Modeling of complex stochastic systems via latent factors
Hedibert F. Lopes (Chicago Booth)
Factor models, and related statistical tools for dimension reduction, have been
widely and routinely used in psychometric, item response theory, geology,
econometric and biological, amongst many other fields, since the late 1960's
when Karl G. J\"oreskog, a Swedish statistician, proposed the first reliable
numerical method for maximum likelihood estimation (MLE) in factor analysis
(J\"oreskog, 1969). Such developments happened, certainly not by chance, around
the same time the computer industry was experiencing major advances.
From a Bayesian perspective, Martin and McDonald (1975) showed that
MLE suffers from several inconsistency issues (for instance, negative
idiosyncratic variances). Nonetheless, Bayesian researchers themselves could
not produce general algorithms for exact posterior inference for factor models
until the early 1990's when the computer industry had another wave of major
advances and Markov chain Monte Carlo (MCMC) schemes were almost instantly
customized for all fields cited above.
In this talk, my goal is to illustrate how such advances, both in
factor modeling and statistical computing, have driven my own research in
financial econometrics, spatio-temporal modeling and macro- and micro-economics,
among others. This will be done by linking my own work to current trends in
modern Bayesian modeling of high dimensional and data enriched problems.