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A fast Bayesian method that seamlessly fuses classification and hypothesis testing via discriminant analysis is developed. Building upon the original discriminant analysis classifier, modelling components are added to identify discriminative variables. A combination of cake priors and a novel form of variational Bayes we call reverse collapsed variational Bayes gives rise to variable selection that can be directly posed as a multiple hypothesis testing approach using likelihood ratio statistics. Some theoretical arguments are presented showing that Chernoff-consistency (asymptotically zero type I and type II error) is maintained across all hypotheses. We apply our method on some publicly available genomics datasets and show that our method performs well in practice for its computational cost. An R package VaDA has also been made available on Github.

Cell reprogramming offers a potential treatment to many diseases, by regenerating specialized somatic cells. Despite decades of research, discovering the transcription factors that promote cell reprogramming has largely been accomplished through trial and error, a time-consuming and costly method. A computational model for cell reprogramming, however, could guide the hypothesis formulation and experimental validation, to efficiently utilize time and resources. Current methods often cannot account for the heterogeneity observed in cell reprogramming, or they only make short-term predictions, without modelling the entire reprogramming process. Here, we present scREMOTE, a novel computational model for cell reprogramming that leverages single cell multiomics data, enabling a more holistic view of the regulatory mechanisms at cellular resolution. This is achieved by first identifying the regulatory potential of each transcription factor and gene to uncover regulatory relationships, then a regression model is built to estimate the effect of transcription factor perturbations. We show that scREMOTE successfully predicts the long-term effect of overexpressing two key transcription factors in hair follicle development by capturing higher-order gene regulations. Together, this demonstrates that integrating the multimodal processes governing gene regulation creates a more accurate model for cell reprogramming with significant potential to accelerate research in regenerative medicine.

Aim To analyse the effects of maternal diabetes mellitus (DM) and body mass Index (BMI) on central and peripheral fat accretion of large for gestational age (LGA) offspring. Methods This retrospective study included LGA fetuses (n = 595) with ultrasound scans at early (19.23 ± 0.68 weeks), mid (28.98 ± 1.62 weeks) and late (36.20 ± 1.59 weeks) stages of adipogenesis and measured abdominal (AFT) and mid-thigh (TFT) fat as surrogates for central and peripheral adiposity. Women were categorised according to BMI and DM status [pre-gestational (P-DM; n = 59), insulin managed (I-GDM; n = 132) and diet managed gestational diabetes (D-GDM; n = 29)]. Analysis of variance and linear regressions were applied. Results AFT and TFT did not differ significantly between BMI categories (normal, overweight and obese). In contrast, AFT was significantly higher in pregnancies affected by D-GDM compared to non-DM pregnancies from mid stage (0.44 mm difference, p = 0.002) and for all DM categories in late stage of adipogenesis (≥ 0.49 mm difference, p < 0.008). Late stage TFT accretion was higher than controls for P-DM and I-GDM but not for D-GDM (0.67 mm difference, p < 0.001; 0.49 mm difference, p = 0.001, 0.56 mm difference, p = 0.22 respectively). In comparison to the early non-DM group with an AFT to TFT ratio of 1.07, the I-GDM group ratio was 1.25 (p < 0.001), which normalised by 28 weeks becoming similar to control ratios. Conclusions DM, independent of BMI, was associated with higher abdominal and mid-thigh fat accretion in fetuses. Use of insulin improved central to peripheral fat ratios in fetuses of GDM mothers.

We introduce a new method of performing high-dimensional discriminant analysis (DA), which we call multiDA. Starting from multiclass diagonal DA classifiers which avoid the problem of high-dimensio...

