Simulation-based Methods for Large Dynamic Latent Variable Models with Unobserved Heterogeneity

点击翻译按钮获取中文摘要

In science and engineering, one often needs to study the behaviour of complex dynamic systems through latent variable models. Most of the time, the systems under study are large. For example, a global-scale numerical weather prediction system in geoscience requires estimation of over 10^9 state variables given about 10^7 observations every few hours. Another example is a network-formation model which contains a large number of parameters which may slowly increase with the data complexity as a direct consequence of unobserved heterogeneity - a phenomenon where units under study have unobserved individual-specific characteristics that may affect their behaviors. Therefore, current research endeavours should be focused on creating new methods with high scalability to estimate these large-scale latent variable models. In this proposal, I propose a new research agenda in this direction, which builds upon my recent work in time series and panel data econometrics. Formally, a latent variable model is defined via the joint probability density function (pdf) of an observation process and an unobserved Markov process and this pdf may not possess a tractable mathematical expression. The processes depend on [unknown] parameters that need to be estimated. This estimation task may be feasible using recent techniques developed from the classical or Bayesian perspective if the data has low dimension and the number of parameters does not increase with the amount of data. These techniques are classified into three categories: a) indirect inference; b) data cloning, iterated filtering, and iterated filtering with Bayes maps (used to maximize intractable likelihood functions); and c) approximate Bayesian computation (ABC) used to compute posterior statistical objects (such as posterior means/modes and probability densities). To circumvent the unscalability problems faced by the existing approaches, I propose simulation-based methods that promise a fast and accurate way to estimate and validate large-scale dynamic latent variable models. Applications of latent variable models with time series/panel and network data are ubiquitous in many areas, including econometrics, biology, ecology, epidemiology, neuroscience, signal processing, and various fields. In fact, many aforementioned statistical methods to compute maximum likelihood estimates for models without tractable likelihood functions were first proposed to address scientific problems in biology, climatology, and ecology. Therefore, the proposed methods are not limited to econometric/statistical applications. In fact, the methods are derived based on very general dynamical models, allowing the readers to make the most of each technique for their specific applications.