Related papers: Discussion: The Dantzig selector: Statistical esti…
We derive an efficient method to calculate exceedance probabilities (EP) for the Dirichlet distribution when the number of event types is larger than two. Also, we present an intuitive application of Dirichlet EPs and compare our method to…
As large and powerful neural language models are developed, researchers have been increasingly interested in developing diagnostic tools to probe them. There are many papers with conclusions of the form "observation X is found in model Y",…
Discussion of ``Statistical analysis of an archeological find'' by Andrey Feuerverger [arXiv:0804.0079]
Sampling distribution, a foundational concept in statistics, is difficult to understand, since we usually have only one realization of the estimator of interest. In this work, we present an innovative method for helping university students…
We consider a class of linear-programming based estimators in reconstructing a sparse signal from linear measurements. Specific formulations of the reconstruction problem considered here include Dantzig selector, basis pursuit (for the case…
Discussion of ``Statistical analysis of an archeological find'' by Andrey Feuerverger [arXiv:0804.0079]
Discussion of ``Statistical analysis of an archeological find'' by Andrey Feuerverger [arXiv:0804.0079]
Discussion of ``Statistical analysis of an archeological find'' by Andrey Feuerverger [arXiv:0804.0079]
Discussion of ``Statistical analysis of an archeological find'' by Andrey Feuerverger [arXiv:0804.0079]
Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here I present an alternative approach…
This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Cand\`es and Tao's approach, we propose an $\ell_1$-minimization…
This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic…
We consider regression under the "extremely small $n$ large $p$" condition, where the number of samples $n$ is so small compared to the dimensionality $p$ that predictors cannot be estimated without prior knowledge. This setup occurs in…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
In the era of big data, analysts usually explore various statistical models or machine learning methods for observed data in order to facilitate scientific discoveries or gain predictive power. Whatever data and fitting procedures are…
Confounding matters in almost all observational studies that focus on causality. In order to eliminate bias caused by connfounders, oftentimes a substantial number of features need to be collected in the analysis. In this case, large p…
Quantum and classical models for delayed choice entanglement swapping by postselection of measurements are discussed.
This paper presents a selective review of statistical computation methods for massive data analysis. A huge amount of statistical methods for massive data computation have been rapidly developed in the past decades. In this work, we focus…
We prove the higher-dimensional analogue of Wolff's local smoothing estimate (Geom. Funct. Anal. 2001) for large p. As in the 2+1-dimensional case, the estimate is sharp for any given value of p, but it is likely that the range of p can be…
Let $\mathbb{Z}_p$ be the ring of $p$-adic integers and $a_n(x)$ be the $n$-th digit of Schneider's $p$-adic continued fraction of $x\in p\mathbb{Z}_p$. We study the growth rate of the digits $\{a_n(x)\}_{n\geq1}$ from the viewpoint of…