© 2018 IEEE. Class labels are required for supervised learning but may be corrupted or missing in various applications. In binary classification, for example, when only a subset of positive instances is labeled whereas the remaining are unlabeled, positive-unlabeled (PU) learning is required to model from both positive and unlabeled data. Similarly, when class labels are corrupted by mislabeled instances, methods are needed for learning in the presence of class label noise (LN). Here we propose adaptive sampling (AdaSampling), a framework for both PU learning and learning with class LN. By iteratively estimating the class mislabeling probability with an adaptive sampling procedure, the proposed method progressively reduces the risk of selecting mislabeled instances for model training and subsequently constructs highly generalizable models even when a large proportion of mislabeled instances is present in the data. We demonstrate the utilities of proposed methods using simulation and benchmark data, and compare them to alternative approaches that are commonly used for PU learning and/or learning with LN. We then introduce two novel bioinformatics applications where AdaSampling is used to: 1) identify kinase-substrates from mass spectrometry-based phosphoproteomics data and 2) predict transcription factor target genes by integrating various next-generation sequencing data.

MotivationHigh parameter histological techniques have allowed for the identification of a variety of distinct cell types within an image, providing a comprehensive overview of the tissue environment. This allows the complex cellular architecture and environment of diseased tissue to be explored. While spatial analysis techniques have revealed how cell-cell interactions are important within the disease pathology, there remains a gap in exploring changes in these interactions within the disease process. Specifically, there are currently no established methods for performing inference on cell localisation changes across images, hindering an understanding of how cellular environments change with a disease pathology.ResultsWe have developed the spicyR R package to perform inference on changes in the spatial localisation of cell types across groups of images. Application to simulated data demonstrates a high sensitivity and specificity. We demonstrate the utility of spicyR by applying it to a type 1 diabetes imaging mass cytometry dataset, revealing changes in cellular associations that were relevant to the disease progression. Ultimately, spicyR allows changes in cellular environments to be explored under different pathologies or disease states.Availability and ImplementationR package freely available at http://bioconductor.org/packages/release/bioc/html/spicyR.html and shiny app implementation at http://shiny.maths.usyd.edu.au/spicyR/Contactellis.patrick@sydney.edu.auSupplementary informationCode for reproducing key figures available at https://github.com/nickcee/spicyRPaper.

In this chapter we consider fitting several different nonstandard flexible regression models using variational Bayes (VB). More specifically we focus on fitting generalised additive models with penalised splines for complicating factors including outliers, heteroscedastic noise, overdispersed count data and missing covariates. For these models the complications arising mean that standard software is not readily available to fit them. We start from the point of standard VB methodology and show some simple tricks can be brought to bear when such methods are not easily applied. Our VB implementation in R is often orders of magnitude faster than state-of-the-art Markov Chain Monte Carlo (MCMC) implementation via stan , often with minor loss of accuracy in the estimation of posterior quantities.

Background Differences in cell-type composition across subjects and conditions often carry biological significance. Recent advancements in single cell sequencing technologies enable cell-types to be identified at the single cell level, and as a result, cell-type composition of tissues can now be studied in exquisite detail. However, a number of challenges remain with cell-type composition analysis – none of the existing methods can identify cell-type perfectly and variability related to cell sampling exists in any single cell experiment. This necessitates the development of method for estimating uncertainty in cell-type composition. Results We developed a novel single cell differential composition (scDC) analysis method that performs differential cell-type composition analysis via bootstrap resampling. scDC captures the uncertainty associated with cell-type proportions of each subject via bias-corrected and accelerated bootstrap confidence intervals. We assessed the performance of our method using a number of simulated datasets and synthetic datasets curated from publicly available single cell datasets. In simulated datasets, scDC correctly recovered the true cell-type proportions. In synthetic datasets, the cell-type compositions returned by scDC were highly concordant with reference cell-type compositions from the original data. Since the majority of datasets tested in this study have only 2 to 5 subjects per condition, the addition of confidence intervals enabled better comparisons of compositional differences between subjects and across conditions. Conclusions scDC is a novel statistical method for performing differential cell-type composition analysis for scRNA-seq data. It uses bootstrap resampling to estimate the standard errors associated with cell-type proportion estimates and performs significance testing through GLM and GLMM models. We have made this method available to the scientific community as part of the scdney package (Single Cell Data Integrative Analysis) R package, available from https://github.com/SydneyBioX/scdney.

