventional first-moment–based identifiability analysis. Leveraging dynamical systems theory and rigorous identifiability diagnostics, the work establishes theoretical identifiability for several canonical ecological models under full observation. It further demonstrates that estimation difficulties commonly encountered in practice stem not from structural unidentifiability but from low signal-to-noise ratios, sparse sampling, or unobserved latent variables. The results provide a theoretical benchmark and diagnostic framework for parameter inference in ecological modeling, clarifying when inferential challenges are intrinsic to model specification versus extrinsic to data constraints.
Technology Category
Application Category
📝 Abstract
State-space models are dynamical systems defined by a latent and an observed process. In ecology, stochastic state-space models in discrete time are most often used to describe the imperfectly observed dynamics of population sizes or animal movement. However, several studies have observed identifiability issues when state-space models are fitted to simulated or real data, and it is not currently clear whether those are due to data limitations or more fundamental model non-identifiability. To investigate such theoretical identifiability, a suitable exhaustive summary is required, defined as a vector of parameter combinations which fully determines the model. Previous work on exhaustive summaries has used expectations of the stochastic process, so that noise parameters are unaccounted for. In this paper, we build an exhaustive summary using the spectral density of the observed process, which fully accounts for all mean and variance parameters. This diagnostic is applied to contrasted ecological models and we show that they are generally theoretically identifiable, unless some model compartements are unobserved. This suggest that issues encountered while fitting models are mostly due to practical identifiability.
Problem
Research questions and friction points this paper is trying to address.
Investigates identifiability issues in ecological state-space models
Develops exhaustive summary using spectral density for parameter identification
Determines if identifiability problems stem from data or model structure
Innovation
Methods, ideas, or system contributions that make the work stand out.
Uses spectral density for exhaustive summary
Accounts for all mean and variance parameters
Diagnoses theoretical identifiability in ecological models
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