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Dan L. Nicolae

Publications and source records attributed to Dan L. Nicolae.

8 recordsLinked to original sources
arXiv2021

Weighted-Graph-Based Change Point Detection

We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when at most one change point occurs and generalize them to multiple change points settings. The proposed statistics leverage edge weight information in the graphs, exhibiting substantial improvements in testing power and localization accuracy in simulations. We derive the null limiting distribution, provide accurate analytic approximations to control type I error, and establish theoretical guarantees on the power consistency under contiguous alternatives for the one change point setting, as well as the minimax localization rate. In the multiple change points setting, the asymptotic correctness of the number and location of change points are also guaranteed. The methods are illustrated on the MIT proximity network data.

stat.ME↗
arXiv2021

Prior sample size extensions for assessing prior impact and prior--likelihood discordance

This paper outlines a framework for quantifying the prior's contribution to posterior inference in the presence of prior-likelihood discordance, a broader concept than the usual notion of prior-likelihood conflict. We achieve this dual purpose by extending the classic notion of \textit{prior sample size}, $M$, in three directions: (I) estimating $M$ beyond conjugate families; (II) formulating $M$ as a relative notion, i.e., as a function of the likelihood sample size $k, M(k),$ which also leads naturally to a graphical diagnosis; and (III) permitting negative $M$, as a measure of prior-likelihood conflict, i.e., harmful discordance. Our asymptotic regime permits the prior sample size to grow with the likelihood data size, hence making asymptotic arguments meaningful for investigating the impact of the prior relative to that of likelihood. It leads to a simple asymptotic formula for quantifying the impact of a proper prior that only involves computing a centrality and a spread measure of the prior and the posterior. We use simulated and real data to illustrate the potential of the proposed framework, including quantifying how weak is a "weakly informative" prior adopted in a study of lupus nephritis. Whereas we take a pragmatic perspective in assessing the impact of a prior on a given inference problem under a specific evaluative metric, we also touch upon conceptual and theoretical issues such as using improper priors and permitting priors with asymptotically non-vanishing influence.

stat.ME↗
arXiv2017

Mixed Effect Dirichlet-Tree Multinomial for Longitudinal Microbiome Data and Weight Prediction

Quantifying the relation between gut microbiome and body weight can provide insights into personalized strategies for improving digestive health. In this paper, we present an algorithm that predicts weight fluctuations using gut microbiome in a healthy cohort of newborns from a previously published dataset. Microbial data has been known to present unique statistical challenges that defy most conventional models. We propose a mixed effect Dirichlet-tree multinomial (DTM) model to untangle these difficulties as well as incorporate covariate information and account for species relatedness. The DTM setup allows one to easily invoke empirical Bayes shrinkage on each node for enhanced inference of microbial proportions. Using these estimates, we subsequently apply random forest for weight prediction and obtain a microbiome-inferred weight metric. Our result demonstrates that microbiome-inferred weight is significantly associated with weight changes in the future and its non-trivial effect size makes it a viable candidate to forecast weight progression.

stat.AP↗
arXiv2015

Prediction and replication from case-control sequencing studies using custom genotyping and additional sequencing

We present two results about using allele-count (AC) burdens of rare SNPs discovered in a case-control sequencing study for prediction or validation in an external prospective study. When genotyping only the SNPs polymorphic in the sequence data, the phenotype to AC correlation tends to be larger in the replication data than the primary study. Conversely, if the replication sample is sequenced, ACs of SNPs which are novel in the replication tend to have much smaller or opposite signed associations. We explain this by first deriving the AC-phenotype association implied by a model of diverse SNP effects, and second accounting for the shifted distribution of SNP effects when using a case-control study as a filter for SNP inclusion. In rare diseases, the case population is depleted of protective SNPs and enriched for deleterious SNPs, creating the above difference in AC associations. This phenomenon is most relevant in re-sequencing for risk prediction in rare diseases with heterogeneous rare mutations because it applies to SNPs with MAF near 1 out of the case-control sample size and is exaggerated when SNP log-odds ratios come from a heavy-tailed distribution. It also suggests a ``winner's curse'' in which most risk increasing SNPs at a particular MAF are quickly discovered and future sequencing finds more protective or irrelevant SNPs.

