LENGTH-BIASING, CHARACTERIZATIONS OF LAWS AND THE MOMENT PROBLEM

A positive random variable X with a finite mean has an induced length-biased law represented by Y, and Y is stochastically larger than X. An independent uniform random contraction of Y, UY, has the same law as X if and only if the latter is exponential. This property is extended to non-uniform contractions and a more general notion of length-biasing. The distributional equality of X and W leads to a functional equation for the moment function of X, which has either Infinitely many solutions or none. When U is constant, X can have a log-normal law, but it can also have laws with the same moment sequence as this log-nod law. The case where U has a certain beta, or generalized beta, law give t3 characterizations of generalized gamma laws, or to products of independent copies of them. This occurs even when these laws are not determined by their moment sequences.     

Fast retraction of evidence in a probabilistic expert system

We present and justify a propagation algorithm to facilitate the simultaneous calculation, for every node in a probabilistic exper system of the distribution of the associated random quantity, conditional on all the evidence obtained about the remaining nodes.     

The Farm Crisis and Mental Health: A Longitudinal Study of the 1980s1

Abstract This paper examines rural/urban differences and trends in mental health during the farm crisis of the 1980s in a large panel sample from a midwestern state. A community research perspective, which attributes differences to life styles, culture, and community context, is contrasted with an economic stress perspective, which focuses on individual differences in economic circumstances as determinants of rural-urban differences in mental health. Survey samples from 1981, 1986, and 1989 are used to examine differences among seven categories of community type. Multiple regression analysis of the trend and panel data provide support for both the individual economic distress and community context models.     

A note on inverse estimation in non-linear models

The problem of estimating the value of an x variable for a given proportion of an observed value of the y variable is consdered for a non-linear model. Asymptotic confidence limits are obtained and an application of the method is illustrated witreal data.     

Children's gender- and age-based categorization in similarity and induction tasks

The present studies examined children's and adults' preferences for gender- or age-based categorization using similarity and inductive inference tasks. Four-year-olds, 6-year-olds, and adults looked at pictures of people and decided which of two was more like a target (similarity condition) or which shared a novel age- or gender-related property with the target (inference condition). Age or gender-based matches were possible. The results are consistent with previous findings that gender-based classification decreases with age. However, they also demonstrate that children use gender more for judging similarity than for making inferences about novel properties. Distinct patterns emerge from the two tasks: 6-year-olds and adults in both conditions categorize more by age than gender; 4-year-olds categorize by gender more than age in the similarity task, but by age more in the induction task. Only adults differentiated by property in the inference condition. These findings suggest that the salience of gender categories cannot entirely be attributed to their inductive potential. Gender has a salience beyond what would be predicted by its power for directing novel generalizations.     

The current state of the labor queue: National and regional Evidence

We employ vector autoregressive techniques to determine the current state of the labor queue. Unemployment rate differentials have narrowed in recent years, potentially due to a change in the queue ordering, though a tight labor market and a stable queue would yield similar results. We find no evidence that the queue ordering has changed, which brings into question the resiliency of gains made by minority groups. We employ the same techniques to reveal the state of the queue across geographic regions and find that substantial differences exist across regions, implying variation in the relative labor force status of demographic groups.     

Statistics for weighing benefits and harms in a proposed genetic substudy of a randomized cancer prevention trial

Summary.  When evaluating potential interventions for cancer prevention, it is necessary to compare benefits and harms. With new study designs, new statistical approaches may be needed to facilitate this comparison. A case in point arose in a proposed genetic substudy of a randomized trial of tamoxifen versus placebo in asymptomatic women who were at high risk for breast cancer. Although the randomized trial showed that tamoxifen substantially reduced the risk of breast cancer, the harms from tamoxifen were serious and some were life threaten-ing. In hopes of finding a subset of women with inherited risk genes who derive greater bene-fits from tamoxifen, we proposed a nested case–control study to test some trial subjects for various genes and new statistical methods to extrapolate benefits and harms to the general population. An important design question is whether or not the study should target common low penetrance genes. Our calculations show that useful results are only likely with rare high penetrance genes.     

Bayesian analysis of a marked point process: Application in seismic hazard assessment

Point processes are the stochastic models most suitable for describing physical phenomena that appear at irregularly spaced times, such as the earthquakes. These processes are uniquely characterized by their conditional intensity, that is, by the probability that an event will occur in the infinitesimal interval (t, t+Δt), given the history of the process up tot. The seismic phenomenon displays different behaviours on different time and size scales; in particular, the occurrence of destructive shocks over some centuries in a seismogenic region may be explained by the elastic rebound theory. This theory has inspired the so-called stress release models: their conditional intensity translates the idea that an earthquake produces a sudden decrease in the amount of strain accumulated gradually over time along a fault, and the subsequent event occurs when the stress exceeds the strength of the medium. This study has a double objective: the formulation of these models in the Bayesian framework, and the assignment to each event of a mark, that is its magnitude, modelled through a distribution that depends at timet on the stress level accumulated up to that instant. The resulting parameter space is constrained and dependent on the data, complicating Bayesian computation and analysis. We have resorted to Monte Carlo methods to solve these problems.     

Population constraints on pooled surveys in demographic hazard modeling

In non-experimental research, data on the same population process may be collected simultaneously by more than one instrument. For example, in the present application, two sample surveys and a population birth registration system all collect observations on first births by age and year, while the two surveys additionally collect information on women’s education. To make maximum use of the three data sources, the survey data are pooled and the population data introduced as constraints in a logistic regression equation. Reductions in standard errors about the age and birth-cohort parameters of the regression equation in the order of three-quarters are obtained by introducing the population data as constraints. A halving of the standard errors about the education parameters is achieved by pooling observations from the larger survey dataset with those from the smaller survey. The percentage reduction in the standard errors through imposing population constraints is independent of the total survey sample size.