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Mathematics
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Advances in Statistical Decision Theory and Applications
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Advances in Statistical Decision Theory and Applications

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

Deadline for manuscript submissions: closed (15 October 2022) | Viewed by 8090

Special Issue Editors

Dr. Silvia Bacci

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Guest Editor
Department of Statistics, Computer Science, Applications “Giuseppe Parenti”, Università degli Studi di Firenze, Viale Morgagni 59, 50134 Firenze, Italy
Interests: item response theory; latent class models; latent variable models; models for longitudinal and multilevel data; statistical decision theory and utility theory
Prof. Dr. Fabrizia Mealli

E-Mail Website
Guest Editor
Department of Statistics, Computer Science, Applications “Giuseppe Parenti”, Università degli Studi di Firenze, Viale Morgagni 59, 50134 Firenze, Italy
Interests: Bayesian inference; causal inference in experimental and observational studies; inference with missing data problems; models for individual data; simulation-based estimation; statistical decision theory
Prof. Dr. Leonardo Boncinelli

E-Mail Website
Guest Editor
Department of Sciences for Economics and Business, Università degli Studi di Firenze, Via delle Pandette 32, 50127 Firenze, Italy
Interests: game theory; behavioural economics; evolutionary theories; social norms; institutions; social preferences; cooperation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

Statistical decision theory is the discipline that merges statistical inference and decision theory. It offers a wide set of methodological tools to face—from a decisional perspective—the challenges of today’s society. The huge amount of data that are produced in continuum by human activities (big data) as well as the complexity of human relations due to globalization require more and more statistically based instruments to manage decision-making processes in any field of human knowledge (e.g., economics, medicine, public policy, and so on).

On the one hand, the availability of big data outlines the importance of artificial intelligence (AI) to help researchers and policy makers to manage data and transform them to information that is useful to make decisions. From this point of view, the developments of AI that include a decisional perspective represent a challenge for future research in the AI field.

On the other hand, the comprehension of how relationships and behaviors arise and develop in today’s global society requires innovative economic theories and advanced statistical instruments to model, in a suitable way, individuals’ and organizations’ behaviors and decisional processes.

This Special Issue on “Advances in Statistical Decision Theory and Applications” invites researchers to submit original research and review contributions on exploring advances along the following two main topics:

  • Artificial intelligence and decision making;
  • Behavioral decision making.

Theoretical developments and applications supported by a solid methodological basis in these two fields are welcomed.

Prof. Silvia Bacci
Prof. Dr. Fabrizia Mealli
Prof. Dr. Leonardo Boncinelli
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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

  • Artificial intelligence
  • Bayesian statistical decision theory
  • Behavioral decision making
  • Behavioral economics
  • Causal statistical decision theory
  • Decision making
  • Experimental economics
  • Markov decision process
  • Psychology and psychometrics of decision making
  • Reinforcement learning
  • Utility theory and generalized utility theories

Published Papers (5 papers)

