Pub Date : 2005-05-01DOI: 10.1142/S0219607705000061
T. C. Brown, M. Fackrell, A. Xia
Melamed (1979) proved that for an open migration process, a necessary and sufficient condition for the equilibrium flow along a link to be Poissonian is the absence of loops: no customer can travel along the link more than once. Barbour and Brown (1996) quantified the statement by allowing the customers a small probability of travelling along the link more than once and proved Poisson process approximation theorems analogous to Melamed's Theorem. Amongst the three bounds presented in Barbour and Brown (1996), the one in terms of the Wasserstein metric is of particular interest since it reveals more insightful information about the closeness between the process of flows and an approximating Poisson process, and it is small when the parameter of the system is small, except a logarithmic factor in terms of time in which the flows are considered. The bound was later improved by Brown, Weinberg and Xia (2000) who showed that the logarithmic factor in terms of time can be lifted at the cost of an extra parameter being introduced into the bound. In this paper, we present a new bound which simplifies and sharpens the bounds in the above-mentioned two papers and compare the performance of these bounds for a simple open migration process.
{"title":"IMPROVED RESULTS ON POISSON PROCESS APPROXIMATION IN JACKSON NETWORKS","authors":"T. C. Brown, M. Fackrell, A. Xia","doi":"10.1142/S0219607705000061","DOIUrl":"https://doi.org/10.1142/S0219607705000061","url":null,"abstract":"Melamed (1979) proved that for an open migration process, a necessary and sufficient condition for the equilibrium flow along a link to be Poissonian is the absence of loops: no customer can travel along the link more than once. Barbour and Brown (1996) quantified the statement by allowing the customers a small probability of travelling along the link more than once and proved Poisson process approximation theorems analogous to Melamed's Theorem. Amongst the three bounds presented in Barbour and Brown (1996), the one in terms of the Wasserstein metric is of particular interest since it reveals more insightful information about the closeness between the process of flows and an approximating Poisson process, and it is small when the parameter of the system is small, except a logarithmic factor in terms of time in which the flows are considered. The bound was later improved by Brown, Weinberg and Xia (2000) who showed that the logarithmic factor in terms of time can be lifted at the cost of an extra parameter being introduced into the bound. In this paper, we present a new bound which simplifies and sharpens the bounds in the above-mentioned two papers and compare the performance of these bounds for a simple open migration process.","PeriodicalId":80753,"journal":{"name":"Bulletin - Cosmos Club. Cosmos Club (Washington, D.C.)","volume":"77 1","pages":"47-55"},"PeriodicalIF":0.0,"publicationDate":"2005-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76126920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-05-01DOI: 10.1142/S021960770500005X
Xuming He, F. Hu
The bootstrap is a computer-based resampling method that can provide good approximations to the distribution of a given statistic. We review some common forms of bootstrap-based confidence intervals, with emphasis on some recent work on the estimating function bootstrap and Markov chain marginal bootstrap.
{"title":"SOME RECENT ADVANCES ON BOOTSTRAP","authors":"Xuming He, F. Hu","doi":"10.1142/S021960770500005X","DOIUrl":"https://doi.org/10.1142/S021960770500005X","url":null,"abstract":"The bootstrap is a computer-based resampling method that can provide good approximations to the distribution of a given statistic. We review some common forms of bootstrap-based confidence intervals, with emphasis on some recent work on the estimating function bootstrap and Markov chain marginal bootstrap.","PeriodicalId":80753,"journal":{"name":"Bulletin - Cosmos Club. Cosmos Club (Washington, D.C.)","volume":"126 1","pages":"75-86"},"PeriodicalIF":0.0,"publicationDate":"2005-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89452865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-05-01DOI: 10.1142/S0219607705000073
A. Lo
A class of distributions on partitions of a finite collection of objects is defined. The probability of a specific partition is a product of functions of clusters of the partition with the product running over all clusters. This class contains Chinese restaurant processes as a special case. The simulation of a distribution in this class is described through the seating probability that gives the conditional probability of joining a new object to an existing cluster. Examples in Bayesian mixture models are given.