Expectation propagation is a general prescription for approximation of integrals in statistical inference problems. Its literature is mainly concerned with Bayesian inference scenarios. However, expectation propagation can also be used to approximate integrals arising in frequentist statistical inference. We focus on likelihood-based inference for binary response mixed models and show that fast and accurate quadrature-free inference can be realized for the probit link case with multivariate random effects and higher levels of nesting. The approach is supported by asymptotic theory in which expectation propagation is seen to provide consistent estimation of the exact likelihood surface. Numerical studies reveal the availability of fast, highly accurate and scalable methodology for binary mixed model analysis., Comment: 35 pages, 5 figures

Concerted examination of multiple collections of single-cell RNA sequencing (RNA-seq) data promises further biological insights that cannot be uncovered with individual datasets. Here we present scMerge, an algorithm that integrates multiple single-cell RNA-seq datasets using factor analysis of stably expressed genes and pseudoreplicates across datasets. Using a large collection of public datasets, we benchmark scMerge against published methods and demonstrate that it consistently provides improved cell type separation by removing unwanted factors; scMerge can also enhance biological discovery through robust data integration, which we show through the inference of development trajectory in a liver dataset collection.

// Ellis Patrick 1, 6, 7, 8, 10 , Sarah-Jane Schramm 2, 3 , John T. Ormerod 1, 9 , Richard A. Scolyer 4, 5 , Graham J. Mann 2, 3 , Samuel Mueller 1, * , Jean Y.H. Yang 1, 3, * 1 School of Mathematics and Statistics, The University of Sydney, Sydney, Australia 2 The Westmead Millennium Institute for Medical Research, The University of Sydney, Sydney, Australia 3 Melanoma Institute Australia, The University of Sydney, Sydney, Australia 4 Tissue Pathology and Diagnostic Oncology, Royal Prince Alfred Hospital, Sydney, Australia 5 Discipline Pathology, Sydney Medical School, The University of Sydney, Sydney, Australia 6 Program in Translational NeuroPsychiatric Genomics, Institute for the Neurosciences, Department of Neurology, Brigham and Women’s Hospital, Boston, MA, USA 7 Harvard Medical School, Boston, MA, USA 8 Program in Medical and Population Genetics, Broad Institute, Cambridge, MA, USA 9 ARC Centre of Excellence for Mathematical & Statistical Frontiers 10 Program in Translational NeuroPsychiatric Genomics, Institute for the Neurosciences, Department of Psychiatry, Brigham and Women’s Hospital, Boston, MA, USA * These authors have contributed equally to this work Correspondence to: Jean Y.H. Yang, email: jean.yang@sydney.edu.au Keywords: biomarker, classification, cancer, pathology, prognosis Received: March 12, 2016 Accepted: September 26, 2016 Published: November 08, 2016 ABSTRACT Cancer research continues to highlight the extensive genetic diversity that exists both between and within tumors. This intrinsic heterogeneity poses one of the central challenges to predicting patient clinical outcome and the personalization of treatments. Despite progress in some individual tumor types, it is not yet possible to prospectively, accurately classify patients by expected survival. One hypothesis proposed to explain this is that the prognostic classifiers developed to date are insufficiently sensitive and specific; however it is also possible that patients are not equally easy to classify by any given biomarker. We demonstrate in a cohort of 45 AJCC stage III melanoma patients that clinico-pathologic biomarkers can identify those patients that are most likely to be misclassified by a molecular biomarker. The process of modelling the classifiability of patients was then replicated in a cohort of 49 stage II breast cancer patients and 53 stage III colon cancer patients. A multi-step procedure incorporating this information not only improved classification accuracy but also indicated the specific clinical attributes that had made classification problematic in each cohort. These findings show that, even when cohorts are of moderate size, including features that explain the patient-specific performance of a prognostic biomarker in a classification framework can improve the modelling and estimation of survival.

Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A novel Bayesian nonparametric discriminant analysis model that performs both variable selection and classification within a seamless framework is proposed. Polya tree priors are assigned to the unknown group-conditional distributions to account for their uncertainty, and allow prior beliefs about the distributions to be incorporated simply as hyperparameters. The adoption of collapsed variational Bayes inference in combination with a chain of functional approximations led to an algorithm with low computational cost. The resultant decision rules carry heuristic interpretations and are related to an existing two-sample Bayesian nonparametric hypothesis test. By an application to some simulated and publicly available real datasets, the proposed method exhibits good performance when compared to current state-of-the-art approaches.

© 2018, American Statistical Association. All rights reserved. We provide several examples of Bayesian semiparametric regression analysis via the Infer.NET package for approximate deterministic inference in Bayesian models. The examples are chosen to encompass a wide range of semiparametric regression situations. Infer.NET is shown to produce accurate inference in comparison with Markov chain Monte Carlo via the BUGS package, but to be considerably faster. Potentially, this contribution represents the start of a new era for semiparametric regression, where large and complex analyses are performed via fast Bayesian inference methodology and software, mainly being developed within Machine Learning.

Concerted examination of multiple collections of single cell RNA-Seq (scRNA-Seq) data promises further biological insights that cannot be uncovered with individual datasets. However, such integrative analyses are challenging and require sophisticated methodologies. To enable effective interrogation of multiple scRNA-Seq datasets, we have developed a novel algorithm, named scMerge, that removes unwanted variation by combining stably expressed genes and utilizing pseudo-replicates across datasets. Analysis of large collections of publicly available datasets demonstrates that scMerge performs well in multiple scenarios and enhances biological discovery, including inferring cell developmental trajectories.

Motivation Genes act as a system and not in isolation. Thus, it is important to consider coordinated changes of gene expression rather than single genes when investigating biological phenomena such as the aetiology of cancer. We have developed an approach for quantifying how changes in the association between pairs of genes may inform the outcome of interest called Differential Correlation across Ranked Samples (DCARS). Modelling gene correlation across a continuous sample ranking does not require the dichotomisation of samples into two distinct classes and can identify differences in gene correlation across early, mid or late stages of the outcome of interest. Results When we evaluated DCARS against the typical Fisher Z-transformation test for differential correlation, as well as a typical approach testing for interaction within a linear model, on real TCGA data, DCARS significantly ranked gene pairs containing known cancer genes more highly across several cancers. Similar results are found with our simulation study. DCARS was applied to 13 cancers datasets in TCGA, revealing several distinct relationships for which survival ranking was found to be associated with a change in correlation between genes. Furthermore, we demonstrated that DCARS can be used in conjunction with network analysis techniques to extract biological meaning from multi-layered and complex data. Availability and implementation DCARS R package and sample data are available at https://github.com/shazanfar/DCARS. Publicly available data from The Cancer Genome Atlas (TCGA) was used using the TCGABiolinks R package. Supplementary Files and DCARS R package is available at https://github.com/shazanfar/DCARS. Supplementary information Supplementary data are available at Bioinformatics online.

Biological networks, like most engineered networks, are not the product of a singular design but rather are the result of a long process of refinement and optimization. Many large real-world networks are comprised of well-defined and meaningful smaller modules. While engineered networks are designed and refined by humans with particular goals in mind, biological networks are created by the selective pressures of evolution. In this paper, we seek to define aspects of network architecture that are shared among different types of evolved biological networks. First, we developed a new mathematical model, the Stochastic Block Model with Path Selection (SBM-PS) that simulates biological network formation based on the selection of edges that increase clustering. SBM-PS can produce modular networks whose properties resemble those of real networks. Second, we analyzed three real networks of very different types, and showed that all three can be fit well by the SBM-PS model. Third, we showed that modular elements within the three networks correspond to meaningful biological structures. The networks chosen for analysis were a proteomic network composed of all proteins required for mitochondrial function in budding yeast, a mesoscale anatomical network composed of axonal connections among regions of the mouse brain, and the connectome of individual neurons in the nematode C. elegans. We find that the three networks have common architectural features, and each can be divided into subnetworks with characteristic topologies that control specific phenotypic outputs.

