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Register a new userMultivariate-from-Univariate MCMC Sampler: R Package MfUSampler
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Added by
Alireza Mahani
Publication date
2014
fields
Mathematical Statistics
and research's language is
English
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The R package MfUSampler provides Monte Carlo Markov Chain machinery for generating samples from multivariate probability distributions using univariate sampling algorithms such as Slice Sampler and Adaptive Rejection Sampler. The sampler function performs a full cycle of univariate sampling steps, one coordinate at a time. In each step, the latest sample values obtained for other coordinates are used to form the conditional distributions. The concept is an extension of Gibbs sampling where each step involves, not an independent sample from the conditional distribution, but a Markov transition for which the conditional distribution is invariant. The software relies on proportionality of conditional distributions to the joint distribution to implement a thin wrapper for producing conditionals. Examples illustrate basic usage as well as methods for improving performance. By encapsulating the multivariate-from-univariate logic, MfUSampler provides a reliable library for rapid prototyping of custom Bayesian models while allowing for incremental performance optimizations such as utilization of conjugacy, conditional independence, and porting function evaluations to compiled languages.
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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.
In this article, we derive a novel non-reversible, continuous-time Markov chain Monte Carlo (MCMC) sampler, called Coordinate Sampler, based on a piecewise deterministic Markov process (PDMP), which can be seen as a variant of the Zigzag sampler. In addition to proving a theoretical validation for this new sampling algorithm, we show that the Markov chain it induces exhibits geometrical ergodicity convergence, for distributions whose tails decay at least as fast as an exponential distribution and at most as fast as a Gaussian distribution. Several numerical examples highlight that our coordinate sampler is more efficient than the Zigzag sampler, in terms of effective sample size.
We introduce hyppo, a unified library for performing multivariate hypothesis testing, including independence, two-sample, and k-sample testing. While many multivariate independence tests have R packages available, the interfaces are inconsistent and most are not available in Python. hyppo includes many state of the art multivariate testing procedures. The package is easy-to-use and is flexible enough to enable future extensions. The documentation and all releases are available at https://hyppo.neurodata.io.
Process data refer to data recorded in the log files of computer-based items. These data, represented as timestamped action sequences, keep track of respondents response processes of solving the items. Process data analysis aims at enhancing educational assessment accuracy and serving other assessment purposes by utilizing the rich information contained in response processes. The R package ProcData presented in this article is designed to provide tools for processing, describing, and analyzing process data. We define an S3 class proc for organizing process data and extend generic methods summary and print for class proc. Two feature extraction methods for process data are implemented in the package for compressing information in the irregular response processes into regular numeric vectors. ProcData also provides functions for fitting and making predictions from a neural-network-based sequence model. These functions call relevant functions in package keras for constructing and training neural networks. In addition, several response process generators and a real dataset of response processes of the climate control item in the 2012 Programme for International Student Assessment are included in the package.
R is a programming language and environment that is a central tool in the applied sciences for writing program. Its impact on the development of modern statistics is inevitable. Current research, especially for big data may not be done solely using R and will likely use different programming languages; hence, having a modern integrated development environment (IDE) is very important. Atom editor is modern IDE that is developed by GitHub, it is described as A hackable text editor for the 21st Century. This report is intended to present a package deployed entitled Rbox that allows Atom Editor to write and run codes professionally in R.
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