Bayesian Linear Inverse Problems in Regularity Scales with Discrete Observations.

We obtain rates of contraction of posterior distributions in inverse problems with discrete observations. In a general setting of smoothness scales we derive abstract results for general priors, with contraction rates determined by discrete Galerkin approximation. The rate depends on the amount of prior concentration near the true function and the prior mass of functions with inferior Galerkin approximation.

Posterolateral or Direct Lateral Surgical Approach for Hemiarthroplasty After a Hip Fracture: A Randomized Clinical Trial Alongside a Natural Experiment.

Importance: Hip fractures in older adults are serious injuries that result in disability, higher rates of illness and death, and a substantial strain on health care resources. High-quality evidence to improve hip fracture care regarding the surgical approach of hemiarthroplasty is lacking.

Objective: To compare 6-month outcomes of the posterolateral approach (PLA) and direct lateral approach (DLA) for hemiarthroplasty in patients with acute femoral neck fracture.

Semi-supervised empirical Bayes group-regularized factor regression.

The features in a high-dimensional biomedical prediction problem are often well described by low-dimensional latent variables (or factors). We use this to include unlabeled features and additional information on the features when building a prediction model. Such additional feature information is often available in biomedical applications.

Applying Pattern Recognition as a Robust Approach for Silicone Oil Droplet Identification in Flow-Microscopy Images of Protein Formulations.

Discrimination between potentially immunogenic protein aggregates and harmless pharmaceutical components, like silicone oil, is critical for drug development. Flow imaging techniques allow to measure and, in principle, classify subvisible particles in protein therapeutics. However, automated approaches for silicone oil discrimination are still lacking robustness in terms of accuracy and transferability.

Adaptive Bayesian credible bands in regression with a Gaussian process prior.

A credible band is the set of all functions between a lower and an upper bound that are constructed so that the set has prescribed mass under the posterior distribution. In a Bayesian analysis such a band is used to quantify the remaining uncertainty on the unknown function in a similar manner as a confidence band. We investigate the validity of a credible band in the nonparametric regression model with the prior distribution on the function given by a Gaussian process.

Adaptive group-regularized logistic elastic net regression.

In high-dimensional data settings, additional information on the features is often available. Examples of such external information in omics research are: (i) $p$-values from a previous study and (ii) omics annotation. The inclusion of this information in the analysis may enhance classification performance and feature selection but is not straightforward.

HIGHER ORDER ESTIMATING EQUATIONS FOR HIGH-DIMENSIONAL MODELS.

We introduce a new method of estimation of parameters in semi-parametric and nonparametric models. The method is based on estimating equations that are -statistics in the observations. The -statistics are based on higher order influence functions that extend ordinary linear influence functions of the parameter of interest, and represent higher derivatives of this parameter.

Gene Network Reconstruction using Global-Local Shrinkage Priors.

Reconstructing a gene network from high-throughput molecular data is an important but challenging task, as the number of parameters to estimate easily is much larger than the sample size. A conventional remedy is to regularize or penalize the model likelihood. In network models, this is often done in the neighbourhood of each node or gene.

An empirical Bayes approach to network recovery using external knowledge.

Reconstruction of a high-dimensional network may benefit substantially from the inclusion of prior knowledge on the network topology. In the case of gene interaction networks such knowledge may come for instance from pathway repositories like KEGG, or be inferred from data of a pilot study. The Bayesian framework provides a natural means of including such prior knowledge.

A powerful and efficient two-stage method for detecting gene-to-gene interactions in GWAS.

For over a decade functional gene-to-gene interaction (epistasis) has been suspected to be a determinant in the "missing heritability" of complex traits. However, searching for epistasis on the genome-wide scale has been challenging due to the prohibitively large number of tests which result in a serious loss of statistical power as well as computational challenges. In this article, we propose a two-stage method applicable to existing case-control data sets, which aims to lessen both of these problems by pre-assessing whether a candidate pair of genetic loci is involved in epistasis before it is actually tested for interaction with respect to a complex phenotype.

