Suppose we observe an infinite series of coin flips X1,X2,…, and wish to sequentially test the null that these binary random variables are exchangeable. Nonnegative supermartingales (NSMs) a workhorse sequential inference, but prove they powerless for this problem. First, utilizing geometric concept called fork-convexity (a analog convexity), show any process is NSM under set distributions, als...

Hierarchically exchangeable data are characterized by the exchangeability of a population of units and the exchangeability of observations from each individual unit. A flexible model for such data is the hierarchical logistic-normal model, which provides unconstrained sampling distributions at the within-unit level and an unconstrained covariance structure at the betweenunit level. Also, the sa...

We give the maximal distance between a copula and itself when the argument is permuted for arbitrary dimension, generalizing a result for dimension two by Nelsen (2007); Klement and Mesiar (2006). Furthermore, we establish a subset of [0, 1] in which this bound might be attained. For each point in this subset we present a copula and a permutation, for which the distance in this point is maximal...

Abstraet--A laboratory study of cadmium exchangeability revealed large differences in extractable cadmium which are dependent on the exchange solution being utilized. The standard exchange solutions employed in this study were: N NaNO3, N NaOAc, N NH4OAc, NCaCI~, and 2N CaCI2, in order of increasing Cd removal. An interpretation of the chemical behavior of Cd and an experiment with mixed sodium...

Controlling false discovery rate (FDR) is crucial for variable selection, multiple testing, among other signal detection problems. In literature, there certainly no shortage of FDR control strategies when selecting individual features, but the relevant works structural change detection, such as profile analysis piecewise constant coefficients and integration with data sources, are limited. this...

We present a new partition-valued Markov chain for modeling latent temporal clustering. The family of Markov chains we consider satisfies notable statistical properties, including exchangeability, consistency under subsampling, and reversibility with respect to a tractable class of two-parameter partition models. These properties endow our model with a robustness to missing data, choice of labe...

The distribution and exchangeability of calcium within subcellular compartments of rat pancreatic islet cells was determined in pulse-chase experiments following isotopic labelling with 45Ca2+. In unstimulated islets the mitochondrial fraction showed the greatest, and the insulin secretory granule fraction the least, uptake of 45Ca2+; subsequently the rate of loss from each compartment during 1...

We propose a flexible non-parametric specification of the emission distribution in hidden Markov models and we introduce a novel methodology for carrying out the computations. Whereas current approaches use a finite mixture model, we argue in favour of an infinite mixture model given by a mixture of Dirichlet processes.The computational framework is based on auxiliary variable representations o...

In [11], Köstler and Speicher showed that de Finetti’s theorem on exchangeable sequences has a free analogue if one replaces exchangeability by the stronger condition of invariance of the joint distribution under quantum permutations. In this paper we study sequences of noncommutative random variables whose joint distribution is invariant under quantum orthogonal transformations. We prove a fre...

Coherent reasoning under uncertainty can be represented in a very general manner by coherent sets of desirable gambles. In this framework, and for a given finite category set, coherent predictive inference under exchangeability can be represented using Bernstein coherent cones of multivariate polynomials on the simplex generated by this category set. This is a powerful generalisation of de Fine...