Cluster’s Number Free Bayes Prediction of General Framework on Mixture of Regression Models

Prediction based on a single linear regression model is one of the most common way in various field of studies. It enables us to understand the structure of data, but might not be suitable to express the data whose structure is complex. To express the structure of data more accurately, we make assumption that the data can be divided in clusters, and has a linear regression model in each cluster. In this case, we can assume that each explanatory variable has their own role; explaining the assignment to the clusters, explaining the regression to the target variable, or being both of them. Introducing probabilistic structure to the data generating process, we derive the optimal prediction under Bayes criterion and the algorithm which calculates it sub-optimally with variational inference method. One of the advantages of our algorithm is that it automatically weights the probabilities of being each number of clusters in the process of the algorithm, therefore it solves the concern about selection of the number of clusters. Some experiments are performed on both synthetic and real data to demonstrate the above advantages and to discover some behaviors and tendencies of the algorithm.

Pareto Type-II Model under Type-I Progressive Hybrid Censoring: Bound Lengths

The Pareto Type-II model is considered here from which, the observable is to be predicted by using Bayesian approach. The Bayes prediction bound lengths are obtained for Type-I progressive hybrid censored data. Both One-sample and Two-sample Bayes prediction scenario has included in the present study. Both known and unknown cases of the scale parameter have considered in the present study. A comparison also has made with the asymptotic interval estimates, are made-up from the Fisher information matrix. Performance of the different methods has studied by simulation and a real data set.

Bayes Prediction Bound Lengths Under Dierent Censoring Criterion: A Two-Sample Approach

The censoring arises when exact lifetimes are known partially only and it is useful inlife testing experiments for time and cost restrictions. In literature, there are several typesof censoring plans available. In which three dierent censoring plans have addressed inpresent comparative study. The Burr Type-XII distribution considered here as the under-lying model and the comparison made on Two-Sample Bayes prediction bound lengths.The analysis of the present discussion has carried out by an example.

Bound lengths based on constant-stress PALT under different censoring patterns

The Gompertz distribution is assumed in the present article for drawing the inferences based on Bayesian methodology. Constant-Stress Partially Accelerated Life Test (CS-PALT) have used for the underlying distribution on first-failure Progressive (FFP) censoring scheme. All special cases of the FFP censoring scheme have used for the present comparative analysis. The comparison has been done between different special cases of FFP based on Approximate Confidence Lengths (ACL) under Normal approximation, Bootstrap Confidence Length (BCL) and One-Sample Bayes Prediction Bound Lengths (BPBL). A simulation study have been carried out for the present analysis.

Death by suicide at the Ward level in Northern Ireland

BackgroundDeaths from suicide, as recorded within the Northern Ireland Coroner's Office for the years 2005–2011 inclusive, were analysed in terms of standardised mortality ratios (SMRs), within Wards and Local Government Districts (LGDs). The aim of the study is to examine factors relating to the ecological context of the area within which the person resided at time of death. Area deprivation, religious composition and age structure are examined in terms of SMRs, while controlling for the number of individuals living within a designated area.MethodsRandom-intercept Poisson regression models were used in conjunction with empirical Bayes prediction to examine area effects.ResultsConsiderable variation occurs between the numbers of recorded deaths within each area. A strong association is shown between deprivation and the number of deaths by suicide within an area. There was considerable variation at the LGD level in terms of the number of deaths, but once the nested nature of Wards was taken into account and adjusted for level of deprivation, the variation between LGD was no longer statistically significant. When adjusted for the number of individuals within each age group, the number of deaths in the younger and middle-aged groups did not show a statistical difference (0.05 level), nor did the religious composition of the area in terms of the number of recorded deaths.ConclusionsBased on SMRs, using empirical Bayes prediction, area effects were shown to be substantial, especially in urban locations where there are high rates of deprivation.

Bound lengths for Burr-XII distribution under step-stress PALT

Some inferences based on Step-Stress Partially Accelerated Life Test (SS-PALT) are discussed in the present article. The Progressive Type-II censoring criterion with Random Removal scheme is used for determining the Approximate Confidence Lengths and One-Sample Bayes Prediction Bound Lengths for the unknown parameters of the Burr Type-XII distribution. Based on the simulated data, the analysis of the present discussion has been carried out.