We develop methodology and theory for a mean field variational Bayes approximation to a linear model with a spike and slab prior on the regression coefficients. In particular we show how our method forces a subset of regression coefficients to be numerically indistinguishable from zero; under mild regularity conditions estimators based on our method consistently estimate the model parameters with easily obtainable and (asymptotically) appropriately sized standard error estimates; and select the true model at an exponential rate in the sample size. We also develop a practical method for simultaneously choosing reasonable initial parameter values and tuning the main tuning parameter of our algorithms which is both computationally efficient and empirically performs as well or better than some popular variable selection approaches. Our method is also faster and highly accurate when compared to MCMC.

Generalized linear latent variable models (GLLVMs) are a powerful class of models for understanding the relationships among multiple, correlated responses. Estimation, however, presents a major challenge, as the marginal likelihood does not possess a closed form for nonnormal responses. We propose a variational approximation (VA) method for estimating GLLVMs. For the common cases of binary, ordinal, and overdispersed count data, we derive fully closed-form approximations to the marginal log-likelihood function in each case. Compared to other methods such as the expectation-maximization algorithm, estimation using VA is fast and straightforward to implement. Predictions of the latent variables and associated uncertainty estimates are also obtained as part of the estimation process. Simulations show that VA estimation performs similar to or better than some currently available methods, both at predicting the latent variables and estimating their corresponding coefficients. They also show that VA estimation offers dramatic reductions in computation time particularly if the number of correlated responses is large relative to the number of observational units. We apply the variational approach to two datasets, estimating GLLVMs to understanding the patterns of variation in youth gratitude and for constructing ordination plots in bird abundance data. R code for performing VA estimation of GLLVMs is available online. Supplementary materials for this article are available online. peerReviewed

The concept of degrees of freedom plays an important role in statistical modeling and is commonly used for measuring model complexity. The number of unknown parameters, which is typically used as the degrees of freedom in linear regression models, may fail to work in some modeling procedures, in particular for linear mixed effects models. In this article, we propose a new definition of generalized degrees of freedom in linear mixed effects models. It is derived from using the sum of the sensitivity of the expected fitted values with respect to their underlying true means. We explore and compare data perturbation and the residual bootstrap to empirically estimate model complexity. We also show that this empirical generalized degrees of freedom measure satisfies some desirable properties and is useful for the selection of linear mixed effects models.

Summary Variational Bayes (VB) estimation is a fast alternative to Markov Chain Monte Carlo for performing approximate Baesian inference. This procedure can be an efficient and effective means of analyzing large datasets. However, VB estimation is often criticised, typically on empirical grounds, for being unable to produce valid statistical inferences. In this article we refute this criticism for one of the simplest models where Bayesian inference is not analytically tractable, that is, the Bayesian linear model (for a particular choice of priors). We prove that under mild regularity conditions, VB based estimators enjoy some desirable frequentist properties such as consistency and can be used to obtain asymptotically valid standard errors. In addition to these results we introduce two VB information criteria: the variational Akaike information criterion and the variational Bayesian information criterion. We show that variational Akaike information criterion is asymptotically equivalent to the frequentist Akaike information criterion and that the variational Bayesian information criterion is first order equivalent to the Bayesian information criterion in linear regression. These results motivate the potential use of the variational information criteria for more complex models. We support our theoretical results with numerical examples.

Although a large collection of classification software packages exist in R, a new generic framework for linking custom classification functions with classification performance measures is needed. A generic classification framework has been designed and implemented as an R package in an object oriented style. Its design places emphasis on parallel processing, reproducibility and extensibility. Finally, a comprehensive set of performance measures are available to ease post-processing. Taken together, these important characteristics enable rapid and reproducible benchmarking of alternative classifiers. Availability and implementation: ClassifyR is implemented in R and can be obtained from the Bioconductor project: http://bioconductor.org/packages/release/bioc/html/ClassifyR.html Contact : dario.strbenac@sydney.edu.au Supplementary information : Supplementary data are available at Bioinformatics online.

