On the Sample Information About Parameter and Prediction

The Bayesian measure of sample information about the parameter, known as Lindley's measure, is widely used in various problems such as developing prior distributions, models for the likelihood functions and optimal designs. The predictive information is defined similarly and used for model selection and optimal designs, though to a lesser extent. The parameter and predictive information measures are proper utility functions and have been also used in combination. Yet the relationship between the two measures and the effects of conditional dependence between the observable quantities on the Bayesian information measures remain unexplored. We address both issues. The relationship between the two information measures is explored through the information provided by the sample about the parameter and prediction jointly. The role of dependence is explored along with the interplay between the information measures, prior and sampling design. For the conditionally independent sequence of observable quantities, decompositions of the joint information characterize Lindley's measure as the sample information about the parameter and prediction jointly and the predictive information as part of it. For the conditionally dependent case, the joint information about parameter and prediction exceeds Lindley's measure by an amount due to the dependence. More specific results are shown for the normal linear models and a broad subfamily of the exponential family. Conditionally independent samples provide relatively little information for prediction, and the gap between the parameter and predictive information measures grows rapidly with the sample size.Comment: Published in at http://dx.doi.org/10.1214/10-STS329 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Class of Models for Uncorrelated Random Variables

We consider the class of multivariate distributions that gives the distribution of the sum of uncorrelated random variables by the product of their marginal distributions. This class is defined by a representation of the assumption of sub-independence, formulated previously in terms of the characteristic function and convolution, as a weaker assumption than independence for derivation of the distribution of the sum of random variables. The new representation is in terms of stochastic equivalence and the class of distributions is referred to as the summable uncorrelated marginals (SUM) distributions. The SUM distributions can be used as models for the joint distribution of uncorrelated random variables, irrespective of the strength of dependence between them. We provide a method for the construction of bivariate SUM distributions through linking any pair of identical symmetric probability density functions. We also give a formula for measuring the strength of dependence of the SUM models. A final result shows that under the condition of positive or negative orthant dependence, the SUM property implies independence

An investigation of the problems experienced by primary school teachers and beginning teachers in the Yemen Arab Republic

AS the title of the thesis suggests, this is a study of the problems and concerns experienced by student teachers in The Yemen at different stages in their training (second, third, first year of teaching). An initial exploratory case study of one teacher training institute, using interviews, was utilized to generate items for two questionnaires (about problems, and related beliefs respectively) completed by about 800 student -s in all 11 General Teacher Training Institutes in the country. The items covered several areas: School Material Conditions and Resources, Teaching Demands, Relationships with Professionals and Adults, Teaching Competencies, Institutes' Courses, Job Rewards, Pupils' Response to Teaching, and Students' Security. Applying Factor Analysis to the ratings of the total population for the 'problems' questionnaire showed no sufficiently strong structure of problems (patterns). Further analysis using commonsense categories showed that most problem areas were of great concern to the majority of student teachers and beginning teachers and these concerns were stable across stages, except for Students' Social/Emotional Security which showed consistently decreased concern over successive stages. When males and females were studied separately, the patterns of change were different, and diverse changes ii were found for the various (single-sex) institutes. Variables such as Background (Urban/Rural), Institutes attended, Primary School Location, Job Location for beginning teachers, seemed to be dominated to a large extent by sex differences. Males mainly expressed higher concern about job rewards, females about their own ability to cope with the tasks of classroom teaching. Variables such as Age within Stages, and Stage of Joining Institutes, did not appear to have influence upon students and beginning teachers' problems. The results of the 'Beliefs' questionnaire were analysed similarly and showed patterns of results which did not correspond with the 'Problems' results in a way which could allow the concerns to be explained by the belief s. The initial exploratory case study sample was followed longitudinally by interviews. This approach showed different patterns of increasing concerns on entry to teaching. Possible explanations for the different patterns are discussed. Interviews with a sample of institutes' lecturers suggest an awareness by the majority of lecturers of some of the common problems expressed by student teachers. iii The substantive findings and methodological issues are discussed in relation to the literature (e. g. Fuller, Gibson, Lacey... ). Some suggestions for improving teacher education in The Yemen are offered

Exploring Deep Learning Techniques for Glaucoma Detection: A Comprehensive Review

Glaucoma is one of the primary causes of vision loss around the world, necessitating accurate and efficient detection methods. Traditional manual detection approaches have limitations in terms of cost, time, and subjectivity. Recent developments in deep learning approaches demonstrate potential in automating glaucoma detection by detecting relevant features from retinal fundus images. This article provides a comprehensive overview of cutting-edge deep learning methods used for the segmentation, classification, and detection of glaucoma. By analyzing recent studies, the effectiveness and limitations of these techniques are evaluated, key findings are highlighted, and potential areas for further research are identified. The use of deep learning algorithms may significantly improve the efficacy, usefulness, and accuracy of glaucoma detection. The findings from this research contribute to the ongoing advancements in automated glaucoma detection and have implications for improving patient outcomes and reducing the global burden of glaucoma

Multivariate dynamic information

AbstractThis paper develops measures of information for multivariate distributions when their supports are truncated progressively. The focus is on the joint, marginal, and conditional entropies, and the mutual information for residual life distributions where the support is truncated at the current ages of the components of a system. The current ages of the components induce a joint dynamic into the residual life information measures. Our study of dynamic information measures includes several important bivariate and multivariate lifetime models. We derive entropy expressions for a few models, including Marshall–Olkin bivariate exponential. However, in general, study of the dynamics of residual information measures requires computational techniques or analytical results. A bivariate gamma example illustrates study of dynamic information via numerical integration. The analytical results facilitate studying other distributions. The results are on monotonicity of the residual entropy of a system and on transformations that preserve the monotonicity and the order of entropies between two systems. The results also include a new entropy characterization of the joint distribution of independent exponential random variables

Elevation of CD56brightCD16- lymphocytes in MDR pulmonary tuberculosis

Background: Protective immune responses induced in the majority of people infected with Mycobacterium tuberculosis enable them to control TB infection. Objective: The aim of this study was to investigate CD56 and CD16 positive peripheral blood mononuclear cells (PBMCs) and leukocyte subsets from multi-drug resistant pulmonary tuberculosis (MDR-TB), and compare them with nonresistant (NR) TB patients and healthy controls. Methods: 13 MDR-tuberculosis patients, 20 NR-TB individuals and 40 healthy subjects were included. Peripheral blood mononuclear cells were double stained with fluorochrome conjugated antibodies against CD56 and CD16 cell surface markers. The phenotype of positive cells was then analyzed by flow cytometry and the percent- ages of CD56+ CD16+, CD56- CD16+, CD56dimCD16+/-, and CD56brightCD16+/- subsets were calculated. Results: There was a significant decline in the percentage of CD56+CD16+ lymphocytes in both MDR and NR-TB patients compared with healthy controls. We also observed lower proportions of CD56dim/brightCD16+ in addition to higher percentages of CD56dim/brightCD16- subsets in all TB patients (p�0.05). In MDR- TB, our findings demonstrated a distinct phenotypic feature with increased levels of CD56brightCD16- in comparison with both NR-TB and healthy subjects. Conclusion: Considering the function of CD56/CD16 expressing cells in TB, we suggest that pheno- typic characteristics of PBMCs in MDR-TB may correlate with their status of drug re- sistance and probably with their high mortality rates