stat.AP↗
arXiv2013

The Convergence of eQTL Mapping, Heritability Estimation and Polygenic Modeling: Emerging Spectrum of Risk Variation in Bipolar Disorder

It is widely held that a substantial genetic component underlies Bipolar Disorder (BD) and other neuropsychiatric disease traits. Recent efforts have been aimed at understanding the genetic basis of disease susceptibility, with genome-wide association studies (GWAS) unveiling some promising associations. Nevertheless, the genetic etiology of BD remains elusive with a substantial proportion of the heritability - which has been estimated to be 80% based on twin and family studies - unaccounted for by the specific genetic variants identified by large-scale GWAS. Furthermore, functional understanding of associated loci generally lags discovery. Studies we report here provide considerable support to the claim that substantially more remains to be gained from GWAS on the genetic mechanisms underlying BD susceptibility, and that a large proportion of the variation in disease risk may be uncovered through integrative functional genomic approaches. We combine recent analytic advances in heritability estimation and polygenic modeling and leverage recent technological advances in the generation of -omics data to evaluate the nature and scale of the contribution of functional classes of genetic variation to a relatively intractable disorder. We identified cis eQTLs in cerebellum and parietal cortex that capture more than half of the total heritability attributable to SNPs interrogated through GWAS and showed that eQTL-based heritability estimation is highly tissue-dependent. Our findings show that a much greater resolution may be attained than has been reported thus far on the number of common loci that capture a substantial proportion of the heritability to disease risk and that the functional nature of contributory loci may be clarified en masse.

q-bio.GN↗
arXiv2013

On Quantifying Dependence: A Framework for Developing Interpretable Measures

We present a framework for selecting and developing measures of dependence when the goal is the quantification of a relationship between two variables, not simply the establishment of its existence. Much of the literature on dependence measures is focused, at least implicitly, on detection or revolves around the inclusion/exclusion of particular axioms and discussing which measures satisfy said axioms. In contrast, we start with only a few nonrestrictive guidelines focused on existence, range and interpretability, which provide a very open and flexible framework. For quantification, the most crucial is the notion of interpretability, whose foundation can be found in the work of Goodman and Kruskal [Measures of Association for Cross Classifications (1979) Springer], and whose importance can be seen in the popularity of tools such as the $R^2$ in linear regression. While Goodman and Kruskal focused on probabilistic interpretations for their measures, we demonstrate how more general measures of information can be used to achieve the same goal. To that end, we present a strategy for building dependence measures that is designed to allow practitioners to tailor measures to their needs. We demonstrate how many well-known measures fit in with our framework and conclude the paper by presenting two real data examples. Our first example explores U.S. income and education where we demonstrate how this methodology can help guide the selection and development of a dependence measure. Our second example examines measures of dependence for functional data, and illustrates them using data on geomagnetic storms.

stat.ME↗
arXiv2011

Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies

Many practical studies rely on hypothesis testing procedures applied to data sets with missing information. An important part of the analysis is to determine the impact of the missing data on the performance of the test, and this can be done by properly quantifying the relative (to complete data) amount of available information. The problem is directly motivated by applications to studies, such as linkage analyses and haplotype-based association projects, designed to identify genetic contributions to complex diseases. In the genetic studies the relative information measures are needed for the experimental design, technology comparison, interpretation of the data, and for understanding the behavior of some of the inference tools. The central difficulties in constructing such information measures arise from the multiple, and sometimes conflicting, aims in practice. For large samples, we show that a satisfactory, likelihood-based general solution exists by using appropriate forms of the relative Kullback--Leibler information, and that the proposed measures are computationally inexpensive given the maximized likelihoods with the observed data. Two measures are introduced, under the null and alternative hypothesis respectively. We exemplify the measures on data coming from mapping studies on the inflammatory bowel disease and diabetes. For small-sample problems, which appear rather frequently in practice and sometimes in disguised forms (e.g., measuring individual contributions to a large study), the robust Bayesian approach holds great promise, though the choice of a general-purpose "default prior" is a very challenging problem.

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