Bayesian Approaches to Shrinkage and Sparse Estimation introduces
the reader to the world of Bayesian model determination by
surveying modern shrinkage and variable selection algorithms and
methodologies. Bayesian inference is a natural probabilistic
framework for quantifying uncertainty and learning about model
parameters, and this feature is particularly important for
inference in modern models of high dimensions and increased
complexity. The authors begin with a linear regression setting in
order to introduce various classes of priors that lead to
shrinkage/sparse estimators of comparable value to popular
penalized likelihood estimators (e.g. ridge, LASSO). They examine
various methods of exact and approximate inference, and discuss
their pros and cons. Finally, they explore how priors developed for
the simple regression setting can be extended in a straightforward
way to various classes of interesting econometric models. In
particular, the following case-studies are considered that
demonstrate application of Bayesian shrinkage and variable
selection strategies to popular econometric contexts: i) vector
autoregressive models; ii) factor models; iii) time-varying
parameter regressions; iv) confounder selection in treatment
effects models; and v) quantile regression models. A MATLAB package
and an accompanying technical manual allows the reader to replicate
many of the algorithms described in this review.
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