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Research

22 pages, 642 KiB  
Article
Answering Multiple-Choice Questions in Which Examinees Doubt What the True Answer Is among Different Options
by Fernando Sánchez Lasheras, José Curbelo, Jaime Baladrón Romero, Alberto García Guerrero, Carmen Peñalver San Cristóbal, Tomás Villacampa and Paula Jiménez Fonseca
Mathematics 2022, 10(23), 4543; https://0-doi-org.brum.beds.ac.uk/10.3390/math10234543 - 01 Dec 2022
Viewed by 1488
Abstract
This research explores the results that an examinee would obtain if taking a multiple-choice questions test in which they have doubts as to what the true answer is among different options. This problem is analyzed by making use of combinatorics and analytical and [...] Read more.
This research explores the results that an examinee would obtain if taking a multiple-choice questions test in which they have doubts as to what the true answer is among different options. This problem is analyzed by making use of combinatorics and analytical and sampling methodologies. The Spanish exam through which doctors become medical specialists has been employed as an example. Although it is difficult to imagine that there are candidates who respond randomly to all the questions of such an exam, it is common that they may doubt over what the correct answer is in some questions. The exam consists of a total of 210 multiple-choice questions with 4 answer options. The cut-off mark is calculated as one-third of the average of the 10 best marks in the exam. According to the results obtained, it is possible to affirm that in the case of doubting over two or three of the four possible answers in certain group questions, answering all of them will in most cases lead to obtaining a positive result. Moreover, in the case of doubting between two answer options in all the questions of the MIR test, it would be possible to exceed the cut-off mark. Full article
(This article belongs to the Special Issue Advances in Statistical Decision Theory and Applications)
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14 pages, 816 KiB  
Article
A Bayesian Causal Model to Support Decisions on Treating of a Vineyard
by Federico Mattia Stefanini and Lorenzo Valleggi
Mathematics 2022, 10(22), 4326; https://0-doi-org.brum.beds.ac.uk/10.3390/math10224326 - 18 Nov 2022
Cited by 2 | Viewed by 1331
Abstract
Plasmopara viticola is one of the main challenges of working in a vineyard as it can seriously damage plants, reducing the quality and quantity of grapes. Statistical predictions on future incidence may be used to evaluate when and which treatments are required in [...] Read more.
Plasmopara viticola is one of the main challenges of working in a vineyard as it can seriously damage plants, reducing the quality and quantity of grapes. Statistical predictions on future incidence may be used to evaluate when and which treatments are required in order to define an efficient and environmentally friendly management. Approaches in the literature describe mechanistic models requiring challenging calibration in order to account for local features of the vineyard. A causal Directed Acyclic Graph is here proposed to relate key determinants of the spread of infection within rows of the vineyard characterized by their own microclimate. The identifiability of causal effects about new chemical treatments in a non-randomized regime is discussed, together with the context in which the proposed model is expected to support optimal decision-making. A Bayesian Network based on discretized random variables was coded after quantifying the expert degree of belief about features of the considered vineyard. The predictive distribution of incidence, given alternative treatment decisions, was defined and calculated using the elicited network to support decision-making on a weekly basis. The final discussion considers current limitations of the approach and some directions for future work, such as the introduction of variables to describe the state of soil and plants after treatment. Full article
(This article belongs to the Special Issue Advances in Statistical Decision Theory and Applications)
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15 pages, 2613 KiB  
Article
Research on Simulation and Decision-Making of Coal Mine Workers’ Behavior Risk
by Kai Yu, Sai Zhang, Pingping Liu, Lujie Zhou and Jing Chen
Mathematics 2022, 10(18), 3297; https://0-doi-org.brum.beds.ac.uk/10.3390/math10183297 - 11 Sep 2022
Cited by 3 | Viewed by 1074
Abstract
The behavior risk of workers is one of the main restricting factors in coal mine safety decision-making and management. In this paper, the behavior and decision-making process of individuals and organizations are modeled and analyzed to solve this challenge, based on data analysis [...] Read more.
The behavior risk of workers is one of the main restricting factors in coal mine safety decision-making and management. In this paper, the behavior and decision-making process of individuals and organizations are modeled and analyzed to solve this challenge, based on data analysis and behavior decision-making. Based on system dynamics (SD), this paper proposes an unsafe behavior correction system (SD-Ipt) for coal miners to reduce occupational risk. The “1 + 1 + 3 + X” behavior risk correction decision-making system is constructed, and the implementation scheme of the system is put forward, which has been applied in coal mines. This study can effectively correct the unsafe behavior of coal mining enterprises and improve the occupational safety and health management ability of coal mining enterprises. Full article
(This article belongs to the Special Issue Advances in Statistical Decision Theory and Applications)
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25 pages, 6977 KiB  
Article
Truncated Cauchy Power Weibull-G Class of Distributions: Bayesian and Non-Bayesian Inference Modelling for COVID-19 and Carbon Fiber Data
by Naif Alotaibi, Ibrahim Elbatal, Ehab M. Almetwally, Salem A. Alyami, A. S. Al-Moisheer and Mohammed Elgarhy
Mathematics 2022, 10(9), 1565; https://0-doi-org.brum.beds.ac.uk/10.3390/math10091565 - 06 May 2022
Cited by 30 | Viewed by 1431
Abstract
The Truncated Cauchy Power Weibull-G class is presented as a new family of distributions. Unique models for this family are presented in this paper. The statistical aspects of the family are explored, including the expansion of the density function, moments, incomplete moments (IMOs), [...] Read more.
The Truncated Cauchy Power Weibull-G class is presented as a new family of distributions. Unique models for this family are presented in this paper. The statistical aspects of the family are explored, including the expansion of the density function, moments, incomplete moments (IMOs), residual life and reversed residual life functions, and entropy. The maximum likelihood (ML) and Bayesian estimations are developed based on the Type-II censored sample. The properties of Bayes estimators of the parameters are studied under different loss functions (squared error loss function and LINEX loss function). To create Markov-chain Monte Carlo samples from the posterior density, the Metropolis–Hasting technique was used with posterior density. Using non-informative and informative priors, a full simulation technique was carried out. The maximum likelihood estimator was compared to the Bayesian estimators using Monte Carlo simulation. To compare the performances of the suggested estimators, a simulation study was carried out. Real-world data sets, such as strength measured in GPA for single carbon fibers and impregnated 1000-carbon fiber tows, maximum stress per cycle at 31,000 psi, and COVID-19 data were used to demonstrate the relevance and flexibility of the suggested method. The suggested models are then compared to comparable models such as the Marshall–Olkin alpha power exponential, the extended odd Weibull exponential, the Weibull–Rayleigh, the Weibull–Lomax, and the exponential Lomax distributions. Full article
(This article belongs to the Special Issue Advances in Statistical Decision Theory and Applications)
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33 pages, 3318 KiB  
Article
Plenty of Fish in the Sea: Divorce Choice and the Quality of Singles
by Giorgio Gronchi, Elena Parilina and Alessandro Tampieri
Mathematics 2021, 9(23), 3059; https://0-doi-org.brum.beds.ac.uk/10.3390/math9233059 - 28 Nov 2021
Viewed by 1513
Abstract
In the literature of marriage, divorce choices are usually assumed to not affect the distribution of types in the pool of singles. The scope of the present paper is to overcome this assumption. We analyse divorce choices when separation decision influences the distribution [...] Read more.
In the literature of marriage, divorce choices are usually assumed to not affect the distribution of types in the pool of singles. The scope of the present paper is to overcome this assumption. We analyse divorce choices when separation decision influences the distribution of singles and, thus, their expected quality. We consider a three-period model where heterogeneous individuals may unilaterally experience divorce and return to the marriage market. The choices of individuals are based on the change in the distribution of singles and the cost of waiting and divorcing, taking into consideration the individual’s eligibility in the marriage market. There are two main findings: Firstly, positive assortative matching dissolves with divorce for some intermediate types. Therefore, the endogenous positive assortative matching that usually emerges in models with nontransferable utility is weakened when matches can dissolve. Secondly, the existence of ranges where divorce emerges among individuals with positive assortative matching implies the existence of two disconnected classes of types. If matchings in the first period were to occur between individuals of different classes, such matches would be dissolved later. Full article
(This article belongs to the Special Issue Advances in Statistical Decision Theory and Applications)
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