{"title":"WEIGHTED CHINESE RESTAURANT PROCESSES","authors":"A. Lo","doi":"10.1142/S0219607705000073","DOIUrl":"https://doi.org/10.1142/S0219607705000073","url":null,"abstract":"A class of distributions on partitions of a finite collection of objects is defined. The probability of a specific partition is a product of functions of clusters of the partition with the product running over all clusters. This class contains Chinese restaurant processes as a special case. The simulation of a distribution in this class is described through the seating probability that gives the conditional probability of joining a new object to an existing cluster. Examples in Bayesian mixture models are given.","PeriodicalId":80753,"journal":{"name":"Bulletin - Cosmos Club. Cosmos Club (Washington, D.C.)","volume":"65 1","pages":"107-111"},"PeriodicalIF":0.0,"publicationDate":"2005-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81966281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-05-01DOI: 10.1142/S0219607705000097
H. Niederreiter
Quasi-Monte Carlo methods are deterministic versions of Monte Carlo methods, in the sense that the random samples used in the implementation of a Monte Carlo method are replaced by judiciously chosen deterministic points with good distribution properties. They outperform classical Monte Carlo methods in many problems of scientific computing. This paper discusses applications of quasi-Monte Carlo methods to computational finance, with a special emphasis on the problems of pricing mortgage-backed securities and options. The necessary background on Monte Carlo and quasi-Monte Carlo methods is also provided.
{"title":"QUASI-MONTE CARLO METHODS IN COMPUTATIONAL FINANCE","authors":"H. Niederreiter","doi":"10.1142/S0219607705000097","DOIUrl":"https://doi.org/10.1142/S0219607705000097","url":null,"abstract":"Quasi-Monte Carlo methods are deterministic versions of Monte Carlo methods, in the sense that the random samples used in the implementation of a Monte Carlo method are replaced by judiciously chosen deterministic points with good distribution properties. They outperform classical Monte Carlo methods in many problems of scientific computing. This paper discusses applications of quasi-Monte Carlo methods to computational finance, with a special emphasis on the problems of pricing mortgage-backed securities and options. The necessary background on Monte Carlo and quasi-Monte Carlo methods is also provided.","PeriodicalId":80753,"journal":{"name":"Bulletin - Cosmos Club. Cosmos Club (Washington, D.C.)","volume":"1 1","pages":"113-125"},"PeriodicalIF":0.0,"publicationDate":"2005-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83352444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-05-01DOI: 10.1142/S0219607705000103
Wenbo V. Li, Q. Shao
This paper surveys briefly some recent developments on lower tail probabilities for real valued Gaussian processes. Connections and applications to various problems are discussed. A new and simplified argument is given and it is of independent interest.
{"title":"RECENT DEVELOPMENTS ON LOWER TAIL PROBABILITIES FOR GAUSSIAN PROCESSES","authors":"Wenbo V. Li, Q. Shao","doi":"10.1142/S0219607705000103","DOIUrl":"https://doi.org/10.1142/S0219607705000103","url":null,"abstract":"This paper surveys briefly some recent developments on lower tail probabilities for real valued Gaussian processes. Connections and applications to various problems are discussed. A new and simplified argument is given and it is of independent interest.","PeriodicalId":80753,"journal":{"name":"Bulletin - Cosmos Club. Cosmos Club (Washington, D.C.)","volume":"312 1","pages":"95-106"},"PeriodicalIF":0.0,"publicationDate":"2005-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76853134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-05-01DOI: 10.1142/S0219607705000048
K. P. Choi, Louxin Zhang
The novel introduction of spaced seed idea in the filtration step of sequence comparison by Ma, Tromp and Li (2002) has greatly increased the sensitivity of homology search without compromising the speed of search. In this paper, we survey some recent works on spaced seeds with main emphasis on their probabilistic and computational aspects.
{"title":"ANALYSIS OF SPACED SEED TECHNIQUE IN SEQUENCE ALIGNMENT","authors":"K. P. Choi, Louxin Zhang","doi":"10.1142/S0219607705000048","DOIUrl":"https://doi.org/10.1142/S0219607705000048","url":null,"abstract":"The novel introduction of spaced seed idea in the filtration step of sequence comparison by Ma, Tromp and Li (2002) has greatly increased the sensitivity of homology search without compromising the speed of search. In this paper, we survey some recent works on spaced seeds with main emphasis on their probabilistic and computational aspects.","PeriodicalId":80753,"journal":{"name":"Bulletin - Cosmos Club. Cosmos Club (Washington, D.C.)","volume":"149 1","pages":"57-73"},"PeriodicalIF":0.0,"publicationDate":"2005-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76796455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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