arXiv: Computation最新文献_第8页

Stochastic Newton Sampler: R Package sns 随机牛顿采样器:R包sns

arXiv: Computation Pub Date : 2015-02-06 DOI: 10.18637/JSS.V074.C02

A. S. Mahani, Asad Hasan, Marshall Jiang, M. Sharabiani

{"title":"Stochastic Newton Sampler: R Package sns","authors":"A. S. Mahani, Asad Hasan, Marshall Jiang, M. Sharabiani","doi":"10.18637/JSS.V074.C02","DOIUrl":"https://doi.org/10.18637/JSS.V074.C02","url":null,"abstract":"The R package sns implements Stochastic Newton Sampler (SNS), a Metropolis-Hastings Monte Carlo Markov Chain algorithm where the proposal density function is a multivariate Gaussian based on a local, second-order Taylor series expansion of log-density. The mean of the proposal function is the full Newton step in Newton-Raphson optimization algorithm. Taking advantage of the local, multivariate geometry captured in log-density Hessian allows SNS to be more efficient than univariate samplers, approaching independent sampling as the density function increasingly resembles a multivariate Gaussian. SNS requires the log-density Hessian to be negative-definite everywhere in order to construct a valid proposal function. This property holds, or can be easily checked, for many GLM-like models. When initial point is far from density peak, running SNS in non-stochastic mode by taking the Newton step, augmented with with line search, allows the MCMC chain to converge to high-density areas faster. For high-dimensional problems, partitioning of state space into lower-dimensional subsets, and applying SNS to the subsets within a Gibbs sampling framework can significantly improve the mixing of SNS chains. In addition to the above strategies for improving convergence and mixing, sns offers diagnostics and visualization capabilities, as well as a function for sample-based calculation of Bayesian predictive posterior distributions.","PeriodicalId":8446,"journal":{"name":"arXiv: Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90604500","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}

引用次数: 7

Polynomial-Chaos-based Kriging Polynomial-Chaos-based克里格

arXiv: Computation Pub Date : 2015-02-01 DOI: 10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2015012467

R. Schöbi, B. Sudret, J. Wiart

{"title":"Polynomial-Chaos-based Kriging","authors":"R. Schöbi, B. Sudret, J. Wiart","doi":"10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2015012467","DOIUrl":"https://doi.org/10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2015012467","url":null,"abstract":"Computer simulation has become the standard tool in many engineering fields for designing and optimizing systems, as well as for assessing their reliability. To cope with demanding analysis such as optimization and reliability, surrogate models (a.k.a meta-models) have been increasingly investigated in the last decade. Polynomial Chaos Expansions (PCE) and Kriging are two popular non-intrusive meta-modelling techniques. PCE surrogates the computational model with a series of orthonormal polynomials in the input variables where polynomials are chosen in coherency with the probability distributions of those input variables. On the other hand, Kriging assumes that the computer model behaves as a realization of a Gaussian random process whose parameters are estimated from the available computer runs, i.e. input vectors and response values. These two techniques have been developed more or less in parallel so far with little interaction between the researchers in the two fields. In this paper, PC-Kriging is derived as a new non-intrusive meta-modeling approach combining PCE and Kriging. A sparse set of orthonormal polynomials (PCE) approximates the global behavior of the computational model whereas Kriging manages the local variability of the model output. An adaptive algorithm similar to the least angle regression algorithm determines the optimal sparse set of polynomials. PC-Kriging is validated on various benchmark analytical functions which are easy to sample for reference results. From the numerical investigations it is concluded that PC-Kriging performs better than or at least as good as the two distinct meta-modeling techniques. A larger gain in accuracy is obtained when the experimental design has a limited size, which is an asset when dealing with demanding computational models.","PeriodicalId":8446,"journal":{"name":"arXiv: Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82706325","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}

引用次数: 230

Enhancing reproducibility and collaboration via management of R package cohorts 通过管理R包队列来增强可重复性和协作性

arXiv: Computation Pub Date : 2015-01-09 DOI: 10.18637/JSS.V082.I01

Gabriel Becker, C. Barr, R. Gentleman, Michael Lawrence

引用次数: 6

On Particle Methods for Parameter Estimation in State-Space Models 状态空间模型参数估计的粒子方法

arXiv: Computation Pub Date : 2014-12-30 DOI: 10.1214/14-STS511

N. Kantas, A. Doucet, Sumeetpal S. Singh, J. Maciejowski, N. Chopin

引用次数: 387

Multivariate-from-Univariate MCMC Sampler: R Package MfUSampler 由单变量多变量MCMC采样器:R封装MfUSampler

arXiv: Computation Pub Date : 2014-12-25 DOI: 10.18637/JSS.V078.C01

A. S. Mahani, M. Sharabiani