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Bayesian Approaches to Shrinkage and Sparse Estimation

Dimitris Korobilis, Kenichi Shimizu

arXiv 22 Dec 2021 · Econometrics · publishedFoundations and Trends® in Econometrics (2022) · 12 citations (OpenAlex)

arXiv:2112.11751 · PDF · DOI · OpenAlex · Extracted main text

Abstract

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference is the norm in several fields of applied econometric work. The purpose of this paper is to introduce 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. We 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). We explore various methods of exact and approximate inference, and discuss their pros and cons. Finally, we 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 allow the reader to replicate many of the algorithms described in this review.

Citation extraction

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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1George, E. I. and McCulloch, R. E (1993) Variable selection via Gibbs sampling1.00094100%
2Kuo, L. and Mallick, B (1998) Variable selection for regression models1.00083100%
3Park, T. and Casella, G (2008) The Bayesian lasso1.00073100%
4Tibshirani, R (1996) Regression shrinkage and selection via the lasso1.00065100%
5Makalic, E. and Schmidt, D. F (2016) A simple sampler for the horseshoe estimator1.00063100%
6Rocková, V. and George, E. I (2018) The spike-and-slab lasso1.00054100%
7Figueiredo, M. A. T (2003) Adaptive sparseness for supervised learning0.92843100%
8Hans, C (2009) Bayesian lasso regression0.874122100%
9Kyung, M., Gill, J., Ghosh, M., and Casella, G (2010) Penalized regression, standard errors, and Bayesian lassos0.87482100%
10Li, Q. and Lin, N (2010) The Bayesian elastic net0.87462100%

Showing the top 10 of 211 scored citations.

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arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Mixing it up: Inflation at risk0.51122
2Monitoring multicountry macroeconomic risk\@thefnmark\@footnotetextWe would like to thank Raffaella Giacomini, Sylvia Kaufmann, Massimiliano Marcellino, Christian Matthes, Mirco Rubin, Neil Shephard, Leif Anders Thorsrud and participants at the following conferences, for useful discussions and comments: 12th European Seminar on Bayesian Econometrics in Salzburg; “Advances in alternative data and machine learning for macroeconomics and finance” in Paris; Barcelona Workshop on Financial Econometrics; 27th International Conference on Macroeconomic Analysis and International Finance in Rethymno; 2023 Finance and Business Analytics Conference in Lefkada; 10th IAAE Annual Conference in Oslo. We would also like to thank seminar participants at the following institutions: BI Norwegian Business School, European Central Bank, University of Lancaster. The views expressed are those of the authors and do not necessarily reflect those of Norges Bank or any of the affiliated institutions0.40511
3myblue Vector Copula Variational Inference and Dependent Block Posterior Approximations0.40511
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