Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

/pdf/fitting-linear-mixed-effects-models-using-lme4-4zzrpoy9lh.pdf

Fitting Linear Mixed-Effects Models Using lme4

https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1977.tb01600.x

Maximum likelihood from incomplete data via the EM algorithm

Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Deep Learning

Meta-Analysis in Clinical Trials*

We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model.

/pdf/latent-dirichlet-allocation-4gmscb06en.pdf

Latent dirichlet allocation

We propose a two-sample permutation test incorporating mixture models as a general tool for detecting and quantifying effects on task performance. We illustrate the proposed method with examples where the dependent measures under investigation are recorded for normal controls and relatives of patients with schizophrenia on a delayed response, spatial and object working memory task. Our mixture modelling in relatives allows the component distributions to arise from different continuous parametric families. We also investigate the effects of the within-family correlation and the prior distribution of the mixing proportion on the test results. The power of the test depends on sample sizes, the mixing proportion, the difference in component means and the ratio of component variances. Copyright © 2002 John Wiley & Sons, Ltd.

Permutation tests for detecting and estimating mixtures in task performance within groups.

Basics of Markov chain simulation

Estimating influence on social media networks is an important practical and theoretical problem, especially because this new medium is widely exploited as a platform for disinformation and propaganda. This paper introduces a novel approach to influence estimation on social media networks and applies it to the real-world problem of characterizing active influence operations on Twitter during the 2017 French presidential elections. The new influence estimation approach attributes impact by accounting for narrative propagation over the network using a network causal inference framework applied to data arising from graph sampling and filtering. This causal framework infers the difference in outcome as a function of exposure, in contrast to existing approaches that attribute impact to activity volume or topological features, which do not explicitly measure nor necessarily indicate actual network influence. Cramer-Rao estimation bounds are derived for parameter estimation as a step in the causal analysis, and used to achieve geometrical insight on the causal inference problem. The ability to infer high causal influence is demonstrated on real-world social media accounts that are later independently confirmed to be either directly affiliated or correlated with foreign influence operations using evidence supplied by the U.S. Congress and journalistic reports.

Influence Estimation on Social Media Networks Using Causal Inference

Inference using simulation has become a dominant theme in modern statistics, whether using the bootstrap to simulate sampling distributions of statis- tics, Markov chain Monte Carlo to simulate posterior distributions of parameters, or multiple imputation to simulate the posterior predictive distribution of missing values. Inference via simulations can, in some cases, be greatly facilitated by ac- companying methods of analysis based on more traditional mathematical statistical techniques. Here we illustrate this point using one example of such technology: the analysis, based on a Markov-normal model of the stationary distribution underly- ing an iterative simulation, of parallel simulations before their convergence, thereby allowing a redesign of the simulation for better performance. The potential value of this approach is documented using an example involving censored data.

/pdf/model-based-analysis-to-improve-the-performance-of-iterative-3es520hkr9.pdf

Model-based analysis to improve the performance of iterative simulations

A central problem in statistics, psychometrics and education, is how to draw inferences about the causal effects of treatments (i.e., interventions) from randomized and nonrandomized data. For example, does the new job-training program really improve the quality of jobs for those trained relative to the jobs they would get without training, or does exposure to that chemical in drinking water increase cancer rates relative to drinking water without that chemical, or, of particular relevance in this volume, does that educational intervention improve the test scores of students relative to the standard program? This presentation provides an overview of the approach to the estimation of such causal effects based on the concept of potential outcomes, including a relatively detailed presentation of the Bayesian approach.

Donald B. Rubin

Papers

Permutation tests for detecting and estimating mixtures in task performance within groups.

Basics of Markov chain simulation

Influence Estimation on Social Media Networks Using Causal Inference

Model-based analysis to improve the performance of iterative simulations

24 Statistical Inference for Causal Effects, with Emphasis on Applications in Psychometrics and Education