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Mathematics
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Bayesian Statistics and Causal Inference
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Bayesian Statistics and Causal Inference

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 31 July 2025 | Viewed by 4137

Special Issue Editors

Dr. Antonino Abbruzzo

E-Mail Website
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
Dr. Chiara Di Maria

E-Mail Website
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

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

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

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Published Papers (4 papers)

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Research

22 pages, 1569 KiB  
Article
Spatial Modeling of Auto Insurance Loss Metrics to Uncover Impact of COVID-19 Pandemic
by Shengkun Xie and Jin Zhang
Mathematics 2025, 13(9), 1416; https://doi.org/10.3390/math13091416 - 25 Apr 2025
Viewed by 97
Abstract
This study addresses key challenges in auto insurance territory risk analysis by examining the complexities of spatial loss data and the evolving landscape of territorial risks before and during the COVID-19 pandemic. Traditional approaches, such as spatial clustering, are commonly used for territory [...] Read more.
This study addresses key challenges in auto insurance territory risk analysis by examining the complexities of spatial loss data and the evolving landscape of territorial risks before and during the COVID-19 pandemic. Traditional approaches, such as spatial clustering, are commonly used for territory risk assessment but offer limited predictive capabilities, constraining their effectiveness in forecasting future losses, an essential component of insurance pricing. To overcome this limitation, we propose an advanced predictive modeling framework that integrates spatial loss patterns while accounting for the pandemic’s impact. Our Bayesian-based spatial model captures stochastic spatial autocorrelations among territory rating units and their neighboring regions. This approach enables more robust pattern recognition through predictive modeling. By applying this approach to regulatory auto insurance loss datasets, we analyze industry-level trends in claim frequency, loss severity, loss cost, and insurance loading. The results reveal significant shifts in spatial loss patterns before and during the pandemic, highlighting the dynamic interplay between regional risk factors and external disruptions. These insights provide valuable guidance for insurers and regulators, facilitating more informed decision-making in risk classification, pricing adjustments, and policy interventions in response to evolving spatial and economic conditions. Full article
(This article belongs to the Special Issue Bayesian Statistics and Causal Inference)
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19 pages, 495 KiB  
Article
Adaptive Bayesian Nonparametric Regression via Stationary Smoothness Priors
by Justin L. Tobias
Mathematics 2025, 13(7), 1162; https://doi.org/10.3390/math13071162 - 31 Mar 2025
Viewed by 184
Abstract
A procedure for Bayesian nonparametric regression is described that automatically adjusts the degree of smoothing as the curvature of the underlying function changes. Relative to previous work adopting a similar approach that either employs a single global smoothing parameter or assumes that the [...] Read more.
A procedure for Bayesian nonparametric regression is described that automatically adjusts the degree of smoothing as the curvature of the underlying function changes. Relative to previous work adopting a similar approach that either employs a single global smoothing parameter or assumes that the smoothing process follows a random walk, the model considered here permits adaptive smoothing and imposes stationarity in the autoregressive smoothing process. An efficient Markov Chain Monte Carlo (MCMC) scheme for model estimation is fully described for this stationary case, and the performance of the method is illustrated in several generated data experiments. An application is also provided, analyzing the relationship between behavioral problems in students and academic achievement. Point estimates from the nonparametric methods suggest (a) expected achievement declines monotonically with a behavioral problems index (BPI) score and (b) the rate of decline is relatively flat at the left tail of the BPI distribution and then becomes sharply more negative. Full article
(This article belongs to the Special Issue Bayesian Statistics and Causal Inference)
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11 pages, 1003 KiB  
Article
Interval Estimation for the Two-Parameter Exponential Distribution Based on Upper Record Value Data Using Bayesian Approaches
by Shu-Fei Wu
Mathematics 2024, 12(23), 3868; https://doi.org/10.3390/math12233868 - 9 Dec 2024
Viewed by 821
Abstract
Using upper record value data, we provide a credible interval estimate for the scale parameter of a two-parameter exponential distribution based on Bayesian methods. Additionally, we propose two Bayesian credible confidence regions for both parameters. In addition to interval estimations for the parameters, [...] Read more.
Using upper record value data, we provide a credible interval estimate for the scale parameter of a two-parameter exponential distribution based on Bayesian methods. Additionally, we propose two Bayesian credible confidence regions for both parameters. In addition to interval estimations for the parameters, we propose a Bayesian prediction interval for a future upper record value. A simulation study is conducted to compare the performance of the proposed Bayesian credible interval, regions and prediction intervals with existing non-Bayesian approaches, focusing on coverage probabilities. The simulation results show that the Bayesian approaches achieve higher coverage probabilities than existing methods. Finally, we use an engineering example to demonstrate all the proposed Bayesian credible estimations for the exponential distribution based on upper record value data. Full article
(This article belongs to the Special Issue Bayesian Statistics and Causal Inference)
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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 2265
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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