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Mathematics
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Analysis and Comparison of Probabilistic Models
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Analysis and Comparison of Probabilistic Models

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

Deadline for manuscript submissions: closed (28 March 2022) | Viewed by 10451

Special Issue Editors

Prof. Dr. Francisco De Asís Torres-Ruiz

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Guest Editor
Department of Statistics and Operations Research, Faculty of Sciences, s/n, Campus de Fuentenueva, University of Granada, 18071 Granada, Spain
Interests: diffusion processes for growth phenomena; inference in diffusion processes; first-passage-times; model selection
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Antonio Barrera García

E-Mail Website
Guest Editor
Department of Mathematical Analysis, Statistics and Operations Research and Applied Mathematics, Faculty of Sciences, University of Málaga, 29010 Málaga, Spain
Interests: diffusion processes for growth phenomena; inference in diffusion processes; first-passage-times; model selection

Special Issue Information

Dear Colleagues,

Modelling and study of phenomena associated with probabilistic and stochastic models has been the object of analysis for a long time in various fields of application. The main reason for this is the need to understand the mechanisms of evolution of the systems in order to provide an explanation of their behaviour, allowing it to be predicted without losing sight of the possible inclusion of influences outside the variables under study that allow alter said behaviour and, with it, have the possibility of externally controlling the evolution of the phenomenon under consideration. Another line of action has been to establish mechanisms that allow the comparison between different models in order to select the one that describes and explains the phenomenon under study best.

The main objective of this Special Issue of Mathematics is to publish original works focused on the study of these types of models. Among them, we can cite stochastic processes, models derived from the theory of stochastic systems, functional data models, and linear models. Both the probabilistic study of the introduced models and the application to research areas are welcome, as well comparison studies between models that can be applied to the description of a specific phenomenon.

Prof. Francisco De Asís Torres-Ruiz
Prof. Dr. Antonio Barrera García
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

  • Modelling by stochastic processes
  • Dynamic prediction
  • Dynamical systems estimation
  • Functional data models
  • Computational methods for dynamical models
  • Model selection
  • Applications in survival theory, medicine, biosciences, engineering, and other areas of interest

Published Papers (6 papers)