A consistent difference in average expression level, often referred to as differential expression (DE), has long been used to identify genes useful for classification. However, recent cancer studies have shown that when transcription factors or epigenetic signals become deregulated, a change in expression variability (DV) of target genes is frequently observed. This suggests that assessing the importance of genes by either differential expression or variability alone potentially misses sets of important biomarkers that could lead to improved predictions and treatments. Here, we describe a new approach for assessing the importance of genes based on differential distribution (DD), which combines information from differential expression and differential variability into a unified metric. We show that feature ranking and selection stability based on DD can perform two to three times better than DE or DV alone, and that DD yields equivalent error rates to DE and DV. Finally, assessing genes via differential distribution produces a complementary set of selected genes to DE and DV, potentially opening up new categories of biomarkers.

Complex biological systems are often represented by network graphs; however, their structural features are not adequately captured by existing computational graph models, perhaps because the datasets used to assemble them are incomplete and contain elements that lack shared functions. Here, we analyze three large, near-complete networks that produce specific cellular or behavioral outputs: a molecular yeast mitochondrial regulatory protein network, and two anatomical networks of very different scale, the mouse brain mesoscale connectivity network, and the C. elegans neuronal network. Surprisingly, these networks share similar characteristics. All consist of large communities composed of modules with general functions, and topologically distinct subnetworks spanning modular boundaries responsible for their more specific phenotypical outputs. We created a new model, SBM-PS, which generates networks by combining communities, followed by adjustment of connections by a ‘path selection’ mechanism. This model captures fundamental architectural features that are common to the three networks.

© 2014, Springer Science+Business Media New York. A new data science tool named wavelet-based gradient boosting is proposed and tested. The approach is special case of componentwise linear least squares gradient boosting, and involves wavelet functions of the original predictors. Wavelet-based gradient boosting takes advantages of the approximate $$\ell _1$$ℓ1 penalization induced by gradient boosting to give appropriate penalized additive fits. The method is readily implemented in R and produces parsimonious and interpretable regression fits and classifiers.

The aged number theoretic concept of continued fractions can enhance certain Bayesian computations. The crux of this claim is due to continued fraction representations of numerically challenging special function ratios that arise in Bayesian computing. Continued fraction approximation via Lentz's Algorithm often leads to efficient and stable computation of such quantities. Copyright © 2012 John Wiley & Sons, Ltd.

Bayesian hierarchical models are attractive structures for conducting regression analyses when the data are subject to missingness. However, the requisite probability calculus is challenging andMonte Carlo methods typically are employed.We develop an alternative approach based on deterministic variational Bayes approximations. Both parametric and nonparametric regression are considered. Attention is restricted to the more challenging case of missing predictor data.We demonstrate that variational Bayes can achieve good accuracy, but with considerably less computational overhead. The main ramification is fast approximate Bayesian inference in parametric and nonparametric regression models with missing data. Supplemental materials accompany the online version of this article. © 2011 American Statistical Association.

Variational methods for approximate Bayesian inference provide fast, flexible, deterministic alternatives to Monte Carlo methods. Unfortunately, unlike Monte Carlo methods, variational approximations cannot, in general, be made to be arbitrarily accurate. This paper develops grid-based variational approximations which endeavor to approximate marginal posterior densities in a spirit similar to the Integrated Nested Laplace Approximation (INLA) of Rue et al. (2009) but which may be applied in situations where INLA cannot be used. The method can greatly increase the accuracy of a base variational approximation, although not in general to arbitrary accuracy. The methodology developed is at least reasonably accurate on all of the examples considered in the paper.

