Let Xn = (X1; ; Xn) be a memoryless source with unknown distribution on a finite alphabet of size k. We identify the asymptotic minimax coding redundancy for this class of sources, and provide a sequence of asymptotically minimax codes. Equivalently, we determine the limiting behavior of the minimax relative entropy minQ maxP D(PX kQX ), where the maximum is over all independent and identically...

Abstract The Jeffreys–Lindley paradox exposes a rift between Bayesian and frequentist hypothesis testing that strikes at the heart of statistical inference. Contrary to what most current literature suggests, was central methodology developed by Sir Harold Jeffreys in late 1930s. showed evidence for point-null $${\mathcal {H}}_0$$ <mml:ms...

We consider the equation of the Jeffreys type as the basic one in three different models of mass transfer, namely, the Jeffreys type and two-phase models, and the D1 approximation to the linear Boltzmann equation. We study two classic 1 + 1D problems in the framework of each model. The first problem is the transfer of a substance initially confined in a point. The second problem is the transfer...

Derivation of tight bounds on f -divergences and related distances is of interest in information theory and statistics. This paper improves some existing bounds on f -divergences. In some cases, an alternative approach leads to a simplified proof of an existing bound. Following bounds on the chi-squared divergence, an improved version of a reversed Pinsker’s inequality is derived for an arbitra...

Rules for assessing compliance with percentile standards commonly limit the number of exceedances permitted in a batch of samples taken over a defined assessment period. Such rules are commonly developed using classical statistical methods. Results from alternative Bayesian methods are presented (using beta-distributed prior information and a binomial likelihood), resulting in "confidence of co...

We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the standard Wald confidence interval has previously been remarked on in the literature (Blyth and Still, Agresti and Coull, Santner and others). We begin by showing that the chaotic coverage properties of the Wald interval are far more persistent than is appreciated. Furt...

Derivation of tight bounds on f -divergences and related distances is of interest in information theory and statistics. This paper improves some existing bounds on f -divergences. In some cases, an alternative approach leads to a simplified proof of an existing bound. Following bounds on the chi-squared divergence, an improved version of a reversed Pinsker’s inequality is derived for an arbitra...

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