A conjugate prior for discrete hierarchical log-linear models

In Bayesian analysis of multi-way contingency tables, the selection of a prior distribution for either the log-linear parameters or the cell probabilities parameters is a major challenge. In this paper, we define a flexible family of conjugate priors for the wide class of discrete hierarchical log-linear models, which includes the class of graphical models. These priors are defined as the Diaconis--Ylvisaker conjugate priors on the log-linear parameters subject to "baseline constraints" under multinomial sampling. We also derive the induced prior on the cell probabilities and show that the induced prior is a generalization of the hyper Dirichlet prior. We show that this prior has several desirable properties and illustrate its usefulness by identifying the most probable decomposable, graphical and hierarchical log-linear models for a six-way contingency table.Comment: Published in at http://dx.doi.org/10.1214/08-AOS669 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

mstate: An R Package for the Analysis of Competing Risks and Multi-State Models

Multi-state models are a very useful tool to answer a wide range of questions in survival analysis that cannot, or only in a more complicated way, be answered by classical models. They are suitable for both biomedical and other applications in which time-to-event variables are analyzed. However, they are still not frequently applied. So far, an important reason for this has been the lack of available software. To overcome this problem, we have developed the mstate package in R for the analysis of multi-state models. The package covers all steps of the analysis of multi-state models, from model building and data preparation to estimation and graphical representation of the results. It can be applied to non- and semi-parametric (Cox) models. The package is also suitable for competing risks models, as they are a special category of multi-state models. This article offers guidelines for the actual use of the software by means of an elaborate multi-state analysis of data describing post-transplant events of patients with blood cancer. The data have been provided by the EBMT (the European Group for Blood and Marrow Transplantation). Special attention will be paid to the modeling of different covariate effects (the same for all transitions or transition-specific) and different baseline hazard assumptions (different for all transitions or equal for some).

netgwas: An R Package for Network-Based Genome-Wide Association Studies

Graphical models are powerful tools for modeling and making statistical inferences regarding complex associations among variables in multivariate data. In this paper we introduce the R package netgwas, which is designed based on undirected graphical models to accomplish three important and interrelated goals in genetics: constructing linkage map, reconstructing linkage disequilibrium (LD) networks from multi-loci genotype data, and detecting high-dimensional genotype-phenotype networks. The netgwas package deals with species with any chromosome copy number in a unified way, unlike other software. It implements recent improvements in both linkage map construction (Behrouzi and Wit, 2018), and reconstructing conditional independence network for non-Gaussian continuous data, discrete data, and mixed discrete-and-continuous data (Behrouzi and Wit, 2017). Such datasets routinely occur in genetics and genomics such as genotype data, and genotype-phenotype data. We demonstrate the value of our package functionality by applying it to various multivariate example datasets taken from the literature. We show, in particular, that our package allows a more realistic analysis of data, as it adjusts for the effect of all other variables while performing pairwise associations. This feature controls for spurious associations between variables that can arise from classical multiple testing approach. This paper includes a brief overview of the statistical methods which have been implemented in the package. The main body of the paper explains how to use the package. The package uses a parallelization strategy on multi-core processors to speed-up computations for large datasets. In addition, it contains several functions for simulation and visualization. The netgwas package is freely available at https://cran.r-project.org/web/packages/netgwasComment: 32 pages, 9 figures; due to the limitation "The abstract field cannot be longer than 1,920 characters", the abstract appearing here is slightly shorter than that in the PDF fil

A geometric characterisation of sensitivity analysis in monomial models

Sensitivity analysis in probabilistic discrete graphical models is usually conducted by varying one probability value at a time and observing how this affects output probabilities of interest. When one probability is varied then others are proportionally covaried to respect the sum-to-one condition of probability laws. The choice of proportional covariation is justified by a variety of optimality conditions, under which the original and the varied distributions are as close as possible under different measures of closeness. For variations of more than one parameter at a time proportional covariation is justified in some special cases only. In this work, for the large class of discrete statistical models entertaining a regular monomial parametrisation, we demonstrate the optimality of newly defined proportional multi-way schemes with respect to an optimality criterion based on the notion of I-divergence. We demonstrate that there are varying parameters choices for which proportional covariation is not optimal and identify the sub-family of model distributions where the distance between the original distribution and the one where probabilities are covaried proportionally is minimum. This is shown by adopting a new formal, geometric characterization of sensitivity analysis in monomial models, which include a wide array of probabilistic graphical models. We also demonstrate the optimality of proportional covariation for multi-way analyses in Naive Bayes classifiers

Glotaran: A Java-Based Graphical User Interface for the R Package TIMP

In this work the software application called Glotaran is introduced as a Java-based graphical user interface to the R package TIMP, a problem solving environment for fitting superposition models to multi-dimensional data. TIMP uses a command-line user interface for the interaction with data, the specification of models and viewing of analysis results. Instead, Glotaran provides a graphical user interface which features interactive and dynamic data inspection, easier -- assisted by the user interface -- model specification and interactive viewing of results. The interactivity component is especially helpful when working with large, multi-dimensional datasets as often result from time-resolved spectroscopy measurements, allowing the user to easily pre-select and manipulate data before analysis and to quickly zoom in to regions of interest in the analysis results. Glotaran has been developed on top of the NetBeans rich client platform and communicates with R through the Java-to-R interface Rserve. The background and the functionality of the application are described here. In addition, the design, development and implementation process of Glotaran is documented in a generic way