Probability inequalities for continuous unimodal random variables with finite support

A paramecer-free Bernstein-type upper bound is derived for the probability that the sum S of n i.i.d, unimodal random variables with finite support, X₁ ,X₂,…,X_n, exceeds its mean E(S) by the positive value nt. The bound for P{S - nμ ≥ nt} depends on the range of the summands, the sample size n, the positive number t, and the type of unimodality assumed for X_i. A two-sided Gauss-type probability inequality for sums of strongly unimodal random variables is also given. The new bounds are contrasted to Hoeffding's inequality for bounded random variables and to the Bienayme-Chebyshev inequality. Finally, the new inequalities are applied to a classic probability inequality example first published by Savage (1961).     

Academic Affiliations of Those Published in Social Work Journals: A Productivity Analysis, 1989–1993

Abstract

The academic affiliations of the authors of all articles published in six social work journals between 1989 and 1993 were reviewed and tabulated to produce a ranking of the colleges and universities whose faculty are making the most substantive contributions to the social work literature. The results of this analysis are compared with the findings of two similar, previously published studies covering the five-year periods of 1979-1983 and 1984-1988.     

On the choice of the prior distribution in hypergeometric sampling

Information in a statistical procedure arising from sources other than sampling is called prior information, and its incorporation into the procedure forms the basis of the Bayesian approach to statistics. Under hypergeometric sampling, methodology is developed which quantifies the amount of information provided by the sample data relative to that provided by the prior distribution and allows for a ranking of prior distributions with respect to conservativeness, where conservatism refers to restraint of extraneous information embedded in any prior distribution. The most conservative prior distribution from a specified class (each member of which carries the available prior information) is that prior distribution within the class over which the likelihood function has the greatest average domination. Four different families of prior distributions are developed by considering a Bayesian approach to the formation of lots. The most conservative prior distribution from each of the four families of prior distributions is determined and compared for the situation when no prior information is available. The results of the comparison advocate the use of the Polya (beta-binomial) prior distribution in hypergeometric sampling.     

Integrating performance and risk aspects of supply chain design processes

Abstract

Supply chain design is a complex and relatively poorly structured process, involving choosing many decisional parameters and it usually requires consideration of numerous sources of uncertainty. Many conventional processes of supply chain design involve taking a deterministic approach, using point estimates, on important measures of supply chain effectiveness such as cost, quality, delivery reliability and service levels. Supply chain disruptions are often separately considered as risks, both in the research literature and in practice, meaning that a purely traditional risk management and risk minimization approach is taken. We have developed and applied an approach that combines the intellect and experience of the supply chain designer with the power of evaluation provided by a Monte Carlo simulation model, which uses decision analysis techniques to explicitly incorporate the full spectrum of uncertain quantities across the set of alternative supply chain designs being considered. After defining and setting out the general decision variables and uncertainty factors for 16 distinct supply chain design decision categories, we then apply that approach to combine the decision-makers’ heuristics with the probabilistic modeling approach, iteratively, to achieve the best of both elements of such an approach. This novel approach to fully integrating performance and risk elements of supply chain designs is then illustrated with a case study. Finally, we call for further developmental research and field work to refine this approach.     

Question Order and Fair Play: Evidence of Even-Handedness in Rural Surveys1

The norm of even-handedness is a question-order effect known to occur in face-to-face interviews when respondents favor one of two complementary or competing opinion questions, both written at the same level of specificity. After defining and illustrating the concept, evidence of even-handedness in opinion questions is explored in a Montana mail survey and in recall of recent behavior in Iowa telephone interviews. The Montana survey provides evidence of education effects that are not consistent with previous theories of cognitive sophistication, suggesting that future research must consider the interaction between substantive issues and cognitive processes. The Iowa poll provides evidence that respondents' recall of their recent behaviors and the behaviors of their partner also are subject to context effects. This poll also provides evidence that even-handedness operates independently of social desirablity, especially among women.     

Construction of the nearest neighbor embracing graph of a point set

This paper gives optimal algorithms for the construction of the Nearest Neighbor Embracing Graph (NNE-graph) of a given point set V of size n in the k-dimensional space (k-D) for k = 2,3. The NNE-graph provides another way of connecting points in a communication network, which has lower expected degree at each point and shorter total length of connections with respect to those using Delaunay triangulation. In fact, the NNE-graph can also be used as a tool to test whether a point set is randomly generated or has some particular properties. We show that in 2-D the NNE-graph can be constructed in optimal time in the worst case. We also present an time algorithm, where d is the -th largest degree in the utput NNE-graph. The algorithm is optimal when . The algorithm is also sensitive to the structure of the NNE-graph, for instance when , the number of edges in NNE-graph is bounded by for any value g with . We finally propose an time algorithm for the problem in 3-D, where d and are the -th largest vertex degree and the largest vertex degree in the NNE-graph, respectively. The algorithm is optimal when the largest vertex degree of the NNE-graph is .     

