We discuss Bayesian model uncertainty analysis and forecasting in sequential dynamic modeling of multivariate time series. The perspective is that of a decision-maker with a specific forecasting objective that guides thinking about relevant models. Based on formal Bayesian decision-theoretic reasoning, we develop a time-adaptive approach to exploring, weighting, combining and selecting models that differ in terms of predictive variables included. The adaptivity allows for changes in the sets of favored models over time, and is guided by the specific forecasting goals. A synthetic example illustrates how decision-guided variable selection differs from traditional Bayesian model uncertainty analysis and standard model averaging. An applied study in one motivating application of long-term macroeconomic forecasting highlights the utility of the new approach in terms of improving predictions as well as its ability to identify and interpret different sets of relevant models over time with respect to specific, defined forecasting goals.

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Factor analysis is routinely used for dimensionality reduction. However, a major issue is 'brittleness' in which one can obtain substantially different factors in analyzing similar datasets. Factor models have been developed for multi-study data by using additive expansions incorporating common and study-specific factors. However, allowing study-specific factors runs counter to the goal of producing a single set of factors that hold across studies. As an alternative, we propose a class of Perturbed Factor Analysis (PFA) models that assume a common factor structure across studies after perturbing the data via multiplication by a study-specific matrix. Bayesian inference algorithms can be easily modified in this case by using a matrix normal hierarchical model for the perturbation matrices. The resulting model is just as flexible as current approaches in allowing arbitrarily large differences across studies, but has substantial advantages that we illustrate in simulation studies and an application to NHANES data. We additionally show advantages of PFA in single study data analyses in which we assign each individual their own perturbation matrix, including reduced generalization error and improved identifiability.

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