Determining the relative contributions of mutation and selection to evolutionary change is a matter of great practical and theoretical significance. In this paper, we examine relative contributions of codon mutation rates and amino acid exchangeability on the frequencies of each type of amino acid difference in alignments of distantly related proteins, alignments of closely related proteins, an...

Conformal predictors are usually defined and studied under the exchangeability assumption. However, their definition can be extended to a wide class of statistical models, called online compression models, while retaining their property of automatic validity. This paper is devoted to conformal prediction under hypergraphical models that are more specific than the exchangeability model. Namely, ...

Abstract. The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to considering a finite horizon framework. However, assuming infinite exchangeability gives rise to fairly tractable a posteriori quantities, which is very at...

In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call symmetry property and the duality principle in option pricing. A particular attention is devoted to the case of asset prices driven by Lévy processes. Based o...

We define a natural partial exchangeability assumption for multi-class systems with Polish state spaces, under which we obtain results extending those for exchangeable systems: the conditional law of a finite system given the vector of the empirical measures of its classes corresponds to independent uniform permutations within classes, and the convergence in law of this vector is equivalent to ...

We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of finitely many coordinates). The relations we consider are defined by cocycles taking values in groups, including some nonabelian ones. This generalizes (half ...

The comparative analysis of protein sequences depends crucially on measures of amino acid similarity or distance. Many such measures exist, yet it is not known how well these measures reflect the operational exchangeability of amino acids in proteins, since most are derived by methods that confound a variety of effects, including effects of mutation. In pursuit of a pure measure of exchangeabil...

We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of finitely many coordinates). The relations we consider are defined by cocycles taking values in groups, including some nonabelian ones. This generalizes (half ...

We introduce a general framework for de Finetti reduction results, applicable to various notions of partially exchangeable probability distributions. Explicit statements are derived for the cases of exchangeability, Markov exchangeability, and some generalizations of these. Our techniques are combinatorial and rely on the “BEST” theorem, enumerating the Eulerian cycles of a multigraph.