Pub Date : 2015-06-19DOI: 10.1007/978-3-319-45026-1_2
Shiwei Lan, B. Shahbaba
{"title":"Sampling Constrained Probability Distributions Using Spherical Augmentation","authors":"Shiwei Lan, B. Shahbaba","doi":"10.1007/978-3-319-45026-1_2","DOIUrl":"https://doi.org/10.1007/978-3-319-45026-1_2","url":null,"abstract":"","PeriodicalId":8446,"journal":{"name":"arXiv: Computation","volume":"18 1","pages":"25-71"},"PeriodicalIF":0.0,"publicationDate":"2015-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86860840","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 : 2015-05-29DOI: 10.3934/DCDS.2016.8.4227
A. Chorin, F. Lu, Robert N. Miller, M. Morzfeld, Xuemin Tu
Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at relatively low cost, making the assimilation more efficient. A new analysis of the feasibility of data assimilation is presented, showing in detail why feasibility depends on the Frobenius norm of the covariance matrix of the noise and not on the number of variables. A discussion of the convergence of particular particle filters follows. A major open problem in numerical data assimilation is the determination of appropriate priors, a progress report on recent work on this problem is given. The analysis highlights the need for a careful attention both to the data and to the physics in data assimilation problems.
{"title":"Sampling, feasibility, and priors in Bayesian estimation","authors":"A. Chorin, F. Lu, Robert N. Miller, M. Morzfeld, Xuemin Tu","doi":"10.3934/DCDS.2016.8.4227","DOIUrl":"https://doi.org/10.3934/DCDS.2016.8.4227","url":null,"abstract":"Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at relatively low cost, making the assimilation more efficient. A new analysis of the feasibility of data assimilation is presented, showing in detail why feasibility depends on the Frobenius norm of the covariance matrix of the noise and not on the number of variables. A discussion of the convergence of particular particle filters follows. A major open problem in numerical data assimilation is the determination of appropriate priors, a progress report on recent work on this problem is given. The analysis highlights the need for a careful attention both to the data and to the physics in data assimilation problems.","PeriodicalId":8446,"journal":{"name":"arXiv: Computation","volume":"128 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74603915","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 : 2015-04-13DOI: 10.1002/9783527694365.CH3
A. Caimo, Isabella Gollini
In this chapter we review some of the most recent computational advances in the rapidly expanding field of statistical social network analysis using the R open-source software. In particular we will focus on Bayesian estimation for two important families of models: exponential random graph models (ERGMs) and latent space models (LSMs).
{"title":"Bayesian computational algorithms for social network analysis","authors":"A. Caimo, Isabella Gollini","doi":"10.1002/9783527694365.CH3","DOIUrl":"https://doi.org/10.1002/9783527694365.CH3","url":null,"abstract":"In this chapter we review some of the most recent computational advances in the rapidly expanding field of statistical social network analysis using the R open-source software. In particular we will focus on Bayesian estimation for two important families of models: exponential random graph models (ERGMs) and latent space models (LSMs).","PeriodicalId":8446,"journal":{"name":"arXiv: Computation","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76002690","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}
Methods of approximate Bayesian computation (ABC) are increasingly used for analysis of complex models. A major challenge for ABC is over-coming the often inherent problem of high rejection rates in the accept/reject methods based on prior:predictive sampling. A number of recent developments aim to address this with extensions based on sequential Monte Carlo (SMC) strategies. We build on this here, introducing an ABC SMC method that uses data-based adaptive weights. This easily implemented and computationally trivial extension of ABC SMC can very substantially improve acceptance rates, as is demonstrated in a series of examples with simulated and real data sets, including a currently topical example from dynamic modelling in systems biology applications.
