About

Daniel Kessler is an Assistant Professor in the Department of Statistics & Operations Research at the University of North Carolina at Chapel Hill. He completed his PhD in 2023 at the University of Michigan's Department of Statistics, where he was advised by Professor Liza Levina. His research interests include the statistical analysis of networks, post-selective inference, high-dimensional statistics, and applications involving human neuroimaging, computational and cognitive neuroscience, and high performance computing.

Research topics

• Computer science
• Mathematics
• Econometrics
• Artificial intelligence
• Statistics

Selected publications

• Marginally specified priors for non-parametric Bayesian estimation

  UNC Libraries · 2020-11-05

  articleOpen access

  Prior specification for non-parametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. A statistician is unlikely to have informed opinions about all aspects of such a parameter but will have real information about functionals of the parameter, such as the population mean or variance. The paper proposes a new framework for non-parametric Bayes inference in which the prior distribution for a possibly infinite dimensional parameter is decomposed into two parts: an informative prior on a finite set of functionals, and a non-parametric conditional prior for the parameter given the functionals. Such priors can be easily constructed from standard non-parametric prior distributions in common use and inherit the large support of the standard priors on which they are based. Additionally, posterior approximations under these informative priors can generally be made via minor adjustments to existing Markov chain approximation algorithms for standard non-parametric prior distributions. We illustrate the use of such priors in the context of multivariate density estimation using Dirichlet process mixture models, and in the modelling of high dimensional sparse contingency tables.

  PublisherDOI

• Bayesian Nonparametric Methods for High-Dimensional Data

  Carolina Digital Repository (University of North Carolina at Chapel Hill) · 2019-08-12

  articleOpen access1st authorCorresponding

  Bayesian nonparametric (BNP or NP Bayes) methods have enjoyed great strides forward in recent years. BNP methods embody the belief that inference is best driven by the data itself with minimal assumptions about the underlying model; this approach has motivated a wide variety of BNP techniques that have met with with much success. In the first dissertation paper, we address a long-standing complaint about the nonparametric priors used in BNP analyses, that they do not necessarily reflect the analyst's prior belief or intention, and so are not really Bayesian. In fact, it can be demonstrated that a supposedly uninformative nonparametric prior framework is actually very informative about certain aspects of the distribution it models. We develop a novel method to incorporate prior information about functionals of the unknown distribution, replacing undesirable induced priors on those functionals with prior distributions that reflect real prior belief. We show that the new prior enjoys the support characteristics of the original prior, and we demonstrate with examples the effect of the marginal prior on the quality of inference. In the second and third dissertation papers, we address challenges in the analysis of high-dimensional data, with a focus on density regression. Many areas of inquiry, particularly in genetics research, are concerned with the modeling of a continuous physical trait as some function of a very large set of predictors. In most cases the number of predictors is much larger than the number of observations. In addition, the response to be modeled may have a nontrivial conditional distribution. In the second dissertation paper we develop a solution for this problem in the context of uncorrelated observations, and apply the technique to a problem in molecular epidemiology. In the third dissertation paper we expand the method to address correlated observations. We illustrate the utility of the proposed method in an application to a family-based data from a whole-genome linkage analysis of a neurological condition.

  PublisherDOI

• Main data extraction: adult subset

  2016-06-01

  article
  Publisher

• Learning phenotype densities conditional on many interacting predictors

  Bioinformatics · 2014-02-05 · 4 citations

  article1st authorCorresponding

  MOTIVATION: Estimating a phenotype distribution conditional on a set of discrete-valued predictors is a commonly encountered task. For example, interest may be in how the density of a quantitative trait varies with single nucleotide polymorphisms and patient characteristics. The subset of important predictors is not usually known in advance. This becomes more challenging with a high-dimensional predictor set when there is the possibility of interaction. RESULTS: We demonstrate a novel non-parametric Bayes method based on a tensor factorization of predictor-dependent weights for Gaussian kernels. The method uses multistage predictor selection for dimension reduction, providing succinct models for the phenotype distribution. The resulting conditional density morphs flexibly with the selected predictors. In a simulation study and an application to molecular epidemiology data, we demonstrate advantages over commonly used methods.

  PublisherDOI

• Marginally Specified Priors for Non-Parametric Bayesian Estimation

  Journal of the Royal Statistical Society Series B (Statistical Methodology) · 2014-03-17 · 17 citations

  articleOpen access1st author

  Prior specification for non-parametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. A statistician is unlikely to have informed opinions about all aspects of such a parameter but will have real information about functionals of the parameter, such as the population mean or variance. The paper proposes a new framework for non-parametric Bayes inference in which the prior distribution for a possibly infinite dimensional parameter is decomposed into two parts: an informative prior on a finite set of functionals, and a non-parametric conditional prior for the parameter given the functionals. Such priors can be easily constructed from standard non-parametric prior distributions in common use and inherit the large support of the standard priors on which they are based. Additionally, posterior approximations under these informative priors can generally be made via minor adjustments to existing Markov chain approximation algorithms for standard non-parametric prior distributions. We illustrate the use of such priors in the context of multivariate density estimation using Dirichlet process mixture models, and in the modelling of high dimensional sparse contingency tables.

  PublisherOA PDFDOI

• Learning Densities Conditional on Many Interacting Features

  arXiv (Cornell University) · 2013-04-26

  preprintOpen access1st authorCorresponding

  Learning a distribution conditional on a set of discrete-valued features is a commonly encountered task. This becomes more challenging with a high-dimensional feature set when there is the possibility of interaction between the features. In addition, many frequently applied techniques consider only prediction of the mean, but the complete conditional density is needed to answer more complex questions. We demonstrate a novel nonparametric Bayes method based upon a tensor factorization of feature-dependent weights for Gaussian kernels. The method makes use of multistage feature selection for dimension reduction. The resulting conditional density morphs flexibly with the selected features.

  PublisherOA PDFDOI

• Marginally Specified Priors for Nonparametric Bayesian Estimation

  arXiv (Cornell University) · 2012-04-29

  preprintOpen access1st authorCorresponding

  Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions about all aspects of such a parameter, but may have real information about functionals of the parameter, such the population mean or variance. This article proposes a new framework for nonparametric Bayes inference in which the prior distribution for a possibly infinite-dimensional parameter is decomposed into two parts: an informative prior on a finite set of functionals, and a nonparametric conditional prior for the parameter given the functionals. Such priors can be easily constructed from standard nonparametric prior distributions in common use, and inherit the large support of the standard priors upon which they are based. Additionally, posterior approximations under these informative priors can generally be made via minor adjustments to existing Markov chain approximation algorithms for standard nonparametric prior distributions. We illustrate the use of such priors in the context of multivariate density estimation using Dirichlet process mixture models, and in the modeling of high-dimensional sparse contingency tables.

  PublisherOA PDFDOI

• Reinventing American Tobacco Policy

  JAMA · 1998-02-18 · 11 citations

  letter
  PublisherDOI

• The scourge of the tobacco industry steps down.

  PubMed · 1997-01-04

  article1st authorCorresponding
  Publisher

Frequent coauthors

• David B. Dunson

  9 shared

• Jack A. Taylor

  Triangle

  5 shared

• Peter D. Hoff

  Statistical and Applied Mathematical Sciences Institute

  5 shared

• Peter Bryden

  University College London

  1 shared

• William Hollingworth

  University of Bristol

  1 shared

• Naomi Fineberg

  Hertfordshire Partnership University NHS Foundation Trust

  1 shared

• Rachel Churchill

  University of York

  1 shared

• Glyn Lewis

  1 shared