arXiv subjects

David Rossell

Publications and source records attributed to David Rossell.

23 records · Page 2Linked to original sources

arXiv2017

Tractable Bayesian variable selection: beyond normality

Bayesian variable selection often assumes normality, but the effects of model misspecification are not sufficiently understood. There are sound reasons behind this assumption, particularly for large $p$: ease of interpretation, analytical and computational convenience. More flexible frameworks exist, including semi- or non-parametric models, often at the cost of some tractability. We propose a simple extension of the Normal model that allows for skewness and thicker-than-normal tails but preserves tractability. It leads to easy interpretation and a log-concave likelihood that facilitates optimization and integration. We characterize asymptotically parameter estimation and Bayes factor rates, in particular studying the effects of model misspecification. Under suitable conditions misspecified Bayes factors are consistent and induce sparsity at the same asymptotic rates than under the correct model. However, the rates to detect signal are altered by an exponential factor, often resulting in a loss of sensitivity. These deficiencies can be ameliorated by inferring the error distribution from the data, a simple strategy that can improve inference substantially. Our work focuses on the likelihood and can thus be combined with any likelihood penalty or prior, but here we focus on non-local priors to induce extra sparsity and ameliorate finite-sample effects caused by misspecification. Our results highlight the practical importance of focusing on the likelihood rather than solely on the prior, when it comes to Bayesian variable selection. The methodology is available in R package `mombf'.

stat.ME↗

arXiv2017

Scalable Bayesian variable selection and model averaging under block orthogonal design

We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral that can be computed upfront, and other quantities of interest such as variable inclusion probabilities and model averaged regression estimates by carrying out an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this article are implemented in the R library mombf.

stat.CO↗

arXiv2015

Quantifying alternative splicing from paired-end RNA-sequencing data

RNA-sequencing has revolutionized biomedical research and, in particular, our ability to study gene alternative splicing. The problem has important implications for human health, as alternative splicing may be involved in malfunctions at the cellular level and multiple diseases. However, the high-dimensional nature of the data and the existence of experimental biases pose serious data analysis challenges. We find that the standard data summaries used to study alternative splicing are severely limited, as they ignore a substantial amount of valuable information. Current data analysis methods are based on such summaries and are hence suboptimal. Further, they have limited flexibility in accounting for technical biases. We propose novel data summaries and a Bayesian modeling framework that overcome these limitations and determine biases in a nonparametric, highly flexible manner. These summaries adapt naturally to the rapid improvements in sequencing technology. We provide efficient point estimates and uncertainty assessments. The approach allows to study alternative splicing patterns for individual samples and can also be the basis for downstream analyses. We found a severalfold improvement in estimation mean square error compared popular approaches in simulations, and substantially higher consistency between replicates in experimental data. Our findings indicate the need for adjusting the routine summarization and analysis of alternative splicing RNA-seq studies. We provide a software implementation in the R package casper.

stat.AP↗

arXiv2015

Non-Local Priors for High-Dimensional Estimation

Simultaneously achieving parsimony and good predictive power in high dimensions is a main challenge in statistics. Non-local priors (NLPs) possess appealing properties for high-dimensional model choice, but their use for estimation has not been studied in detail. We show that, for regular models, Bayesian model averaging (BMA) estimates based on NLPs shrink spurious parameters either at fast polynomial or quasi-exponential rates as the sample size $n$ increases (depending on the chosen prior density). Non-spurious parameter estimates only differ from the oracle MLE by a factor of $n^{-1}$. We extend some results to linear models with dimension $p$ growing with $n$. Coupled with our theoretical investigations, we outline the constructive representation of NLPs as mixtures of truncated distributions. From a practitioners' perspective, our work enables simple posterior sampling and extending NLPs beyond previous proposals. Our results show notable high-dimensional estimation for linear models with $p>>n$ at reduced computational cost. NLPs provided lower estimation error than benchmark and hyper-g priors, SCAD and LASSO in simulations, and in gene expression data achieved higher cross-validated $R^2$ with an order of magnitude less predictors. Remarkably, these results were obtained without the need to pre-screen predictors. Our findings contribute to the debate of whether different priors should be used for estimation and model selection, showing that selection priors may actually be desirable for high-dimensional estimation.

math.ST↗

arXiv2009

GaGa: A parsimonious and flexible model for differential expression analysis

Hierarchical models are a powerful tool for high-throughput data with a small to moderate number of replicates, as they allow sharing information across units of information, for example, genes. We propose two such models and show its increased sensitivity in microarray differential expression applications. We build on the gamma--gamma hierarchical model introduced by Kendziorski et al. [Statist. Med. 22 (2003) 3899--3914] and Newton et al. [Biostatistics 5 (2004) 155--176], by addressing important limitations that may have hampered its performance and its more widespread use. The models parsimoniously describe the expression of thousands of genes with a small number of hyper-parameters. This makes them easy to interpret and analytically tractable. The first model is a simple extension that improves the fit substantially with almost no increase in complexity. We propose a second extension that uses a mixture of gamma distributions to further improve the fit, at the expense of increased computational burden. We derive several approximations that significantly reduce the computational cost. We find that our models outperform the original formulation of the model, as well as some other popular methods for differential expression analysis. The improved performance is specially noticeable for the small sample sizes commonly encountered in high-throughput experiments. Our methods are implemented in the freely available Bioconductor gaga package.

stat.AP↗