Related papers: Bayes, E-values and Testing
The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…
Identifying a reasonably small Hilbert space that completely describes an unknown quantum state is crucial for efficient quantum information processing. We introduce a general dimension-certification protocol for both discrete and…
Online controlled experiments (A/B tests) are fundamental to data-driven decision-making in the digital economy. However, their real-world application is frequently compromised by two critical shortcomings: the use of statistically flawed…
Likelihood methods for measuring statistical evidence obey the likelihood principle while maintaining bounded and well-controlled frequency properties. These methods lend themselves to sequential study designs because they measure the…
Bayesian methods have proven themselves to be successful across a wide range of scientific problems and have many well-documented advantages over competing methods. However, these methods run into difficulties for two major and prevalent…
Word2vec (Mikolov et al., 2013) has proven to be successful in natural language processing by capturing the semantic relationships between different words. Built on top of single-word embeddings, paragraph vectors (Le and Mikolov, 2014)…
Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual…
In the context of supervised parametric models, we introduce the concept of e-values. An e-value is a scalar quantity that represents the proximity of the sampling distribution of parameter estimates in a model trained on a subset of…
We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and…
Approximate Bayesian Computational (ABC) methods (or likelihood-free methods) have appeared in the past fifteen years as useful methods to perform Bayesian analyses when the likelihood is analytically or computationally intractable. Several…
We construct a classifier which attains the rate of convergence $\log n/n$ under sparsity and margin assumptions. An approach close to the one met in approximation theory for the estimation of function is used to obtain this result. The…
Beta regression models provide an adequate approach for modeling continuous outcomes limited to the interval (0,1). This paper deals with an extension of beta regression models that allow for explanatory variables to be measured with error.…
Motivated by recent findings in Li and Zhang (2025), which established an equivalence between certain p-value-based multiple testing procedures and the e-Benjamini-Hochberg procedure (Wang and Ramdas, 2022), we introduce a general framework…
A series of monte carlo studies were performed to compare the behavior of some alternative procedures for reasoning under uncertainty. The behavior of several Bayesian, linear model and default reasoning procedures were examined in the…
Decision trees are widely used for interpretable machine learning due to their clearly structured reasoning process. However, this structure belies a challenge we refer to as predictive equivalence: a given tree's decision boundary can be…
Credibility building activities in computational research include verification and validation, reproducibility and replication, and uncertainty quantification. Though orthogonal to each other, they are related. This paper presents…
As in many fields of medical research, survival analysis has witnessed a growing interest in the application of deep learning techniques to model complex, high-dimensional, heterogeneous, incomplete, and censored medical data. Current…
Based on independent progressively Type-II censored samples from two-parameter Rayleigh distributions with the same location parameter but different scale parameters, the UMVUE and maximum likelihood estimator of $R=P(Y<X)$ are obtained.…
Bayesian optimization is a popular framework for efficiently tackling black-box search problems. As a rule, these algorithms operate by iteratively choosing what to evaluate next until some predefined budget has been exhausted. We…
E-variables are nonnegative random variables with expected value at most one under any distribution from a given null hypothesis. Every nonasymptotically valid test can be obtained by thresholding some e-variable. As such, e-variables arise…