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Research

17 pages, 772 KiB  
Article
Distributed Fusion Estimation in Network Systems Subject to Random Delays and Deception Attacks
by María Jesús García-Ligero, Aurora Hermoso-Carazo and Josefa Linares-Pérez
Mathematics 2022, 10(4), 662; https://0-doi-org.brum.beds.ac.uk/10.3390/math10040662 - 20 Feb 2022
Cited by 2 | Viewed by 1160
Abstract
This paper focuses on the distributed fusion estimation problem in which a signal transmitted over wireless sensor networks is subject to deception attacks and random delays. We assume that each sensor can suffer attacks that may corrupt and/or modify the output measurements. In [...] Read more.
This paper focuses on the distributed fusion estimation problem in which a signal transmitted over wireless sensor networks is subject to deception attacks and random delays. We assume that each sensor can suffer attacks that may corrupt and/or modify the output measurements. In addition, communication failures between sensors and their local processors can delay the receipt of processed measurements. The randomness of attacks and transmission delays is modelled by different Bernoulli random variables with known probabilities of success. According to these characteristics of the sensor networks and assuming that the measurement noises are cross-correlated at the same time step between sensors and are also correlated with the signal at the same and subsequent time steps, we derive a fusion estimation algorithm, including prediction and filtering, using the distributed fusion method. First, for each sensor, the local least-squares linear prediction and filtering algorithm are derived, using a covariance-based approach. Then, the distributed fusion predictor and the corresponding filter are obtained as the matrix-weighted linear combination of corresponding local estimators, checking that the mean squared error is minimised. A simulation example is then given to illustrate the effectiveness of the proposed algorithms. Full article
(This article belongs to the Special Issue Analysis and Comparison of Probabilistic Models)
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26 pages, 748 KiB  
Article
Study of a Modified Kumaraswamy Distribution
by Rashad A. R. Bantan, Christophe Chesneau, Farrukh Jamal, Mohammed Elgarhy, Waleed Almutiry and Amani Abdullah Alahmadi
Mathematics 2021, 9(21), 2836; https://0-doi-org.brum.beds.ac.uk/10.3390/math9212836 - 08 Nov 2021
Cited by 4 | Viewed by 1860
Abstract
In this article, a structural modification of the Kumaraswamy distribution yields a new two-parameter distribution defined on (0,1), called the modified Kumaraswamy distribution. It has the advantages of being (i) original in its definition, mixing logarithmic, power and [...] Read more.
In this article, a structural modification of the Kumaraswamy distribution yields a new two-parameter distribution defined on (0,1), called the modified Kumaraswamy distribution. It has the advantages of being (i) original in its definition, mixing logarithmic, power and ratio functions, (ii) flexible from the modeling viewpoint, with rare functional capabilities for a bounded distribution—in particular, N-shapes are observed for both the probability density and hazard rate functions—and (iii) a solid alternative to its parental Kumaraswamy distribution in the first-order stochastic sense. Some statistical features, such as the moments and quantile function, are represented in closed form. The Lambert function and incomplete beta function are involved in this regard. The distributions of order statistics are also explored. Then, emphasis is put on the practice of the modified Kumaraswamy model in the context of data fitting. The well-known maximum likelihood approach is used to estimate the parameters, and a simulation study is conducted to examine the performance of this approach. In order to demonstrate the applicability of the suggested model, two real data sets are considered. As a notable result, for the considered data sets, statistical benchmarks indicate that the new modeling strategy outperforms the Kumaraswamy model. The transmuted Kumaraswamy, beta, unit Rayleigh, Topp–Leone and power models are also outperformed. Full article
(This article belongs to the Special Issue Analysis and Comparison of Probabilistic Models)
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27 pages, 851 KiB  
Article
On the First-Passage Time Problem for a Feller-Type Diffusion Process
by Virginia Giorno and Amelia G. Nobile
Mathematics 2021, 9(19), 2470; https://0-doi-org.brum.beds.ac.uk/10.3390/math9192470 - 03 Oct 2021
Cited by 4 | Viewed by 1428
Abstract
We consider the first-passage time problem for the Feller-type diffusion process, having infinitesimal drift B1(x,t)=α(t)x+β(t) and infinitesimal variance [...] Read more.
We consider the first-passage time problem for the Feller-type diffusion process, having infinitesimal drift B1(x,t)=α(t)x+β(t) and infinitesimal variance B2(x,t)=2r(t)x, defined in the space state [0,+∞), with α(t)∈R, β(t)>0, r(t)>0 continuous functions. For the time-homogeneous case, some relations between the first-passage time densities of the Feller process and of the Wiener and the Ornstein–Uhlenbeck processes are discussed. The asymptotic behavior of the first-passage time density through a time-dependent boundary is analyzed for an asymptotically constant boundary and for an asymptotically periodic boundary. Furthermore, when β(t)=ξr(t), with ξ>0, we discuss the asymptotic behavior of the first-passage density and we obtain some closed-form results for special time-varying boundaries. Full article
