The many facets of statistical modeling

Statistics is the science of gaining and elevating insight from data. Data are pieces of information (often numerical but not always) gathered on people, objects or processes. The science of statistics involves all aspects of inquiry about data. Statistical modeling involves the finding of general laws from observed data, which amounts to extracting information from the data. Often the problem of main interest is to obtain a measure of both the complexity and the (useful) information in a set of data. Statistical modeling can be perceived also as a general framework for the application of statistical ideas. This presentation focuses on my experiences and endeavors in developing statistical models in order to capture the wide spectrum of data that arise from experiments, observations and other phenomena- producing data. Survival analysis is a collection of statistical models to explain the phenomena of survival data. The inherent property of survival data is the censored observation. There exists complexity in the censored mechanisms in which the usual survival models need to be modified or new survival models need to be developed to address this issue. One of the main objectives of survival analysis is to test the survival curves, and in the presence of partly interval-censored data goodness of fit tests have been developed for both parametric and nonparametric settings. Fundamental survival models do not include patients who are cured. In reality with the advancement of medical technology some patients are not susceptible to the disease (e.g. cancer) and this gives us the motivation to look into and consider models that will accommodate cure fraction for interval censored data with change point. When an event occurs and the death (example) of a patient can be due to several causes (risks), the survival model of interest is the competing risks model. A regression tree technique has been developed by using the subdistrbution function of competing risks to attain a better insight of a set of data. Bayesian is another approach that is fast gaining popularity in developing statistical models. Survival models with Bayesian approach considering several priors with right and interval-censoring are explored and developed. Regression Bayesian survival model with Jeffreys prior can be considered a frontier to Bayesian survival analysis. Simple and multiple linear regressions handle continuous response data with the assumption that the observations are independent. Substantial researches have been carried out to model scenarios of correlated data with binary and nominal response data. The models developed are based on Generalized Estimating Equation (GEE) for both semiparametric and nonparametric set-ups. Claim dependence model to include a third factor has been developed and its properties investigated. Due to certain limitations, the existing water quality index (WQI) measures which was based on experts opinions is very subjective in nature and does not provide an accurate picture of the water quality characteristics of a river. The subjectivity assumptions in developing WQI can be reduced by using statistical approaches. Moreover these statistical approaches can help to identify important parameters in determining the quality of a water body as well as the extent of their significance. Issues relating to this end this inaugural presentation

Bayesian Inference of the Weibull Model Based on Interval-Censored Survival Data

Interval-censored data consist of adjacent inspection times that surround an unknown failure time. We have in this paper reviewed the classical approach which is maximum likelihood in estimating the Weibull parameters with interval-censored data. We have also considered the Bayesian approach in estimating the Weibull parameters with interval-censored data under three loss functions. This study became necessary because of the limited discussion in the literature, if at all, with regard to estimating the Weibull parameters with interval-censored data using Bayesian. A simulation study is carried out to compare the performances of the methods. A real data application is also illustrated. It has been observed from the study that the Bayesian estimator is preferred to the classical maximum likelihood estimator for both the scale and shape parameters