The quincunx: history and mathematics

Received: December 30, 1999; revised version: July 19, 2000     

Maximum entropy sampling and optimal Bayesian experimental design

When Shannon entropy is used as a criterion in the optimal design of experiments, advantage can be taken of the classical identity representing the joint entropy of parameters and observations as the sum of the marginal entropy of the observations and the preposterior conditional entropy of the parameters. Following previous work in which this idea was used in spatial sampling, the method is applied to standard parameterized Bayesian optimal experimental design. Under suitable conditions, which include non-linear as well as linear regression models, it is shown in a few steps that maximizing the marginal entropy of the sample is equivalent to minimizing the preposterior entropy, the usual Bayesian criterion, thus avoiding the use of conditional distributions. It is shown using this marginal formulation that under normality assumptions every standard model which has a two-point prior distribution on the parameters gives an optimal design supported on a single point. Other results include a new asymptotic formula which applies as the error variance is large and bounds on support size.     

On some probability distributions associated with random walks

The probability distribution of the total number of games to ruin in a gambler's ruin random walk with initial position n, the probability distribution of the total size of an epidemic starting with n cases and the probability distribution of the number of customers served during a busy period M/M/1 when the service starts with n waiting customers are identical. All these can be easily obtained by using Lagrangian expansions instead of long combinatorial methods. The binomial, trinomial, quadrinomial and polynomial random walks of a particle have been considered with an absorbing barrier at 0 when the particle starts its walks from a point n, and the pgfs. and the probability distributions of the total number of jumps (trials) before absorption at 0 have been obtained. The values for the mean and variance of such walks have also been given.     

Facilitating the Transition from Student to Social Worker: Challenges of the Younger Student

Abstract

The transition from student to social worker is a process which social work educators cannot control but can facilitate. Through classroom and field instruction faculty assumer responsibility of preparing students' professional knowledge, skills, and values; however, our responsibilities should extend beyond curriculum delivery. Drawing on Schlossberg's (1984) model of transitions, this article discusses two primary factors which affect the younger student in transition—developmental needs and the external environment—and strategies for assisting in the transition through intervention in academic advising and teaching roles.     

Involvement of Ministries of Health in Health Service Coverage Decisions: Is England an Aberrant Case?

This article examines the involvement of ministries of health in making health service coverage decisions in Denmark, England, France and Germany. The study aims to inform debate in England about the feasibility of reducing perceived ministerial and bureaucratic ‘interference’ in decisions affecting the National Health Service, based on interviews with senior government officials and other health system stakeholders. Ministries of health differ in their involvement in health system governance and coverage decisions (‘the benefits package’), reflecting differences in institutional arrangements. In all four countries, organizations at arm's length or independent from government are either involved in providing technical advice to the ministry of health or have been mandated to take these decisions themselves. However, ministries of health occasionally intervene in the decision‐making process or ignore the advice of these organizations. The Department of Health in England is not an aberrant case, at least in relation to coverage decisions. Indeed, ministries of health in Denmark and France play a larger role in making these decisions. Public pressure, often amplified by the media, is a shared reason for ministerial and ministry involvement in all four countries. This dynamic may thus limit the feasibility of attempts to further separate the NHS from both the Department of Health and wider political pressures.     

The behavior of estimated measures of association in small and moderate sample sizes for 2×3 tables

We consider the distributions of Goodman and Kruskal's G, Kendall's tau-b, and correlation coefficients rho and rho-s for sample sizes 10‘10’40 from 2×3 tables. The results are compared with asymptotic theory. It is found that the convergence of G to its asymptotic normal distribution is much slower than the convergence of the other measures to theirs, and that G is more likely to be significantly biased. However, the variances and biases of all four measures come close to their asymptotic values for quite moderate sample sizes.     

The pitman nearness criterion and its determination

A general method for determining Pitman Nearness is given In the case of univariate estimators. This method is then applied to some estimation problems. The concept of Pitman Nearness is also generalized to the multivariate case. The James-Stein estimators are used to illustrate the multivariate comparison.     

Chain ratio type estimator for ratio of two population m3ans using auxiliary characters

In this paper we have proposed chain ratio type estimators for ratio of two population means using two auxiliary characters. The expressions for bias and mean square error of these estimators have been derived. A comparison of the proposed estimator with that of double sampling estimator has been made in terms of mean square error. An emperical study has also been made.     

On the total sojourn time of particles in semi-markov compartmental system with branching particles

We consider a semi-Markov compartroental system with branching particles, Me study the total sojourn time of all the particles and obtain the asymptotic behaviour of its mean. We also discuss some special systems.     

A Preliminary Investigation of a Telephone Administration of the Quality of Marriage Index

Follow‐up data collection presents many challenges for longitudinal research. Validating paper‐and‐pencil assessments for use via telephone may alleviate these issues. This study evaluates psychometric properties of the Quality of Marriage Index (QMI; Norton, 1983, Journal of Marriage and the Family, 45, 141) when administered by telephone and compares scores with the paper‐and‐pencil version. Participants included women with major depressive disorder and dyadic discord and their male spouses (n = 24 couples). Results suggest excellent scale reliability for the verbal QMI. However, a significant mean difference was found: participants scored on average 3 points higher on the telephone‐administered QMI than on the written QMI. Recommendations for future research and clinical implications are discussed.