• Count data are often modeled using a Poisson model. • If y ∼ Poisson(μ) then E(y) = var(y) = μ. • When counts are assumed exchangeable given μ and the rates μ can also be assumed to be exchangeable, a Gamma population model for the rates is often chosen. • The hierarchical model is then yi ∼ Poisson(μi) μi ∼ Gamma(α, β). • Priors for the hyperparameters are often taken to be Gamma (or exponen...

We consider a class of haploid population models with nonoverlapping generations and fixed population size N assuming that the family sizes within a generation are exchangeable random variables. A weak convergence criterion is established for a properly scaled ancestral process as N → ∞. It results in a full classification of the coalescent generators in the case of exchangeable reproduction. I...

Serial determinations of the exchangeable sodium content and sodium24 (Na24) space were made by the radioisotope dilution method in patients with congestive failure during the course of intensive therapy. In most instances, the decrease in body weight was too great to be accounted for solely on the basis of the change in sodium24 space or exchangeable sodium content. This excess weight loss is ...

We define and study a family of Markov processes with state space the compact set of all partitions of N that we call exchangeable fragmentation-coalescence processes. They can be viewed as a combination of exchangeable fragmentation as defined by Bertoin and of homogenous coalescence as defined by Pitman and Schweinsberg or Möhle and Sagitov. We show that they admit a unique invariant probabil...

We present a generalization of Lindeberg’s method of proving the central limit theorem to encompass general smooth functions (instead of just sums) and dependent random variables. The technique is then used to obtain an invariance result for smooth functions of exchangeable random variables. As an illustrative application of this theorem, we then establish “convergence to Wigner’s law” for eige...

1. Potassium depletion was induced in rabbits with frusemide and measurements were made of plasma, leucocyte, erythrocyte and total exchangeable potassium before and during potassium depletion. 2. All measurements, except erythrocyte potassium expressed as mmol/kg of cells, decreased during the depletion period. 3. Significant correlations were observed between change in leucocyte potassium and...

We introduce the notion of exchangeable equilibria of a symmetric bimatrix game, defined as those correlated equilibria in which players’ strategy choices are conditionally independently and identically distributed given some hidden variable. The set of these equilibria is convex and lies between the symmetric Nash equilibria and the symmetric correlated equilibria. The notion of exchangeable e...

Seven patients with chronic renal failure treated with haemodialysis for 4 to 24 months were found to have low exchangeable potassium levels. Before dialysis the plasma potassium was normal or somewhat raised (possibly owing to acidosis), though the exchangeable potassium was low. Acidosis was corrected during dialysis; plasma potassium levels fell, but clinical and electrocardiographic changes...

The signature of a coherent system S is a feature of its structure function that, in the case when the lifetimes of the components of S are exchangeable, has a key role in the computation of the reliability function. We detail several aspects of this property and discuss the role that the concept of signature can have also for the case when the components’ lifetimes are not exchangeable.