We devise a classification algorithm based on generalized linear mixed model (GLMM) technology. The algorithm incorporates spline smoothing, additive model-type structures and model selection. For reasons of speed we employ the Laplace approximation, rather than Monte Carlo methods. Tests on real and simulated data show the algorithm to have good classification performance. Moreover, the resulting classifiers are generally interpretable and parsimonious. © 2010 Springer Science+Business Media, LLC.

In this paper, we present knowledge-based support vector machine (SVM) classifiers using semidefinite linear programming. SVMs are an optimization-based solution method for large-scale data classification problems. Knowledge-based SVM classifiers, where prior knowledge is in the form of ellipsoidal constraints, result in a semidefinite linear programme with a set containment constraint. These problems are reformulated as standard semidefinite linear programming problems by the application of a dual characterization of the set containment under a mild regularity condition. The reformulated semidefinite linear programme is solved by the publicly available solvers. Computational results show that prior knowledge can often improve correctness of the classifier.

© 2014, Institute of Mathematical Statistics. All rights received. We investigate mean field variational approximate Bayesian inference for models that use continuous distributions, Horseshoe, Negative-Exponential-Gamma and Generalized Double Pareto, for sparse signal shrinkage. Our principal finding is that the most natural, and simplest, mean field variational Bayes algorithm can perform quite poorly due to posterior dependence among auxiliary variables. More sophisticated algorithms, based on special functions, are shown to be superior. Continued fraction approximations via Lentz's Algorithm are developed to make the algorithms practical.

A mean field variational Bayes approach to support vector machines (SVMs) using the latent variable representation on Polson & Scott (2012) is presented. This representation allows circumvention of many of the shortcomings associated with classical SVMs including automatic penalty parameter selection, the ability to handle dependent samples, missing data and variable selection. We demonstrate on simulated and real datasets that our approach is easily extendable to non-standard situations and outperforms the classical SVM approach whilst remaining computationally efficient., 18 pages, 4 figures

Detection-nondetection data are often used to investigate species range dynamics using Bayesian occupancy models which rely on the use of Markov chain Monte Carlo (MCMC) methods to sample from the posterior distribution of the parameters of the model. In this article we develop two Variational Bayes (VB) approximations to the posterior distribution of the parameters of a single-season site occupancy model which uses logistic link functions to model the probability of species occurrence at sites and of species detection probabilities. This task is accomplished through the development of iterative algorithms that do not use MCMC methods. Simulations and small practical examples demonstrate the effectiveness of the proposed technique. We specifically show that (under certain circumstances) the variational distributions can provide accurate approximations to the true posterior distributions of the parameters of the model when the number of visits per site ( K ) are as low as three and that the accuracy of the approximations improves as K increases. We also show that the methodology can be used to obtain the posterior distribution of the predictive distribution of the proportion of sites occupied (PAO).

Variational approximation methods have become a mainstay of contemporary machine learning methodology, but currently have little presence in statistics. We devise an effective variational approximation strategy for fitting generalized linear mixed models (GLMMs) appropriate for grouped data. It involves Gaussian approximation to the distributions of random effects vectors, conditional on the responses. We show that Gaussian variational approximation is a relatively simple and natural alternative to Laplace approximation for fast, non-Monte Carlo, GLMM analysis. Numerical studies show Gaussian variational approximation to be very accurate in grouped data GLMM contexts. Finally, we point to some recent theory on consistency of Gaussian variational approximation in this context. Supplemental materials are available online. © 2012 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

Low detection limits are common in measure environmental variables. Building models using data containing low or high detection limits without adjusting for the censoring produces biased models. This paper offers approaches to estimate an inverse Gaussian distribution when some of the data used are censored because of low or high detection limits. Adjustments for the censoring can be made if there is between 2% and 20% censoring using either the EM algorithm or MCMC. This paper compares these approaches.

