A review of representation issues and modeling challenges with influence diagrams

Since their introduction in the mid 1970s, influence diagrams have become a de facto standard for representing Bayesian decision problems. The need to represent complex problems has led to extensions of the influence diagram methodology designed to increase the ability to represent complex problems. In this paper, we review the representation issues and modeling challenges associated with influence diagrams. In particular, we look at the representation of asymmetric decision problems including conditional distribution trees, sequential decision diagrams, and sequential valuation networks. We also examine the issue of representing the sequence of decision and chance variables, and how it is done in unconstrained influence diagrams, sequential valuation networks, and sequential influence diagrams. We also discuss the use of continuous chance and decision variables, including continuous conditionally deterministic variables. Finally, we discuss some of the modeling challenges faced in representing decision problems in practice and some software that is currently available.     

论英国侵藏新阶段的开启--以贝尔对十三世达赖喇嘛的笼络为例

英国人贝尔边境工作经验丰富,很早就对西藏兴趣浓厚。1908年接管西藏事务后,即通过各种方式加强与西藏的联系,特别是在十三世达赖喇嘛流亡印度期间,二者建立相互间的“信任”与“友谊”。作为英印边境骨干官员,贝尔通过对西藏所谓的援助和“现代化”,成功地实施了英国的一些殖民政策,形成了英国渗透西藏的新模式。因此,有必要对英国侵略西藏过程中的实施者予以详细研究,希望可以管窥此一历史时期英国对外殖民方式,以期拓宽英国侵华史的研究。     

Deducing simple majorities from approval voting ballot data

An approval voting election allows each voter to vote for as many candidates as he wishes. The winner of such an election is the candidate with the most approval votes. Ballot data aggregated for individual voters tell how many voters voted for each subset of candidates. Given reasonable assumptions about what voters' ballots reveal about their preferences, this report shows what must be true of the ballot data in order to conclude that the electorate has a majority preference for one candidate over another. A simple corollary tells what must be true of the ballot data to conclude that the winner is preferred by a majority of voters to every other candidate. Both hypothetical and reconstructed ballot data from a mayoral election in Boston are used to illustrate the results. It is also shown that the likelihood of being able to draw conclusions about majority candidates tends to increase as voters tend to vote for fewer candidates.     

A modification of the Fisher-Cornish approximation for the student t percentiles

An asymptotic expansion of the Student t distribution is derived by expanding the standardized Student t distribution in terms of the normal distribution. This expansion is inverted to obtain corresponding asymptotic expansions for the Student t percentiles as functions of the standard normal percentiles0 Using the first two, three or four terms of these expansions, we get approximations of the Student t percentiles which are generally more accurate than the approximations given by Fisher and Cornish(1960) and Koehler (1983).An approximation of the distribution function obtained from this expansion is compared with the approximations discussed by Ling (1978) andfound to be more accurate for moderate degrees of freedom.     

On Stein Identity,Chernoff Inequality,and Orthogonal Polynomials

In this article, we present a general method for deriving Stein-like identity and Chernoff-like inequality based on orthogonal polynomials. In order to illustrate our method, some applications are given with respect to normal, Gamma, Beta, Poisson, binomial, and negative binomial distribution, not only for random variables but also for random vectors, resulting corresponding Stein-like identity and Chernoff-like inequality are obtained consequently. Within our best knowledge, some of our matrix version results are new in the literature. In addition, forward difference formulae of Charlier polynomials, Krawtchouk polynomials and Meixner polynomials, Stein-like identity, and Chernoff-like inequality with respect to Beta distribution, as well as Rodrigues formula of Meixner polynomials are also prepared in the first time within our limited information. Interestingly, as far as normal, Gamma, Beta, Poisson, binomial, and negative binomial distribution are concerned, we found that their Stein-like identity and corresponding Chernoff-like inequality are related closely, by examining their Rodrigues formula.     

Inference in affine shape theory under elliptical models

This paper studies the elliptical statistical affine shape theory under certain particular conditions on the evenness or oddness of the number of landmarks. In such a case, the related distributions are polynomials, and the inference is easily performed; as an example, a landmark data is studied, and the performance of the polynomial density versus the usual series density is compared.     

Testing sphericity using small samples

It is shown here that with small sample sizes, the null distribution of the ellipticity, or sphericity, likelihood criterion W(n, p) can be obtained very accurately, either by computation using the Meijer function, or by Monte Carlo simulation. Testing in repeated measures design can now be carried out with much more accuracy.     

Empiric bayes estimation of binomial probability

An empirical Bayes estimator of a binomial parameter, based on orthogonal polynomials on (0,1), is introduced. The resulting estimator of the prior density is asymptotically optimal. The method allows one to combine Bayes and empiric Bayes methods with smoothing in a natural way.     

Normality testing for a long-memory sequence using the empirical moment generating function

Moment generating functions and more generally, integral transforms for goodness-of-fit tests have been in use in the last several decades. Given a set of observations, the empirical transforms are easy to compute, being simply a sample mean, and due to uniqueness properties, these functions can be used for goodness-of-fit tests. This paper focuses on time series observations from a stationary process for which the moment generating function exists and the correlations have long-memory. For long-memory processes, the infinite sum of the correlations diverges and the realizations tend to have spurious trend like patterns where there may be none. Our aim is to use the empirical moment generating function to test the null hypothesis that the marginal distribution is Gaussian. We provide a simple proof of a central limit theorem using ideas from Gaussian subordination models (Taqqu, 1975) and derive critical regions for a graphical test of normality, namely the T₃-plot ( Ghosh, 1996). Some simulated and real data examples are used for illustration.