emulation of utility functions over a set of permutations sequencing reliability growth tasks abstractwe consider bayesian design of experiments problems in which we maximise the prior expectation of a utility function over a set of permutations for example when sequencing a number of tasks to perform when the number of tasks is large and the expected utility is expensive to compute it may be unreasonable or infeasible to evaluate the expected utility of all permutations we propose an approach to emulate the expected utility using a surrogate function based on a parametric probabilistic model for permutations the surrogate function is fitted by maximising the correlation with the expected utility over a set of training points we propose a suitable transformation of the expected utility to improve the fit we provide results linking the correlation between the two functions and the number of expected utility evaluations to undertake the approach is applied to the sequencing of reliability growth tasks in the development of hardware systems in which there is a large number of potential tasks

an extended mallows model for ranked data aggregation in this article we study the rank aggregation problem which aims to find a consensus ranking by aggregating multiple ranking lists to address the problem probabilistically we formulate an elabo

on the separation of the cohomology of universal coverings of 1 convex surfaces abstract we construct a 1 convex surface x such that its universal covering x has the property that h 1 x o x is not separated

use of nested orthogonal contrasts in analyzing rank data abstract a data set consisting of 143 rankings of 10 occupations from a survey of goldberg has been analyzed in a number of recent papers the purpose of this paper is to use so called nested orthogonal contrasts of the occupations to gain further insight into the data a contrast is a comparison of subsets of the occupations based on their relative ranks contrasts are orthogonal if the comparisons they represent are not confounded various models based on sets of orthogonal contrasts including contingency table models models analogous to those of fligner and verducci and latent class models are applied to the data it is found that there are three main groups of occupations based on overall prestige and within each group are distinctions between managerial and technical occupations

multistage ranking models abstract suppose that a sample of people independently examines a fixed set of k items and then ranks these items according to personal judgment the process of ranking the items is decomposed into k 1 stages in the forward model the most preferred item is selected at the first stage the best of the remaining items is selected at the second stage and so on until the least preferred item is selected by default various probability models are adopted at each stage and properties of the resulting models for randomly sampled rankings are investigated luce 1959 first proposed such a modeling scheme where each item i was thought to have an intrinsic value i and the probability of choosing a particular item i at any stage conditional on the set s of items not previously chosen was given by i i s i j s j where i is an indicator function plackett 1975 began with the same model but added interaction terms that would theoretically extend the usefulness of this approach when the basic m

some approximate evidence factors in observational studies an observational study or nonrandomized experiment has exact evidence factors if it permits several statistically independent tests of the same null hypothesis h0 of no treatment effect where these several tests depend upon different assumptions about bias from nonrandom treatment assignment in an observational study we are typically uncertain about what assumptions truly describe treatment assignment if independent tests each reject h0 and if each of these tests is valid under assumptions about treatment assignment that would invalidate the others then rejection of h0 does not depend upon the truth of any one of these assumptions although exact evidence factors do exist the requirement of exact independence may limit the class of test statistics in ways that reduce pitman efficiency and design sensitivity so one might wish to be free of these limitations a much larger class of statistics permits approximate evidence factors which are not independent but which preserve some of the important con

evidence factors in observational studies some experiments involve more than one random assignment of treatments to units an analogous situation arises in certain observational studies although randomization is not used so each assignment may be biased if each assignment is suspect it is natural to ask whether there are separate pieces of information dependent upon different assumptions and perhaps whether conclusions about treatment effects are not critically dependent upon one or another suspect assumption the design of an observational study contains evidence factors if it permits several statistically independent tests of the same null hypothesis about treatment effects where these tests rely on different assumptions about treatment assignments at several levels of assignment two designs and two empirical examples are considered one example of each design in the dose control design there are matched pairs of a treated subject and an untreated control and doses of treatment vary between pairs for treated subjects this yields two evidence factors in the varied intensity design there are matched sets with two treated subjects and one or more untreated controls where the two treated subjects within the same matched set receive different doses of treatment and in a technically different way the design yields two evidence factors

convexity properties of coverings of 1 convex surfaces we prove that there exists a 1 convex surface whose universal covering does not satisfy the discrete disk property

models for distributions on permutations abstract a parametric distribution on permutations of k objects is derived from gamma random variables the probability of a permutation is set equal to the probability that k independent gamma random variables with common shape parameter and different scale parameters are ranked according to that permutation this distribution is motivated by considering a competition in which k players scoring points according to independent poisson processes are ranked according to the time until r points are scored the distributions obtained in this way include the popular luce plackett and thurstone mosteller daniels ranking models these gamma based distributions can serve as alternatives to the null ranking model in which all permutations are equally likely here the gamma models are used to estimate the probability distribution of the order of finish in a horse race when only the probability of finishing first is given for each horse gamma models with shape parameters larger than 1 are found to be superior to

unexpected distribution phenomenon resulting from cantor series expansions abstract we explore in depth the number theoretic and statistical properties of certain sets of numbers arising from their cantor series expansions as a direct consequence of our main theorem we deduce numerous new results as well as strengthen the known ones

