Bayesian Statistics and Causal Inference

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: closed (25 November 2023) | Viewed by 1653

Special Issue Editors


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Guest Editor
Department of Economics, Business and Statistics, Università degli Studi di Palermo, Viale delle Scienze, Ed. 13, 90138 Palermo, Italy
Interests: statistical analysis; Bayesian inference; high-dimensional data analysis; probabilistic graphical models

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Guest Editor
Department of Economics Business and Statistics, University of Palermo, Viale delle Scienze, ed. 13, 90128 Palermo, Italy
Interests: mediation analysis; causal inference; graphical models

Special Issue Information

Dear Colleagues,

In recent decades, causal inference and Bayesian statistics have experienced remarkable developments due to the rise in the interest of scholars across many fields.  Causal inference aims to estimate the causal effects of a treatment or an exposure on a response of interest. This task is of paramount importance in many contexts, including, for example, medicine, economics and public health. Still, drawing causal conclusions from data requires assumptions and methods that differ from those used in traditional associational studies. Bayesian statistics provides a way to combine researchers’ prior information with that coming from data. In recent years, some attempts have been made to integrate the two approaches to exploit their strengths. This Special Issue is open to methodological and applied works which can provide insightful contributions to the topic and show the advantages of combining the two ‘worlds’.  Examples of possible subjects include, but are not limited to, high-dimensional data, graphical models, missing data, machine learning, matching methods, nonparametric estimation and computational aspects. Contributions from different fields are welcome. 

Dr. Antonino Abbruzzo
Dr. Chiara Di Maria
Guest Editors

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Keywords

  • causal inference
  • Bayesian statistics
  • treatment effects
  • missing data
  • nonparametric models
  • machine learning
  • high-dimensional data
  • graphical models

Published Papers (1 paper)

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Research

20 pages, 746 KiB  
Article
Estimating the Capital Asset Pricing Model with Many Instruments: A Bayesian Shrinkage Approach
by Cássio Roberto de Andrade Alves and Márcio Laurini
Mathematics 2023, 11(17), 3776; https://doi.org/10.3390/math11173776 - 2 Sep 2023
Cited by 2 | Viewed by 1238
Abstract
This paper introduces an instrumental variable Bayesian shrinkage approach specifically designed for estimating the capital asset pricing model (CAPM) while utilizing a large number of instruments. Our methodology incorporates horseshoe, Laplace, and factor-based shrinkage priors to construct Bayesian estimators for CAPM, accounting for [...] Read more.
This paper introduces an instrumental variable Bayesian shrinkage approach specifically designed for estimating the capital asset pricing model (CAPM) while utilizing a large number of instruments. Our methodology incorporates horseshoe, Laplace, and factor-based shrinkage priors to construct Bayesian estimators for CAPM, accounting for the presence of measurement errors. Through the use of simulated data, we illustrate the potential of our approach in mitigating the bias arising from errors-in-variables. Importantly, the conventional two-stage least squares estimation of the CAPM beta is shown to experience bias escalation as the number of instruments increases. In contrast, our approach effectively counters this bias, particularly in scenarios with a substantial number of instruments. In an empirical application using real-world data, our proposed methodology generates subtly distinct estimated CAPM beta values compared with both the ordinary least squares and the two-stage least squares approaches. This disparity in estimations carries notable economic implications. Furthermore, when applied to average cross-sectional asset returns, our approach significantly enhances the explanatory power of the CAPM framework. Full article
(This article belongs to the Special Issue Bayesian Statistics and Causal Inference)
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