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Everitt, Richard G.; Johansen, Adam M.; Rowing, Ellen; EvdemonHogan, Melina
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8 Citations
Models for which the likelihood function can be evaluated only up to a parameterdependent unknown normalizing constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to the intractability of their likelihood functions. Several methods that permit exact, or close to exact, simulation from the posterior distribution have recently been developed. However, estimating the evidence and Bayes’ factors for these models remains challenging in general. This paper describes new random weight importance sampling and sequential Monte Carlo methods for estimating BFs that use simulation to circumvent the evaluation of the intractable likelihood, and compares them to existing methods. In some cases we observe an advantage in the use of biased weight estimates. An initial investigation into the theoretical and empirical properties of this class of methods is presented. Some support for the use of biased estimates is presented, but we advocate caution in the use of such estimates.
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Stanforth, Robert; Kolossov, Evgueni; Mirkin, Boris
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4 Citations
This paper further extends the ‘kernel’based approach to clustering proposed by E. Diday in early 70s. According to this approach, a cluster’s centroid can be represented by parameters of any analytical model, such as linear regression equation, built over the cluster. We address the problem of producing regressionwise clusters to be separated in the input variable space by building a hybrid clustering criterion that combines the regressionwise clustering criterion with the conventional centroidbased one.
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Torsney, Ben; Gunduz, Necla
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We consider the problem of deriving optimal designs for generalised linear models depending on several design variables. Ford, Torsney and Wu (1992) consider a two parameter/single design variable case. They derive a range of optimal designs, while making conjectures about Doptimal designs for all possible design intervals in the case of binary regression models. Motivated by these we establish results concerning the number of support points in the multidesignvariable case, an area which, in respect of nonlinear models, has uncharted prospects.
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Giglio, Beatrice; Wynn, Henry P.; Riccomagno, Eva
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The theory of mixture designs has a considerable history. We address here the important issue of the analysis of an experiment having in mind the algebraic interpretation of the structural restriction Σx_{i} = 1. We present an approach for rewriting models for mixture experiments, based on constructing homogeneous orthogonal polynomials using Gröbner bases. Examples are given utilising the approach.
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Besbeas, Panagiotis; Borysiewicz, Rachel S.; Morgan, Bryon J.T.
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10 Citations
A challenge for integrated population methods is to examine the extent to which different surveys that measure different demographic features for a given species are compatible. Do the different pieces of the jigsaw fit together? One convenient way of proceeding is to generate a likelihood for census data using the Kalman filter, which is then suitably combined with other likelihoods that might arise from independent studies of mortality, fecundity, and so forth. The combined likelihood may then be used for inference. Typically the underlying model for the census data is a statespace model, and capture–recapture methods of various kinds are used to construct the additional likelihoods. In this paper we provide a brief review of the approach; we present a new way to start the Kalman filter, designed specifically for ecological processes; we investigate the effect of breakdown of the independence assumption; we show how the Kalman filter may be used to incorporate densitydependence, and we consider the effect of introducing heterogeneity in the statespace model.
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ChuangStein, Christy; Kirby, Simon
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In this chapter, we compare successive trials designed and conducted to assess the efficacy of a new drug to a series of diagnostic tests. The condition to diagnose is whether the new drug has a clinically meaningful efficacious effect. This comparison offers us the opportunity to apply properties pertaining to diagnostic tests discussed in Chap. 3 to clinical trials. Building on the results in Chap. 3, we discuss why replication is such a critically important concept in drug development and show why replication is not as easy as some might have hoped. We end the chapter by highlighting the difference between statistical power and the probability of a positive trial. This last point becomes more important as a new drug moves through the various development stages as will be illustrated in Chap. 9.
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Higson, Edward; Handley, Will; Hobson, Michael; Lasenby, Anthony
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We introduce dynamic nested sampling: a generalisation of the nested sampling algorithm in which the number of “live points” varies to allocate samples more efficiently. In empirical tests the new method significantly improves calculation accuracy compared to standard nested sampling with the same number of samples; this increase in accuracy is equivalent to speeding up the computation by factors of up to
$$\sim 72$$
for parameter estimation and
$$\sim 7$$
for evidence calculations. We also show that the accuracy of both parameter estimation and evidence calculations can be improved simultaneously. In addition, unlike in standard nested sampling, more accurate results can be obtained by continuing the calculation for longer. Popular standard nested sampling implementations can be easily adapted to perform dynamic nested sampling, and several dynamic nested sampling software packages are now publicly available.
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By
Till, Roger
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The word statistics was first used in 1770, but with a rather different meaning from that used today. One chapter of Hooper’s The Elements of Universal Erudition published in 1770 is entitled ‘Statistics’ and deals with ‘the science that teaches us what is the political arrangement of all the modern States of the known world’ (Yule and Kendall, 1953). In the early decades of the nineteenth century the change to ‘statistics’ representing the characters of a State by numerical methods was taking place. Only by the end of the century were ‘statistics’ the summary figures used to describe and compare the properties of a set of observations. At about this time the theoretical basis of the science of statistics was being laid, and today we find the ideas of statistics on a firm basis and applied to the collection, summary and analysis of all types of data.
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Einbeck, Jochen; Meintanis, Simos
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A novel family of tests based on the self–consistency property is developed. Our developments can be motivated by the wellknown fact that a two–dimensional spherically symmetric distribution X is self–consistent with respect to the circle EX; that is, each point on that circle is the expectation of all observations that project onto that point. This fact allows the use of the self–consistency property in order to test for spherical symmetry. We construct an appropriate test statistic based on empirical characteristic functions, which turns out to have an appealing closed–form representation. Critical values of the test statistics are obtained empirically. The nominal level attainment of the test is verified in simulation, and the test power under several alternatives is studied. A similar test based on the self–consistency property is then also developed for the question of whether a given straight line corresponds to a principal component. The extendibility of this concept to further test problems for multivariate distributions is briefly discussed.
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By
Martin, R. J.; Jones, G.; Eccleston, J. A.
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4 Citations
Abstract.
Dependent observations commonly arise in factorial experiments. Apart from maineffects twolevel designs formed by the Cheng & Steinberg reverse foldover algorithm, which are known to be very efficient designs under dependence using the Dcriterion, little is known about other designs, models and criteria, and the range of possible behaviour. In this paper, we investigate in detail 8run twolevel designs.
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