posterior probabilities for a consensus ordering in the situation where subjects independently rank order a fixed set of items the idea of a consensus ordering of the items is defined and employed as a parameter in a class of probability models for rankings in the context of such models which generalize those of mallows posterior probabilities may be easily formed about the population consensus ordering an example of rankings obtained by the graduate record examination board is presented to demonstrate the adequacy of these generalized mallows models for describing actual data sets of rankings and to illustrate convenient summaries of the posterior probabilities for the consensus ordering

remarks on the identifiability of thurstonian ranking models case v case iii or neither it is well known that the representations of the thurstonian case iii and case v models for paired comparison data are not unique similarly when analyzing ranking data other equivalent covariance structures can substitute for those given by thurstone in these cases that is we may more broadly define the family of covariance structures satisfying case iii and case v conditions this paper introduces the notion of equivalence classes which defines a more meaningful partition of the covariance structures of the thurstonian ranking models in addition the equivalence classes of case v and case iii are completely characterized

the repeated insertion model for rankings missing link between two subset choice models several probabilistic models for subset choice have been proposed in the literature for example to explain approval voting data we show that marley et al s latent scale model is subsumed by falmagne and regenwetter s size independent model in the sense that every choice probability distribution generated by the former can also be explained by the latter our proof relies on the construction of a probabilistic ranking model which we label the repeated insertion model this model is a special case of marden s orthogonal contrast model class and in turn includes the classical mallows model as a special case we explore its basic properties as well as its relationship to fligner and verducci s multistage ranking model

a polynomial time algorithm for computing absolutely normal numbers we give an algorithm to compute an absolutely normal number so that the first n digits in its binary expansion are obtained in time polynomial in n in fact just above quadratic the algorithm uses combinatorial tools to control divergence from normality speed of computation is achieved at the sacrifice of speed of convergence to normality

on the compactification of concave ends let x be a complex manifold which admits a proper strictly plurisubharmonic function x a b where a b it is well known that the hausdorffness of h1 x is necessary for the existence of a stein completion of x we show that this condition is also sufficient

use of nonnull models for rank statistics in bivariate two sample and analysis of variance problems abstract a nonnull model for rank statistics based on kendall s tau has received quite a bit of attention in the ranking literature lately in this article we analyze this model with an eye towards applying it to situations in which nonparametric statistics such as kendall s tau the mann whitney wilcoxon u the jonckheere terpstra statistic the kruskal wallis statistic and friedman s statistic for randomized blocks designs are often used the data for the basic model are a pair of vectors of length n where both are permutations of the first n integers or one is a fixed and arbitrary design vector and the other a permutation the model is mallow s model a one parameter exponential family with natural statistic the number of discordant pairs between the two vectors this model originated with mann and has appeared in many articles since we extend the model to cases in which there may be ties in the observations and to analysis of variance problems in which there are several parameters the first

revealing subgroup structure in ranked data using a bayesian wand ranked data arise in many areas of application ranging from the ranking of up regulated genes for cancer to the ranking of academic statistics journals complications can arise when rankers do not

an example of a computable absolutely normal number the first example of an absolutely normal number was given by sierpinski in 1916 twenty years before the concept of computability was formalized in this note we give a recursive reformulation of sierpinski s construction which produces a computable absolutely normal number

parameter estimation for the thurstone case iii model a monte carlo study was conducted to investigate the ability of three estimation criteria to recover the parameters of case v and case iii models from comparative judgment data significant differences in recovery are shown to exist

turing s unpublished algorithm for normal numbers in an unpublished manuscript alan turing gave a computable construction to show that absolutely normal real numbers between 0 and 1 have lebesgue measure 1 furthermore he gave an algorithm for computing instances in this set we complete his manuscript by giving full proofs and correcting minor errors while doing this we recreate turing s ideas as accurately as possible one of his original lemmas remained unproved but we have replaced it with a weaker lemma that still allows us to maintain turing s proof idea and obtain his result

resource bounded randomness and weakly complete problems we introduce and study resource bounded random sets based on lutz s concept of resource bounded measure 5 6 we concentrate on nc randomness c 2 which corresponds to the polynomial time bounded p measure of lutz and which is adequate for studying the internal and quantative structure of e dtime 2lin first we show that the class of nc random sets has p measure 1 this provides a new simplified approach to p measure 1 results next we compare randomness with genericity in the sense of 1 2 and we show that nc 1 random sets are nc generic whereas the converse fails from the former we conclude thatnc random sets are not p btt complete for e our technical main results describe the distribution of the nc random sets under p m reducibility we show that every nc random set in e has nk random predecessors in e for any k 1 whereas the amount of randomness of the successors is bounded we apply this result to answer a question raised by lutz 8 we show that the class of weakly complete sets has measure 1 in e and that there are weakly complete problems which are not p btt complete for e

permutation probabilities as models for horse races summary some properties of models for the outcomes of races are described these properties being consequences of a stochastic ordering of the permutations which define the outcomes of a race order statistics models which lead to stochastic ordering are also discussedparticular cases of these are the first order model of plackett 1975 and the normal model of upton and brook 1974 an approximation for the normal model is suggested

distance based ranking models on examine le modele de type mallows pour une distance generale et on etudie ensuite les distances pour lesquelles le modele peut etre decompose en facteurs representant des etapes independantes dans le processus de classement