{"title":"Sequential Monte Carlo with Adaptive Weights for Approximate Bayesian Computation","authors":"Fernando V. Bonassi, M. West","doi":"10.1214/14-BA891","DOIUrl":"https://doi.org/10.1214/14-BA891","url":null,"abstract":"Methods of approximate Bayesian computation (ABC) are increasingly used for analysis of complex models. A major challenge for ABC is over-coming the often inherent problem of high rejection rates in the accept/reject methods based on prior:predictive sampling. A number of recent developments aim to address this with extensions based on sequential Monte Carlo (SMC) strategies. We build on this here, introducing an ABC SMC method that uses data-based adaptive weights. This easily implemented and computationally trivial extension of ABC SMC can very substantially improve acceptance rates, as is demonstrated in a series of examples with simulated and real data sets, including a currently topical example from dynamic modelling in systems biology applications.","PeriodicalId":8446,"journal":{"name":"arXiv: Computation","volume":"525 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78155624","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}
Daniel Turek, P. Valpine, C. Paciorek, Clifford Anderson-Bergman
Markov chain Monte Carlo (MCMC) sampling is an important and commonly used tool for the analysis of hierarchical models. Nevertheless, practitioners generally have two options for MCMC: utilize existing software that generates a black-box "one size fits all" algorithm, or the challenging (and time consuming) task of implementing a problem-specific MCMC algorithm. Either choice may result in inefficient sampling, and hence researchers have become accustomed to MCMC runtimes on the order of days (or longer) for large models. We propose an automated procedure to determine an efficient MCMC algorithm for a given model and computing platform. Our procedure dynamically determines blocks of parameters for joint sampling that result in efficient sampling of the entire model. We test this procedure using a diverse suite of example models, and observe non-trivial improvements in MCMC efficiency for many models. Our procedure is the first attempt at such, and may be generalized to a broader space of MCMC algorithms. Our results suggest that substantive improvements in MCMC efficiency may be practically realized using our automated blocking procedure, or variants thereof, which warrants additional study and application.
{"title":"Automated Parameter Blocking for Efficient Markov-Chain Monte Carlo Sampling","authors":"Daniel Turek, P. Valpine, C. Paciorek, Clifford Anderson-Bergman","doi":"10.1214/16-BA1008","DOIUrl":"https://doi.org/10.1214/16-BA1008","url":null,"abstract":"Markov chain Monte Carlo (MCMC) sampling is an important and commonly used tool for the analysis of hierarchical models. Nevertheless, practitioners generally have two options for MCMC: utilize existing software that generates a black-box \"one size fits all\" algorithm, or the challenging (and time consuming) task of implementing a problem-specific MCMC algorithm. Either choice may result in inefficient sampling, and hence researchers have become accustomed to MCMC runtimes on the order of days (or longer) for large models. We propose an automated procedure to determine an efficient MCMC algorithm for a given model and computing platform. Our procedure dynamically determines blocks of parameters for joint sampling that result in efficient sampling of the entire model. We test this procedure using a diverse suite of example models, and observe non-trivial improvements in MCMC efficiency for many models. Our procedure is the first attempt at such, and may be generalized to a broader space of MCMC algorithms. Our results suggest that substantive improvements in MCMC efficiency may be practically realized using our automated blocking procedure, or variants thereof, which warrants additional study and application.","PeriodicalId":8446,"journal":{"name":"arXiv: Computation","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73638678","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}
Label switching is a well-known and fundamental problem in Bayesian estimation of mixture or hidden Markov models. In case that the prior distribution of the model parameters is the same for all states, then both the likelihood and posterior distribution are invariant to permutations of the parameters. This property makes Markov chain Monte Carlo (MCMC) samples simulated from the posterior distribution non-identifiable. In this paper, the pkg{label.switching} package is introduced. It contains one probabilistic and seven deterministic relabelling algorithms in order to post-process a given MCMC sample, provided by the user. Each method returns a set of permutations that can be used to reorder the MCMC output. Then, any parametric function of interest can be inferred using the reordered MCMC sample. A set of user-defined permutations is also accepted, allowing the researcher to benchmark new relabelling methods against the available ones
{"title":"label.switching: An R Package for Dealing with the Label Switching Problem in MCMC Outputs","authors":"Panagiotis Papastamoulis","doi":"10.18637/jss.v069.c01","DOIUrl":"https://doi.org/10.18637/jss.v069.c01","url":null,"abstract":"Label switching is a well-known and fundamental problem in Bayesian estimation of mixture or hidden Markov models. In case that the prior distribution of the model parameters is the same for all states, then both the likelihood and posterior distribution are invariant to permutations of the parameters. This property makes Markov chain Monte Carlo (MCMC) samples simulated from the posterior distribution non-identifiable. In this paper, the pkg{label.switching} package is introduced. It contains one probabilistic and seven deterministic relabelling algorithms in order to post-process a given MCMC sample, provided by the user. Each method returns a set of permutations that can be used to reorder the MCMC output. Then, any parametric function of interest can be inferred using the reordered MCMC sample. A set of user-defined permutations is also accepted, allowing the researcher to benchmark new relabelling methods against the available ones","PeriodicalId":8446,"journal":{"name":"arXiv: Computation","volume":"338 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80716091","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}
The cross-entropy (CE) method is simple and versatile technique for optimization, based on Kullback-Leibler (or cross-entropy) minimization. The method can be applied to a wide range of optimization tasks, including continuous, discrete, mixed and constrained optimization problems. The new package CEoptim provides the R implementation of the CE method for optimization. We describe the general CE methodology for optimization and well as some useful modifications. The usage and efficacy of CEoptim is demonstrated through a variety of optimization examples, including model fitting, combinatorial optimization, and maximum likelihood estimation.