DIVINATORY DISCOURSE*

Using data from an ethnographic study of tarot divination, occult claims to knowledge are analyzed and interpreted. Attention is focused on the procedures parties to occult divination employ to claim and sustain what they regard as extraordinary knowledge. This view of occult knowledge stands opposed to efforts to discredit occult claims as unscientific or the result of psychosocial conditions like deprivation and marginality. Like knowledge in general, occult knowledge is a product of sociohistorical influences, interactional negotiation, and interpretation. The challenge for sociology therefore is the pursuit of the social interactional and historical processes whereby knowledge and interpretation are accomplished in everyday life.     

Smokers' behavioural responses before and after the 2012 tobacco excise increase

The New Zealand tobacco tax has been increased annually since 2010, and this paper determines the short-term impacts of the 2012 tax increase. We analysed two separate sets of telephone surveys of current smokers and recent quitters conducted over a six-month period (three months before and three months after the tax increase), and compared the level of behaviour change before and after the tax increase. We found that the 14.5% increase in tobacco excise had an impact on smokers. From both surveys, we saw an increase in smoking-related behavioural change (quit/tried to quit/cut down). However, the rate of change was different by ethnicity and past three-month quit attempt status. Specifically, non-Māori and those who have made a recent quit attempt had increased likelihood of reporting a smoking-related change. Despite being a major priority target group in tobacco control, Māori smokers were not benefited by the 2012 increase in tax excise.     

Approximating <Emphasis Type="Italic">k</Emphasis>-generalized connectivity via collapsing HSTs

An instance of the k -generalized connectivity problem consists of an undirected graph G=(V,E), whose edges are associated with non-negative costs, and a collection \({\mathcal{D}}=\{(S_{1},T_{1}),\ldots,(S_{d},T_{d})\}\) of distinct demands, each of which comprises a pair of disjoint vertex sets. We say that a subgraph ??G connects a demand (S _i ,T _i ) when it contains a path with one endpoint in S _i and the other in T _i . Given an integer parameter k, the goal is to identify a minimum cost subgraph that connects at least k demands in \({\mathcal{D}}\).Alon, Awerbuch, Azar, Buchbinder and Naor (SODA ’04) seem to have been the first to consider the generalized connectivity paradigm as a unified machinery for incorporating multiple-choice decisions into network formation settings. Their main contribution in this context was to devise a multiplicative-update online algorithm for computing log-competitive fractional solutions, and to propose provably-good rounding procedures for important special cases. Nevertheless, approximating the generalized connectivity problem in its unconfined form, where one makes no structural assumptions about the underlying graph and collection of demands, has remained an open question up until a recent O(log?² nlog?² d) approximation due to Chekuri, Even, Gupta and Segev (SODA ’08). Unfortunately, the latter result does not extend to connecting a pre-specified number of demands. Furthermore, even the simpler case of singleton demands has been established as a challenging computational task, when Hajiaghayi and Jain (SODA ’06) related its inapproximability to that of dense k -subgraph.In this paper, we present the first non-trivial approximation algorithm for k-generalized connectivity, which is derived by synthesizing several techniques originating in probabilistic embeddings of finite metrics, network design, and randomization. Specifically, our algorithm constructs, with constant probability, a feasible subgraph whose cost is within a factor of O(n ^2/3?polylog(n,k)) of optimal. We believe that the fundamental approach illustrated in the current writing is of independent interest, and may be applicable in other settings as well.     

Mobile facility location: combinatorial filtering via weighted occupancy

An instance of the mobile facility location problem consists of a complete directed graph \(G = (V, E)\) , in which each arc \((u, v) \in E\) is associated with a numerical attribute \(\mathcal M (u,v)\) , representing the cost of moving any object from \(u\) to \(v\) . An additional ingredient of the input is a collection of servers \(S = \{ s_1, \ldots , s_k \}\) and a set of clients \(C = \{ c_1, \ldots , c_\ell \}\) , which are located at nodes of the underlying graph. With this setting in mind, a movement scheme is a function \(\psi : S \rightarrow V\) that relocates each server \(s_i\) to a new position, \(\psi ( s_i )\) . We refer to \(\mathcal M ( s_i, \psi ( s_i ) )\) as the relocation cost of \(s_i\) , and to \(\min _{i \in [k]} \mathcal M (c_j, \psi ( s_i ) )\) , the cost of assigning client \(c_j\) to the nearest final server location, as the service cost of \(c_j\) . The objective is to compute a movement scheme that minimizes the sum of relocation and service costs. In this paper, we resolve an open question posed by Demaine et al. (SODA ’07) by characterizing the approximability of mobile facility location through LP-based methods. We also develop a more efficient algorithm, which is based on a combinatorial filtering approach. The latter technique is of independent interest, as it may be applicable in other settings as well. In this context, we introduce a weighted version of the occupancy problem, for which we establish interesting tail bounds, not before demonstrating that existing bounds cannot be extended.