Binary-image restoration

We consider the problem of binary-image restoration. The image being restored is not random, and we make no assumption about the nature of its contents. The estimate of the colour at each site is a fixed (the same for all sites) function of the data available in a neighbourhood of that site. Under this restriction, the estimate minimizing the overall mean squared error of prediction is the conditional expectation of the true colour given the observations in the neighbourhood of a site. The computation of this conditional expectation leads to the formal definition of the local characteristics of an image, namely, the frequency with which each pattern appears in the true unobserved image. When the “true” distribution of the patterns is unknown, it can be estimated from the records. The conditional expectation described above can then be evaluated using the estimated distribution of the patterns, and this procedure leads to a very natural estimate of the colour at each site. We propose two unbiased and consistent estimates for the distribution of patterns when the noise is a Gaussian white noise. Since the size of realistic images is very large, the estimated pattern distribution is usually close to the true one. This suggests that the estimated conditional expectation can be expected to be nearly optimal. An interesting feature of the proposed restoration methods is that they do not require prior knowledge of the local or global properties of the true underlying image. Several examples based on synthetic images show that the new methods perform fairly well for a variety of images with different degrees of colour continuity or textures.     

Bayesian binary segmentation procedure for detecting streakiness in sports

Summary.  When an individual player or team enjoys periods of good form, and when these occur, is a widely observed phenomenon typically called 'streakiness'. It is interesting to assess which team is a streaky team, or who is a streaky player in sports. Such competitors might have a large number of successes during some periods and few or no successes during other periods. Thus, their success rate is not constant over time. We provide a Bayesian binary segmentation procedure for locating changepoints and the associated success rates simultaneously for these competitors. The procedure is based on a series of nested hypothesis tests each using the Bayes factor or the Bayesian information criterion. At each stage, we only need to compare a model with one changepoint with a model based on a constant success rate. Thus, the method circumvents the computational complexity that we would normally face in problems with an unknown number of changepoints. We apply the procedure to data corresponding to sports teams and players from basketball, golf and baseball.     

Binary Event String Analysis: A Compact Numerical Representation of the Event Tree

While the event tree is a useful diagrammatic aid to an appreciation of various event sequence possibilities, it is of a nature that suggests no obvious manner in which the associated probability data may be compiled as computer input. Here, we propose a complementary numerical representation of scenario possibilities which incorporates probability data in a succinct fashion. While its mnemonic properties facilitate the logical development of a system's characteristics, its compactness and unambiguity permit its utilization directly as computer input.     

Alcohol Use and Prior Substance Abuse Treatment in Relation to Gambling Problem Severity and Gambling Treatment Outcome

Recent research has made it clear that problematic gambling is often accompanied by problematic alcohol use. Unfortunately, little is known about the nature of this association, especially as it relates to gambling treatment outcome. The purpose of this study is to explore the effect of current alcohol use level and previous substance abuse treatment on the symptoms of a large cohort of pathological gamblers as well as on their response to treatment for pathological gambling. The sample included 464 men and 301 women recruited at six gambling treatment programs in Minnesota. Gambling treatment patients were assessed on a number of gambling problem severity and related clinical variables using the Gambling Treatment Outcome Monitoring System (GAMTOMS). Patients with frequent alcohol use had greater gambling involvement at baseline than infrequent alcohol users. Patients with a previous history of substance abuse treatment had more severe psychosocial problems, ostensibly resulting from their gambling behavior, than patients without past substance abuse treatment. A MANOVA with repeated measures showed that neither pretreatment alcohol use, nor past substance abuse treatment exerted significant effects on gambling treatment outcome. While the level of pretreatment alcohol use and a history of substance abuse treatment are markers for greater gambling problem severity, treatment outcome for pathological gambling was not adversely impacted by these variables.     

