This talk aims to introduce a Bayesian idea on multiple comparisons or simultaneous inference. Instead of constructing statistics for comparing variety means in pairs, we start with an infinitely exchangeable Gaussian prior for the variety effects such that each pair of varieties is equal with positive prior probability. Consistency conditions on joint exchangeable priors involving set partitio...

For a bivariate random vector (X, Y ), symmetry conditions are presented that yield stochastic orderings among |X|, |Y |, |max(X, Y )|, and |min(X, Y )|. Partial extensions of these results for multivariate random vectors (X1, ..., Xn) are also given.

Under weak and reasonable assumptions, mainly that data are exchangeable under the null hypothesis, permutation tests can provide exact control of false positives and allow the use of various non-standard statistics. There are, however, various common examples in which global exchangeability can be violated, including paired tests, tests that involve repeated measurements, tests in which subjec...

In current practice, such as GWAS (genome-wide association studies), permutation is often applied to multiple testing for association between large number of features [e.g. single nucleotide polymorphisms (SNPs)] and phenotypes (Hahn et al., 2008). Inferring that there is a difference between the phenotypic groups X and Y in some of the features is not very useful. One has to know for which fea...

We compare the data obtained through time diaries and survey questions on time use. Based on German data, we assess the exchangeability of time diary and survey estimates for several statistics. We find that both measures yield rather consistent findings. We interpret this rather good congruence of our time budgets as a result of our decomposed survey questions.

This paper presents an approach to designing adaptive learning environments based on IMS LD, which separates its elements (i.e. objectives, prerequisites, method, learning activities, adaptive rules, personalization properties, etc.) in order to use them in different Learning Designs and enforce their reusability and exchangeability. Moreover, it briefly presents an authoring tool under develop...

We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of “symmetric measure”: exchangeability and the Gibbs (or conformal) property. We show that equilibrium measures for such shifts (unique and weak Bernoulli in the one dimensional case) exhibit a variety of spectral properties.

Despite the small numbers that appear in the table, L-N invited us to expand the sample size by whatever proportion to make it a large-sample scenario – accidental correlation due to sample variation is not an issue here. Calculate the relative frequencies, and we find a standard case of Simpson’s reversal: P(Y=1 | X=1) > P(Y=1 | X=0), but P(Y=1 | X=1, Z=0) < P(Y=1 | X=0, Z=0) and P(Y=1 | X=1, ...