Dynamic Inspection of Latent Variables in State-Space Systems

The state-space models (SSMs) are widely used in a variety of areas where a set of observable variables are used to track some latent variables. While most existing works focus on the statistical modeling of the relationship between the latent variables and observable variables or statistical inferences of the latent variables based on the observable variables, it comes to our awareness that an important problem has been largely neglected. In many applications, although the latent variables cannot be routinely acquired, they can be occasionally acquired to enhance the monitoring of the state-space system. Therefore, in this paper, novel dynamic inspection (DI) methods under a general framework of SSMs are developed to identify and inspect the latent variables that are most uncertain. Extensive numeric studies are conducted to demonstrate the effectiveness of the proposed methods. Note to Practitioners-The SSM aims to estimate crucial latent variables that characterize the states of a system but cannot be measured routinely or directly. The conventional way has been solely based on a measurement capacity dedicated to observed variables. However, we realize there are situations that, although latent variables cannot be measured routinely, it is possible to inspect a small portion of latent variables at a given frequency. Thus, the problem is how to allocate the inspection resources to help monitor the latent variables of the state-space system optimally, conditioning on the established statistical machinery of the SSM for model estimation and inference. We propose a DI method to select and partially measure the latent variables and improve the estimation accuracy by combining the measured latent variables and observations.