A generalisation of the ecm algorithm (Meng & Rubin, 1993), which is itself an extension em (Dempster, Laird 1977), can be obtained by replacing some CM-steps ECM, maximise constrained expected complete-data loglikelihood function, with steps that correspondingly actual likelihood function. This algorithm, we call ecme for Expectation/Conditional Maximisation Either, shares both and their stable monotone convergence basic simplicity implementation relative to competing faster converging...

Linear mixed-effects models are frequently used to analyze repeated measures data, because they model flexibly the within-subject correlation often present in this type of data. The most popular linear for a continuous response assumes normal distributions random effects and errors, making it sensitive outliers. Such outliers more problematic than fixed-effects models, may occur effects, or both, them harder be detected practice. Motivated by real dataset from an orthodontic study, we...

AbstractThe Wang–Landau (WL) algorithm is an adaptive Markov chain Monte Carlo used to calculate the spectral density for a physical system. A remarkable feature of WL that it not trapped by local energy minima, which very important systems with rugged landscapes. This has led many successful applications in statistical physics and biophysics; however, there does exist rigorous theory support its convergence, estimates produced can reach only limited accuracy. In this article we propose...

Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster–Shafer theory of belief functions, and Bayesian with default are attempts to achieve this goal but, date, none has given a completely satisfactory picture. This article presents new framework for based on inferential models (IMs), which not only provides data-dependent measures uncertainty about the unknown parameter, also does automatic long-run...

Abstract We present a method of analyzing series independent cross-sectional surveys in which some questions are not answered and respondents do answer the posed. The is also applicable to single survey different asked or sampling methods used strata clusters. Our involves multiply imputing missing items by adding existing imputation designed for hierarchical regression model that allows covariates at individual levels. Information from weights exploited including analysis variables on were...

A new method for multinomial inference is proposed by representing the cell probabilities as unordered segments on unit interval and following Dempster-Shafer (DS) theory. The resulting DS posterior then strengthened to improve symmetry learning properties with final model being characterized a Dirichlet distribution. In addition computational simplicity, has desirable invariance related category permutations, refinements, coarsenings. Furthermore, relative amongst certain cells depends only...

Abstract Big mechanically-active culture systems (BigMACS) are promising to stimulate, control, and pattern cell tissue behaviours with less soluble factor requirements. However, it remains challenging predict if how distributed mechanical forces impact single-cell tissue. In this study, we introduce a tissue-scale finite element analysis (FEA) framework able correlate sub-cellular quantitative histology centimetre-scale biomechanics. Our is relevant diverse BigMACS, including media...

Summary. Many chemical and environmental data sets are complicated by the existence of fully missing values or censored known to lie below detection thresholds. For example, week‐long samples airborne particulate matter were obtained at Alert, NWT, Canada, between 1980 1991, where some concentrations 24 constituents coarsened in sense being either limits. To facilitate scientific analysis, it is appealing create complete filling so that standard complete‐data methods can be applied. We...

Abstract The multivariate t distribution and other normal/independent distributions, such as the slash contaminated distribution, are used for robust regression with complete or incomplete data. Most previous work focused on method of maximum likelihood estimation linear using distributions. This article considers Bayesian models distributions fully observed predictor variables possible missing values from outcome variables. A monotone data augmentation algorithm posterior simulation...

The Dempster--Shafer (DS) theory is a powerful tool for probabilistic reasoning based on formal calculus combining evidence. DS has been widely used in computer science and engineering applications, but yet to reach the statistical mainstream, perhaps because belief functions do not satisfy long-run frequency properties. Recently, two of authors proposed an extension DS, called weak (WB) approach, that can incorporate desirable properties into framework by systematically enlarging focal...

The inferential models (IM) framework provides prior-free, frequency-calibrated, posterior probabilistic inference. key is the use of random sets to predict unobservable auxiliary variables connected observable data and unknown parameters. When nuisance parameters are present, a marginalization step can reduce dimension variable which, in turn, leads more efficient For regular problems, exact be achieved, we give conditions for marginal IM validity. We show that our approach inference...

Summary The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based can be challenging when the variable is of higher dimension than parameter. Here we show that features are often fully observed and, in such cases, a simultaneous reduction and information aggregation achieved conditioning. This proposed conditioning strategy leads to IM casts new light Fisher's notions sufficiency,...

In this study, an abbreviated introduction to hierarchical statistical models for quantifying and explaining variations in the utilization of medical care is presented. The illustrative example was derived from analysis interstate variation coronary angiography Medicare patients with a recent acute myocardial infarction. model distinguished within-from between-states variation: former modeled via separate logistic regression each state, age sex as independent variables, while latter...

AbstractThis article describes a fast, statistically principled method for monitoring streams of network counts, which have long-term trends, rough cyclical patterns, outliers, and missing data. The key step is to build reference (predictive) model the counts that captures their complex, salient features but has just few parameters can be kept up-to-date as flow by, without requiring access past This justifies using negative binomial distribution with capture trends patterns moment...

Multivariate ordinal data arise in many applications. This article proposes a new, efficient method for Bayesian inference multivariate probit models using Markov chain Monte Carlo techniques. The key idea is the novel use of parameter expansion to sample correlation matrices. A nice feature approach that performed straightforward Gibbs sampling. methods model selection are also discussed. Our motivated by study how women make decisions on taking medication reduce risk breast cancer....

The work of A. P. Dempster in 1960s extending Fisher's fiducial infer- ence for parametric inference using multivalued mapping, and that G. Shafer 1970s on the assessment combination evidence led to what is now known as Dempster-Shafer (DS) theory belief functions. However, application DS has been limited due, perhaps, its computational diffi- culty, non-uniqueness, lack frequency properties. In this paper, we return Dempster's original approach constructing functions ence, called basic...

A central focus of data science is the transformation empirical evidence into knowledge. As such, key insights and scientific attitudes deep thinkers like Fisher, Popper, Tukey are expected to inspire exciting new advances in machine learning artificial intelligence years come. Along these lines, present paper a novel {\em typicality principle} which states, roughly, that if observed sufficiently ``atypical'' certain sense relative posited theory, then theory unwarranted. This emphasis on...

From a model-building perspective, we propose paradigm shift for fitting over-parameterized models. Philosophically, the mindset is to fit models future observations rather than observed sample. Technically, given an imputation method generate observations, these by optimizing approximation of desired expected loss function based on its sample counterpart and adaptive duality function. The required also developed using same estimation technique with m-out-of-n bootstrap approach. We...