(This article belongs to the Special Issue Analysis and Comparison of Probabilistic Models)
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32 pages, 432 KiB  
Article
Generalized Fractional Calculus for Gompertz-Type Models
by Giacomo Ascione and Enrica Pirozzi
Mathematics 2021, 9(17), 2140; https://0-doi-org.brum.beds.ac.uk/10.3390/math9172140 - 02 Sep 2021
Cited by 3 | Viewed by 1506
Abstract
This paper focuses on the construction of deterministic and stochastic extensions of the Gompertz curve by means of generalized fractional derivatives induced by complete Bernstein functions. Precisely, we first introduce a class of linear stochastic equations involving a generalized fractional integral and we [...] Read more.
This paper focuses on the construction of deterministic and stochastic extensions of the Gompertz curve by means of generalized fractional derivatives induced by complete Bernstein functions. Precisely, we first introduce a class of linear stochastic equations involving a generalized fractional integral and we study the properties of its solutions. This is done by proving the existence and uniqueness of Gaussian solutions of such equations via a fixed point argument and then by showing that, under suitable conditions, the expected value of the solution solves a generalized fractional linear equation. Regularity of the absolute p-moment functions is proved by using generalized Grönwall inequalities. Deterministic generalized fractional Gompertz curves are introduced by means of Caputo-type generalized fractional derivatives, possibly with respect to other functions. Their stochastic counterparts are then constructed by using the previously considered integral equations to define a rate process and a generalization of lognormal distributions to ensure that the median of the newly constructed process coincides with the deterministic curve. Full article
(This article belongs to the Special Issue Analysis and Comparison of Probabilistic Models)
19 pages, 399 KiB  
Article
A Longitudinal Study of the Bladder Cancer Applying a State-Space Model with Non-Exponential Staying Time in States
by Delia Montoro-Cazorla, Rafael Pérez-Ocón and Alicia Pereira das Neves-Yedig
Mathematics 2021, 9(4), 363; https://0-doi-org.brum.beds.ac.uk/10.3390/math9040363 - 11 Feb 2021
Viewed by 1377
Abstract
A longitudinal study for 847 bladder cancer patients for a period of fifteen years is presented. After the first surgery, the patients undergo successive ones (recurrences). A state-model is selected for analyzing the evolution of the cancer, based on the distribution of the [...] Read more.
A longitudinal study for 847 bladder cancer patients for a period of fifteen years is presented. After the first surgery, the patients undergo successive ones (recurrences). A state-model is selected for analyzing the evolution of the cancer, based on the distribution of the times between recurrences. These times do not follow exponential distributions, and are approximated by phase-type distributions. Under these conditions, a multidimensional Markov process governs the evolution of the disease. The survival probability and mean times in the different states (levels) of the disease are calculated empirically and also by applying the Markov model, the comparison of the results indicate that the model is well-fitted to the data to an acceptable significance level of 0.05. Two sub-cohorts are well-differenced: those reaching progression (the bladder is removed) and those that do not. These two cases are separately studied and performance measures calculated, and the comparison reveals details about the characteristics of the patients in these groups. Full article
(This article belongs to the Special Issue Analysis and Comparison of Probabilistic Models)
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14 pages, 540 KiB  
Article
Iterative Variable Selection for High-Dimensional Data: Prediction of Pathological Response in Triple-Negative Breast Cancer
by Juan C. Laria, M. Carmen Aguilera-Morillo, Enrique Álvarez, Rosa E. Lillo, Sara López-Taruella, María del Monte-Millán, Antonio C. Picornell, Miguel Martín and Juan Romo
Mathematics 2021, 9(3), 222; https://0-doi-org.brum.beds.ac.uk/10.3390/math9030222 - 23 Jan 2021
Cited by 2 | Viewed by 1993
Abstract
Over the last decade, regularized regression methods have offered alternatives for performing multi-marker analysis and feature selection in a whole genome context. The process of defining a list of genes that will characterize an expression profile remains unclear. It currently relies upon advanced [...] Read more.
Over the last decade, regularized regression methods have offered alternatives for performing multi-marker analysis and feature selection in a whole genome context. The process of defining a list of genes that will characterize an expression profile remains unclear. It currently relies upon advanced statistics and can use an agnostic point of view or include some a priori knowledge, but overfitting remains a problem. This paper introduces a methodology to deal with the variable selection and model estimation problems in the high-dimensional set-up, which can be particularly useful in the whole genome context. Results are validated using simulated data and a real dataset from a triple-negative breast cancer study. Full article
(This article belongs to the Special Issue Analysis and Comparison of Probabilistic Models)
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