To investigate whether a variable tends to be larger in one population than another, the t test is standard procedure. In some situations, parametric inappropriate, and nonparametric procedure should used instead. The default Mann-Whitney’s U test. Despite being test, associated with strong assumption, known as exchangeability. I demonstrate that if exchangeability violated, can lead wrong stat...

According to Bruno de Finetti’s Representation Theorem, exchangeable beliefs over infinite sequences of observable Bernoulli quantities can be represented as mixtures of independent coin tossing experiments. Extensions of this theorem give rise to representations as mixtures of other familiar sampling distributions. This paper offers a subjectivist primer based on the premise that appreciation ...

Popular algorithms for optimal design do not account for non-exchangeability of the basic experimental units. This paper introduces an algorithm for searching for D-optimal experimental designs in the presence of certain kinds of non-exchangeability|in particular, when there are xed covariates associated with units and/or when the units have a non-trivial covariance structure; this algorithm ex...

Though the notion of exchangeability has been discussed in causal inference literature under various guises, it rarely taken its original meaning as a symmetry property probability distributions. As this is standard component Bayesian inference, we argue that natural to link model, including confounding and definition contrasts interest, concept exchangeability. Here, propose probabilistic betw...

Multiagent sequential decision making has seen rapid progress with formal models such as decentralized MDPs and POMDPs. However, scalability to large multiagent systems and applicability to real world problems remain limited. To address these challenges, we study multiagent planning problems where the collective behavior of a population of agents affects the joint-reward and environment dynamic...

We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum random trees; second-order limits of distances in random graphs; isometry classes of metric spaces with probability measures; limits of dense random graphs; ...

The general concept of exchangeability allows the more flexible modelling of most experimental setups. The representation theorems for exchangeable sequences of random variables establish that any coherent analysis of the information thus modelled requires the specification of a joint probability distribution on all the parameters involved, hence forcing a Bayesian approach. The concept of part...

We discuss the implications of Bayes’ postulate in the setting of exchangeable Bernoulli random variables. Bayes’ postulate, here, stipulates a uniform distribution on the total number of successes in any number of trials. For an infinite sequence of exchangeable Bernoulli variables the conditions of Bayes’ postulate are equivalent to a uniform (prior) distribution on the underlying mixing vari...