Jyotishka Datta

Composition as Direction: An Active-Set Ray-Based Model for Sparse High-Dimensional Compositional Data

Michael R. Schwob, Jyotishka Datta

[Working Draft] Compositional data are central to microbial, ecological, and environmental research, yet often have four features that are difficult to accommodate jointly: exact zeros, latent dependence among components, high-dimensionality, and a unit-sum constraint that induces a non-Euclidean geometry. Conventional Dirichlet-type and …

Composition as Direction: An Active-Set Ray-Based Model for Sparse High-Dimensional Compositional Data

Michael R. Schwob, Jyotishka Datta

[Working Draft] Compositional data are central to microbial, ecological, and environmental research, yet often have four features that are difficult to accommodate jointly: exact zeros, latent dependence among components, high-dimensionality, and a unit-sum constraint that induces a non-Euclidean geometry. Conventional Dirichlet-type and …

us (code pays fourni par la source)

A New Look at Bayesian Testing

Jyotishka Datta, Nicholas G. Polson, Vadim Sokolov, Daniel Zantedeschi

We identify the critical deviation scale governing Bayesian evidence accumulation in regular parametric testing. Under integrated Bayes risk with zero-one loss, the risk-optimal rejection boundary lies in a moderate deviation regime, with a square-root logarithmic inflation relative to the usual local asymptotic …

A New Look at Bayesian Testing

Jyotishka Datta, Nicholas G. Polson, Vadim Sokolov, Daniel Zantedeschi

We identify the critical deviation scale governing Bayesian evidence accumulation in regular parametric testing. Under integrated Bayes risk with zero-one loss, the risk-optimal rejection boundary lies in a moderate deviation regime, with a square-root logarithmic inflation relative to the usual local asymptotic …

us (code pays fourni par la source)

Inverse Probability Weighting: From Survey Sampling to Evidence Estimation

Jyotishka Datta, Nicholas Polson

We consider the class of inverse probability weight (IPW) estimators, including the popular Horvitz–Thompson and Hájek estimators used routinely in survey sampling, causal inference and for Bayesian computation. We focus on the ‘weak paradoxes’ for these estimators due to two counterexamples by …

us (code pays fourni par la source)

Predictive Minimaxity, The GLX Connecting Formula, and the Horseshoe Prior

Jyotishka Datta, Nicholas G. Polson, Vadim Sokolov, Daniel Zantedeschi

us (code pays fourni par la source)

Conformal Prediction = Bayes?

Jyotishka Datta, Nicholas G. Polson, Vadim Sokolov, Daniel Zantedeschi

Conformal prediction (CP) is widely presented as distribution-free predictive inference with finite-sample marginal coverage under exchangeability. We argue that CP is best understood as a rank-calibrated descendant of the Fisher-Dempster-Hill fiducial/direct-probability tradition rather than as Bayesian conditioning in disguise. We establish four …

Conformal Prediction = Bayes?

Jyotishka Datta, Nicholas G. Polson, Vadim Sokolov, Daniel Zantedeschi

Conformal prediction (CP) is widely presented as distribution-free predictive inference with finite-sample marginal coverage under exchangeability. We argue that CP is best understood as a rank-calibrated descendant of the Fisher-Dempster-Hill fiducial/direct-probability tradition rather than as Bayesian conditioning in disguise. We establish four …

us (code pays fourni par la source)

Bayesian Global-Local Regularization

Jyotishka Datta, Nick Polson, Vadim Sokolov

We propose a unified framework for global-local regularization that bridges the gap between classical techniques -- such as ridge regression and the nonnegative garotte -- and modern Bayesian hierarchical modeling. By estimating local regularization strengths via marginal likelihood under order constraints, our …

Polynomial Log-Marginals and Tweedie's Formula : When Is Bayes Possible?

Jyotishka Datta, Nicholas G. Polson

Motivated by Tweedie's formula for the Compound Decision problem, we examine the theoretical foundations of empirical Bayes estimators that directly model the marginal density $m(y)$. Our main result shows that polynomial log-marginals of degree $k \ge 3 $ cannot arise from any …

Quantile importance sampling

Jyotishka Datta, Nicholas G. Polson

In Bayesian inference, the approximation of integrals of the form ψ=EFl(X)=∫χl(x)dF(x) is a fundamental challenge. Such integrals are crucial for evidence estimation, which is important for various purposes, including model selection and numerical analysis. The existing strategies for evidence estimation are classified …

us (code pays fourni par la source)

Quantile importance sampling

Jyotishka Datta, Nicholas G. Polson

In Bayesian inference, the approximation of integrals of the form ψ=EFl(X)=∫χl(x)dF(x) is a fundamental challenge. Such integrals are crucial for evidence estimation, which is important for various purposes, including model selection and numerical analysis. The existing strategies for evidence estimation are classified …

us (code pays fourni par la source)