{"title":"CEoptim: Cross-Entropy R Package for Optimization","authors":"Tim Benham, Q. Duan, Dirk P. Kroese, B. Liquet","doi":"10.18637/JSS.V076.I08","DOIUrl":"https://doi.org/10.18637/JSS.V076.I08","url":null,"abstract":"The cross-entropy (CE) method is simple and versatile technique for optimization, based on Kullback-Leibler (or cross-entropy) minimization. The method can be applied to a wide range of optimization tasks, including continuous, discrete, mixed and constrained optimization problems. The new package CEoptim provides the R implementation of the CE method for optimization. We describe the general CE methodology for optimization and well as some useful modifications. The usage and efficacy of CEoptim is demonstrated through a variety of optimization examples, including model fitting, combinatorial optimization, and maximum likelihood estimation.","PeriodicalId":8446,"journal":{"name":"arXiv: Computation","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75343796","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}
The R package lcmm provides a series of functions to estimate statistical models based on linear mixed model theory. It includes the estimation of mixed models and latent class mixed models for Gaussian longitudinal outcomes (hlme), curvilinear and ordinal univariate longitudinal outcomes (lcmm) and curvilinear multivariate outcomes (multlcmm), as well as joint latent class mixed models (Jointlcmm) for a (Gaussian or curvilinear) longitudinal outcome and a time-to-event that can be possibly left-truncated right-censored and defined in a competing setting. Maximum likelihood esimators are obtained using a modified Marquardt algorithm with strict convergence criteria based on the parameters and likelihood stability, and on the negativity of the second derivatives. The package also provides various post-fit functions including goodness-of-fit analyses, classification, plots, predicted trajectories, individual dynamic prediction of the event and predictive accuracy assessment. This paper constitutes a companion paper to the package by introducing each family of models, the estimation technique, some implementation details and giving examples through a dataset on cognitive aging.
{"title":"Estimation of extended mixed models using latent classes and latent processes: the R package lcmm","authors":"C. Proust-Lima, V. Philipps, B. Liquet","doi":"10.18637/jss.v078.i02","DOIUrl":"https://doi.org/10.18637/jss.v078.i02","url":null,"abstract":"The R package lcmm provides a series of functions to estimate statistical models based on linear mixed model theory. It includes the estimation of mixed models and latent class mixed models for Gaussian longitudinal outcomes (hlme), curvilinear and ordinal univariate longitudinal outcomes (lcmm) and curvilinear multivariate outcomes (multlcmm), as well as joint latent class mixed models (Jointlcmm) for a (Gaussian or curvilinear) longitudinal outcome and a time-to-event that can be possibly left-truncated right-censored and defined in a competing setting. Maximum likelihood esimators are obtained using a modified Marquardt algorithm with strict convergence criteria based on the parameters and likelihood stability, and on the negativity of the second derivatives. The package also provides various post-fit functions including goodness-of-fit analyses, classification, plots, predicted trajectories, individual dynamic prediction of the event and predictive accuracy assessment. This paper constitutes a companion paper to the package by introducing each family of models, the estimation technique, some implementation details and giving examples through a dataset on cognitive aging.","PeriodicalId":8446,"journal":{"name":"arXiv: Computation","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78344576","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 : 2015-02-17DOI: 10.1016/J.IFACOL.2015.12.255
J. Olsson, Johan Westerborn
{"title":"An efficient particle-based online EM algorithm for general state-space models","authors":"J. Olsson, Johan Westerborn","doi":"10.1016/J.IFACOL.2015.12.255","DOIUrl":"https://doi.org/10.1016/J.IFACOL.2015.12.255","url":null,"abstract":"","PeriodicalId":8446,"journal":{"name":"arXiv: Computation","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83803631","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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