Asymptotic Normality of Quadratic Estimators.

We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data.

Transcriptomic Heterogeneity in Cancer as a Consequence of Dysregulation of the Gene-Gene Interaction Network.

Many pathways are dysregulated in cancer. Dysregulation of the regulatory network results in less control of transcript levels in the cell. Hence, dysregulation is reflected in the heterogeneity of the transcriptome: the more dysregulated the pathway, the more the transcriptomic heterogeneity.

On the correction of the asymptotic distribution of the likelihood ratio statistic if nuisance parameters are estimated based on an external source.

In practice, nuisance parameters in statistical models are often replaced by estimates based on an external source, for instance if estimates were published before or a second dataset is available. Next these estimates are assumed to be known when the parameter of interest is estimated, a hypothesis is tested or confidence intervals are constructed. By this assumption, the level of the test is, in general, higher than supposed and the coverage of the confidence interval is too low.

Accurate prediction of a minimal region around a genetic association signal that contains the causal variant.

In recent years, genome-wide association studies have been very successful in identifying loci for complex traits. However, typically these findings involve noncoding and/or intergenic SNPs without a clear functional effect that do not directly point to a gene. Hence, the challenge is to identify the causal variant responsible for the association signal.

Bayesian analysis of RNA sequencing data by estimating multiple shrinkage priors.

Next generation sequencing is quickly replacing microarrays as a technique to probe different molecular levels of the cell, such as DNA or RNA. The technology provides higher resolution, while reducing bias. RNA sequencing results in counts of RNA strands.

CHEK2*1100delC homozygosity is associated with a high breast cancer risk in women.

Background: Mutations in the CHEK2 gene confer a moderately increased breast cancer risk. The risk for female carriers of the CHEK2*1100delC mutation is twofold increased. Breast cancer risk for carrier women is higher in a familial breast cancer setting which is due to coinheritance of additional genetic risk factors.

Higher Order Inference On A Treatment Effect Under Low Regularity Conditions.

We describe a novel approach to nonparametric point and interval estimation of a treatment effect in the presence of many continuous confounders. We show the problem can be reduced to that of point and interval estimation of the expected conditional covariance between treatment and response given the confounders. Our estimators are higher order U-statistics.

Data-driven modeling of phase interactions between spontaneous MEG oscillations.

Objective: Synchronization between distributed rhythms in the brain is commonly assessed by estimating the synchronization strength from simultaneous measurements. This approach, however, does not elucidate the phase dynamics that underlies synchronization. For this, an explicit dynamical model is required.

A local maximal inequality under uniform entropy.

We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant δ. The bound is expressed in the uniform entropy integral of the class at δ. The bound yields a rate of convergence of minimum contrast estimators when applied to the modulus of continuity of the contrast functions.

Statistical analysis of the cancer cell's molecular entropy using high-throughput data.

Motivation: As cancer progresses, DNA copy number aberrations accumulate and the genomic entropy (chromosomal disorganization) increases. For this surge to have any oncogenetic effect, it should (to some extent) be reflected at other molecular levels of the cancer cell, in particular that of the transcriptome. Such a coincidence of cancer progression and the propagation of an entropy increase through the molecular levels of the cancer cell would enhance the understanding of cancer evolution.

Quadratic semiparametric Von Mises calculus.

We discuss a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on U-statistics constructed from quadratic influence functions. The latter extend ordinary linear influence functions of the parameter of interest as defined in semiparametric theory, and represent second order derivatives of this parameter.

Semiparametric Minimax Rates.

We consider the minimax rate of testing (or estimation) of non-linear functionals defined on semiparametric models. Existing methods appear not capable of determining a lower bound on the minimax rate of testing (or estimation) for certain functionals of interest. In particular, if the semiparametric model is indexed by several infinite-dimensional parameters.