Pub Date : 2023-11-07DOI: 10.1007/s11009-023-10065-8
Oscar Peralta, Matthieu Simon
{"title":"Ruin Problems for Risk Processes with Dependent Phase-Type Claims","authors":"Oscar Peralta, Matthieu Simon","doi":"10.1007/s11009-023-10065-8","DOIUrl":"https://doi.org/10.1007/s11009-023-10065-8","url":null,"abstract":"","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"40 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135431078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-04DOI: 10.1007/s11009-023-10060-z
Jingqi Zhang, Mitra Fouladirad, Nikolaos Limnios
{"title":"A Semi-Markov Model with Geometric Renewal Processes","authors":"Jingqi Zhang, Mitra Fouladirad, Nikolaos Limnios","doi":"10.1007/s11009-023-10060-z","DOIUrl":"https://doi.org/10.1007/s11009-023-10060-z","url":null,"abstract":"","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"37 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135774380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.1007/s11009-023-10053-y
Ben O’Neill
Abstract The classical and extended occupancy distributions are useful for examining the number of occupied bins in problems involving random allocation of balls to bins. We examine the extended occupancy problem by framing it as a Markov chain and deriving the spectral decomposition of the transition probability matrix. We look at three distributions of interest that arise from the problem, all involving the noncentral Stirling numbers of the second kind. These distributions give a useful generalisation to the binomial and negative-binomial distributions. We examine how these distributions relate to one another, and we derive recursive properties and mixture properties that characterise the distributions.
{"title":"Three Distributions in the Extended Occupancy Problem","authors":"Ben O’Neill","doi":"10.1007/s11009-023-10053-y","DOIUrl":"https://doi.org/10.1007/s11009-023-10053-y","url":null,"abstract":"Abstract The classical and extended occupancy distributions are useful for examining the number of occupied bins in problems involving random allocation of balls to bins. We examine the extended occupancy problem by framing it as a Markov chain and deriving the spectral decomposition of the transition probability matrix. We look at three distributions of interest that arise from the problem, all involving the noncentral Stirling numbers of the second kind. These distributions give a useful generalisation to the binomial and negative-binomial distributions. We examine how these distributions relate to one another, and we derive recursive properties and mixture properties that characterise the distributions.","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136102436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-27DOI: 10.1007/s11009-023-10056-9
Paul A. Jenkins, Murray Pollock, Gareth O. Roberts
Abstract We introduce a flexible method to simultaneously infer both the drift and volatility functions of a discretely observed scalar diffusion. We introduce spline bases to represent these functions and develop a Markov chain Monte Carlo algorithm to infer, a posteriori, the coefficients of these functions in the spline basis. A key innovation is that we use spline bases to model transformed versions of the drift and volatility functions rather than the functions themselves. The output of the algorithm is a posterior sample of plausible drift and volatility functions that are not constrained to any particular parametric family. The flexibility of this approach provides practitioners a powerful investigative tool, allowing them to posit a variety of parametric models to better capture the underlying dynamics of their processes of interest. We illustrate the versatility of our method by applying it to challenging datasets from finance, paleoclimatology, and astrophysics. In view of the parametric diffusion models widely employed in the literature for those examples, some of our results are surprising since they call into question some aspects of these models.
{"title":"Flexible Bayesian Inference for Diffusion Processesusing Splines","authors":"Paul A. Jenkins, Murray Pollock, Gareth O. Roberts","doi":"10.1007/s11009-023-10056-9","DOIUrl":"https://doi.org/10.1007/s11009-023-10056-9","url":null,"abstract":"Abstract We introduce a flexible method to simultaneously infer both the drift and volatility functions of a discretely observed scalar diffusion. We introduce spline bases to represent these functions and develop a Markov chain Monte Carlo algorithm to infer, a posteriori, the coefficients of these functions in the spline basis. A key innovation is that we use spline bases to model transformed versions of the drift and volatility functions rather than the functions themselves. The output of the algorithm is a posterior sample of plausible drift and volatility functions that are not constrained to any particular parametric family. The flexibility of this approach provides practitioners a powerful investigative tool, allowing them to posit a variety of parametric models to better capture the underlying dynamics of their processes of interest. We illustrate the versatility of our method by applying it to challenging datasets from finance, paleoclimatology, and astrophysics. In view of the parametric diffusion models widely employed in the literature for those examples, some of our results are surprising since they call into question some aspects of these models.","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"43 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136262695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-23DOI: 10.1007/s11009-023-10058-7
François Castella, Bruno Sericola, Emmanuelle Anceaume, Yves Mocquard
{"title":"Continuous-Time Stochastic Analysis of Rumor Spreading with Multiple Operations","authors":"François Castella, Bruno Sericola, Emmanuelle Anceaume, Yves Mocquard","doi":"10.1007/s11009-023-10058-7","DOIUrl":"https://doi.org/10.1007/s11009-023-10058-7","url":null,"abstract":"","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135366355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-17DOI: 10.1007/s11009-023-10057-8
Amit N. Kumar, P. Vellaisamy
{"title":"Binomial Approximation to Locally Dependent Collateralized Debt Obligations","authors":"Amit N. Kumar, P. Vellaisamy","doi":"10.1007/s11009-023-10057-8","DOIUrl":"https://doi.org/10.1007/s11009-023-10057-8","url":null,"abstract":"","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136033235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-02DOI: 10.1007/s11009-023-10052-z
V. Deepa, M. Haridass
{"title":"Simulation Analysis of a Base Station Using Finite Buffer M/G/1 Queueing System with Variant Sleeps","authors":"V. Deepa, M. Haridass","doi":"10.1007/s11009-023-10052-z","DOIUrl":"https://doi.org/10.1007/s11009-023-10052-z","url":null,"abstract":"","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135893084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-02DOI: 10.1007/s11009-023-10054-x
Lingjiao Zhang, Jinting Wang, Yilin Wang
{"title":"Strategic Behavior and Optimization of an M/M/1 Queuewith N-Policy and Hysteretic Control","authors":"Lingjiao Zhang, Jinting Wang, Yilin Wang","doi":"10.1007/s11009-023-10054-x","DOIUrl":"https://doi.org/10.1007/s11009-023-10054-x","url":null,"abstract":"","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135834488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-22DOI: 10.1007/s11009-023-10055-w
Jorge Navarro, Francesco Buono, Jorge M. Arevalillo
Abstract The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well.
{"title":"A New Separation Index and Classification Techniques Based on Shannon Entropy","authors":"Jorge Navarro, Francesco Buono, Jorge M. Arevalillo","doi":"10.1007/s11009-023-10055-w","DOIUrl":"https://doi.org/10.1007/s11009-023-10055-w","url":null,"abstract":"Abstract The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well.","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136060079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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