We introduce the concept of penalized wavelets to facilitate seamless embedding of wavelets into semiparametric regression models. In particular, we show that penalized wavelets are analogous to penalized splines; the latter being the established approach to function estimation in semiparametric regression. They differ only in the type of penalization that is appropriate. This fact is not borne out by the existing wavelet liter- ature, where the regression modelling and fitting issues are overshadowed by computational issues such as efficiency gains afforded by the Discrete Wavelet Transform and partially obscured by a tendency to work in the wavelet coefficient space. With penalized wavelet structurein place, we then show that fitting and inference can be achieved via the same general approaches used for penalized splines: penalized least squares, maximum likelihood and best prediction within a frequentist mixed model framework, and Markov chain Monte Carlo and mean field variational Bayes within a Bayesian framework. Penalized wavelets are also shown have a close rela- tionship with wide data ("p ≫ n") regression and benefit from ongoing research on that topic.

We develop strategies for mean field variational Bayes approximate inference for Bayesian hierarchical models containing elaborate distributions. We loosely define elaborate distributions to be those having more complicated forms compared with common distributions such as those in the Normal and Gamma families. Examples are Asymmetric Laplace, Skew Normal and Generalized Extreme Value distributions. Such models suffer from the difficulty that the parameter updates do not admit closed form solutions. We circumvent this problem through a combination of (a) specially tailored auxiliary variables, (b) univariate quadrature schemes and (c) finite mixture approximations of troublesome density functions. An accuracy assessment is conducted and the new methodology is illustrated in an application. © 2011 International Society for Bayesian Analysis.

Variational approximations facilitate approximate inference for the parameters in complex statistical models and provide fast, deterministic alternatives to Monte Carlo methods. However, much of the contemporary literature on variational approximations is in Computer Science rather than Statistics, and uses terminology, notation, and examples from the former field. In this article we explain variational approximation in statistical terms. In particular, we illustrate the ideas of variational approximation using examples that are familiar to statisticians. © 2010 American Statistical Association.

We study computational issues for support vector classification with penalised spline kernels. We show that, compared with traditional kernels, computational times can be drastically reduced in large problems making such problems feasible for sample sizes as large as ~106. The optimisation technology known as interior point methods plays a central role. Penalised spline kernels are also shown to allow simple incorporation of low-dimensional structure such as additivity. This can aid both interpretability and performance. © 2008 Springer-Verlag.

An exposition on the use of O'Sullivan penalized splines in contemporary semiparametric regression, including mixed model and Bayesian formulations, is presented. O'Sullivan penalized splines are similar to P-splines, but have the advantage of being a direct generalization of smoothing splines. Exact expressions for the O'Sullivan penalty matrix are obtained. Comparisons between the two types of splines reveal that O'Sullivan penalized splines more closely mimic the natural boundary behaviour of smoothing splines. Implementation in modern computing environments such as Matlab, r and bugs is discussed. © 2008 Australian Statistical Publishing Association Inc.

Background Large scale single cell transcriptome profiling has exploded in recent years and has enabled unprecedented insight into the behavior of individual cells. Identifying genes with high levels of expression using data from single cell RNA sequencing can be useful to characterize very active genes and cells in which this occurs. In particular single cell RNA-Seq allows for cell-specific characterization of high gene expression, as well as gene coexpression. Results We offer a versatile modeling framework to identify transcriptional states as well as structures of coactivation for different neuronal cell types across multiple datasets. We employed a gamma-normal mixture model to identify active gene expression across cells, and used these to characterize markers for olfactory sensory neuron cell maturity, and to build cell-specific coactivation networks. We found that combined analysis of multiple datasets results in more known maturity markers being identified, as well as pointing towards some novel genes that may be involved in neuronal maturation. We also observed that the cell-specific coactivation networks of mature neurons tended to have a higher centralization network measure than immature neurons. Conclusion Integration of multiple datasets promises to bring about more statistical power to identify genes and patterns of interest. We found that transforming the data into active and inactive gene states allowed for more direct comparison of datasets, leading to identification of maturity marker genes and cell-specific network observations, taking into account the unique characteristics of single cell transcriptomics data. Electronic supplementary material The online version of this article (doi:10.1186/s12918-016-0370-4) contains supplementary material, which is available to authorized users.