arXiv subjects

Surya Tokdar

Publications and source records attributed to Surya Tokdar.

7 recordsLinked to original sources

arXiv2026

Covariate-localized False Discovery Rates

We introduce a flexible model for covariate-dependent multiple testing which can be encoded using a nonparametric Gaussian mixture model. Weight-localized predictive recursion (PRx), a new development in the methodology of Newton's predictive recursion algorithm, is then leveraged to estimate the components of this mixture model, allowing for recovery of the covariate-localized false discovery rate $\text{Pr}(H_i = 0|z_i,x_i)$ using a single, unified algorithm. This quantity represents the most direct extension of Efron's local false discovery rate to the covariate-dependent setting, and admits provable Bayesian FDR control properties under simple rejection rules. We introduce several procedures for estimating and thresholding the local false discovery rate, and show using various simulations and a real-data example that our procedures lead to increased power, tighter Bayesian FDR control, and more interpretable rejections. We furthermore show that this holds for fixed and randomized hypothesis labels, indicating that our proposed methods perform well under both frequentist and Bayesian interpretations of multiple testing.

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arXiv2026

Fast Semiparametric Density Regression with Weight-localized Predictive Recursion

Predictive recursion (PR) is a fast algorithm for nonparametric estimation of a mixing density, with connections to sequential Bayesian updating under a Dirichlet process prior and rigorous frequentist consistency guarantees. Extending PR to the regression setting, where one seeks to estimate how a mixing density varies with covariate, is nontrivial: dependent Dirichlet process priors, the natural Bayesian generalization, gives no simple recursive updating formula. We introduce PRx, which overcomes this challenge through combining kernel-based weight localization with the recursive scheme of the original PR algorithm. The algorithm scales linearly in sample size and covariate dimension, completing in seconds to minutes where MCMC-based competitors require hours. Exactly as with ordinary PR, the algorithm produces as a byproduct a likelihood score, the PRMLx, whose maximizer is shown to be a consistent estimator for unmixed parameters. In simulations and case studies PRx produces conditional density estimates competitive with established Bayesian procedures at a fraction of the computational cost, and can also be adapted for a wide range of statistical applications including Bayesian model comparison and covariate-dependent multiple testing.

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arXiv2025

Selective and marginal selective inference for exceptional groups

Statistical analyses of multipopulation studies often use the data to select a particular population as the target of inference. For example, a confidence interval may be constructed for a population only in the event that its sample mean is larger than that of the other populations. We show that for the normal means model, confidence interval procedures that maintain strict coverage control conditional on such a selection event will have infinite expected width. For applications where such selective coverage control is of interest, this result motivates the development of procedures with finite expected width and approximate selective coverage control over a range of plausible parameter values. To this end, we develop selection-adjusted empirical Bayes confidence procedures that use information from the data to approximate an oracle confidence procedure that has exact selective coverage control and finite expected width. In numerical comparisons of the oracle and empirical Bayes procedures to procedures that only guarantee selective coverage control marginally over selection events, we find that improved selective coverage control comes at the cost of increased expected interval width.

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arXiv2025

Asymptotically well-calibrated Bayesian $p$-value using the Kolmogorov-Smirnov statistic

The posterior predictive $p$-value (ppp) is widely used in Bayesian model evaluation. However, due to double use of the data, the ppp may not be a valid $p$-value even in large samples: The asymptotic null distribution of the ppp can be non-uniform unless the underlying test statistic satisfies certain well-calibration conditions. Such conditions have been studied in the literature for asymptotically normal test statistics. We extend this line of work by establishing well-calibration conditions for test statistics that are not necessarily asymptotically normal. In particular, we show that Kolmogorov-Smirnov (KS)-type test statistics satisfy these conditions, such that their ppps are asymptotically well-calibrated Bayesian $p$-values. KS-type statistics are versatile, omnibus, and sensitive to model misspecifications. They apply to i.i.d. real-valued data, as well as non-identically distributed observations under regression models. Numerical experiments demonstrate that such $p$-values are well behaved in finite samples and can effectively detect a wide range of alternative models.

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arXiv2021

Consistent Bayesian Community Detection

Stochastic Block Models (SBMs) are a fundamental tool for community detection in network analysis. But little theoretical work exists on the statistical performance of Bayesian SBMs, especially when the community count is unknown. This paper studies a special class of SBMs whose community-wise connectivity probability matrix is diagonally dominant, i.e., members of the same community are more likely to connect with one another than with members from other communities. The diagonal dominance constraint is embedded within an otherwise weak prior, and, under mild regularity conditions, the resulting posterior distribution is shown to concentrate on the true community count and membership allocation as the network size grows to infinity. A reversible-jump Markov Chain Monte Carlo posterior computation strategy is developed by adapting the allocation sampler of Mcdaid et al (2013). Finite sample properties are examined via simulation studies in which the proposed method offers competitive estimation accuracy relative to existing methods under a variety of challenging scenarios.

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arXiv2015

Joint estimation of quantile planes over arbitrary predictor spaces

In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parametrization that characterizes any collection of non-crossing quantile planes over arbitrarily shaped convex predictor domains in any dimension by means of unconstrained scalar, vector and function valued parameters. Statistical models based on this parametrization inherit a fast computation of the likelihood function, enabling penalized likelihood or Bayesian approaches to model fitting. We introduce a complete Bayesian methodology by using Gaussian process prior distributions on the function valued parameters and develop a robust and efficient Markov chain Monte Carlo parameter estimation. The resulting method is shown to offer posterior consistency under mild tail and regularity conditions. We present several illustrative examples where the new method is compared against existing approaches and is found to offer better accuracy, coverage and model fit.

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arXiv2011

Efficient Gaussian Process Regression for Large Data Sets

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use is the expensive computation, typically O($n^3$) in performing the necessary matrix inversions with $n$ denoting the number of data points. In large data sets, data storage and processing also lead to computational bottlenecks and numerical stability of the estimates and predicted values degrades with $n$. To address these problems, a rich variety of methods have been proposed, with recent options including predictive processes in spatial data analysis and subset of regressors in machine learning. The underlying idea in these approaches is to use a subset of the data, leading to questions of sensitivity to the subset and limitations in estimating fine scale structure in regions that are not well covered by the subset. Motivated by the literature on compressive sensing, we propose an alternative random projection of all the data points onto a lower-dimensional subspace. We demonstrate the superiority of this approach from a theoretical perspective and through the use of simulated and real data examples. Some Keywords: Bayesian; Compressive Sensing; Dimension Reduction; Gaussian Processes; Random Projections; Subset Selection

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