Inverse Regression in Binary Response LDV Model

Sliced inverse regression, a link-free and distribution-free method, is applied to binary response limited dependent variable models. An inverse regression property of binary response LDV model is found. Based on this property, if the distributions of X _j (j = 1, 2,…, p) satisfy the linearity condition, then β can be estimated up to a positive multiplicative scalar without any assumptions on the distribution of error ε. Moreover, the estimator can be proved to be asymptotically normal based on which testing hypotheses are considered. Simulations results are reported.     

Monte-Carlo Sensitivity Analysis for Controlled Direct Effects Using Marginal Structural Models in the Presence of Confounded Mediators

In randomized trials, investigators are frequently interested in estimating the direct effect of a treatment on an outcome that is not relayed by intermediate variables, in addition to the usual intention-to-treat (ITT) effect. Even if the ITT effect is not confounded due to randomization, the direct effect is not identified when unmeasured variables affect the intermediate and outcome variables. Although the unmeasured variables cannot be adjusted for in the models, it is still important to evaluate the potential bias of these variables quantitatively. This article proposes a sensitivity analysis method for controlled direct effects using a marginal structural model that is an extension of the sensitivity analysis method of unmeasured confounding introduced in the context of observational studies. The proposed method is illustrated using a randomized trial of depression.     

Binary Regression with Stochastic Covariates

In binary regression the risk factor X has been treated in the literature as a non-stochastic variable. In most situations, however, X is stochastic. We present solutions applicable to such situations. We show that our solutions are more precise than those obtained by treating X as non-stochastic when, in fact, it is stochastic.     

Probabilistic frontier regression models for binary type output data

This paper proposes a probabilistic frontier regression model for binary type output data in a production process setup. We consider one of the two categories of outputs as ‘selected’ category and the reduction in probability of falling in this category is attributed to the reduction in technical efficiency (TE) of the decision-making unit. An efficiency measure is proposed to determine the deviations of individual units from the probabilistic frontier. Simulation results show that the average estimated TE component is close to its true value. An application of the proposed method to the data related to the Indian public sector banking system is provided where the output variable is the indicator of level of non-performing assets. Individual TE is obtained for each of the banks under consideration. Among the public sector banks, Andhra bank is found to be the most efficient, whereas the United Bank of India is the least.     

Bayesian sample‐size determination methods considering both worthwhileness and unpromisingness for exploratory two‐arm randomized clinical trials with binary endpoints

A randomized exploratory clinical trial comparing an experimental treatment with a control treatment on a binary endpoint is often conducted to make a go or no‐go decision. Such an exploratory trial needs to have an adequate sample size such that it will provide convincing evidence that the experimental treatment is either worthwhile or unpromising relative to the control treatment. In this paper, we propose three new sample‐size determination methods for an exploratory trial, which utilize the posterior probabilities calculated from predefined efficacy and inefficacy criteria leading to a declaration of the worthwhileness or unpromisingness of the experimental treatment. Simulation studies, including numerical investigation, showed that all three methods could declare the experimental treatment as worthwhile or unpromising with a high probability when the true response probability of the experimental treatment group is higher or lower, respectively, than that of the control treatment group.     

Edge Estimation in the Population of a Binary Tree Using Node-Sampling

Suppose a finite population of several vertices, each connected to single or multiple edges. This constitutes a structure of graphical population of vertices and edges. As a special case, the graphical population like a binary tree having only two child vertices associated to parent vertex is taken into consideration. The entire binary tree is divided into two sub-graphs such as a group of left-nodes and a group of right-nodes. This paper takes into account a mixture of graph structured and population sampling theory together and presents a methodology for mean-edge-length estimation of left sub-graph using right edge sub-graph as an auxiliary source of information. A node-sampling procedure is developed for this purpose and a class of estimators is proposed containing several good estimators. Mathematical conditions for minimum bias and optimum mean squared error of the class are derived and theoretical results are numerically supported with a test of 99% confidence intervals. It is shown that suggested class has a sub-class of optimum estimators, and sample-based estimates are closer to the true value of the population parameter.