Bayesian statistical decision theory

Wellness and healthy life are the most common concerns for an individual to lead a happy life. A web-based approach known as Wellness Scoring is being developed taking into people’s concerns for their health issues. In this approach, four different classifiers are being investigated to predict the wellness. In this thesis, we investigated four different classifiers (a probabilistic graphical model, simple probabilistic classifier, probabilistic statistical classification and an artificial neural network) to predict the wellness outcome. An approach to calculate wellness score is also addressed. All these classifiers are trained on real data, hence giving more accurate results. With this solution, there is a better way of keeping track of an individuals’ health. In this thesis, we present the design and development of such a system and evaluate the performance of the classifiers and design considerations to maximize the end user experience with the application. A user experience model capable of predicting the wellness score for a given set of risk factors is developed.

This thesis contains two parts. The first part derives the Bayesian estimator of
the parameters in a piecewise exponential Cox proportional hazard regression model,
with one unknown change point for a right censored survival data. The second part
surveys the applications of change point problems to various types of data, such as
long-term survival data, longitudinal data and time series data. Furthermore, the
proposed method is then used to analyse a real survival data.

This thesis presents the theory and an application of Bayesian econometrics. The classical theory of econometrics is also presented for a comparison study. In the Bayesian case the theory of the prior information, which is the distinguishing characteristic of the Bayesian approach, is presented by considering the cases of informative and non-informative priors. The classical and Bayesian approach represent the two fundamental, although opposite in the concept of probability, schools of thought in statistics and econometrics. An application to the estimation of standard macroeconomic equations is also included where both classical and Bayesian techniques are employed.

In today's competitive environment for software products, quality has become an increasingly important asset to software development organizations. Software quality models are tools for focusing efforts to find faults early in the development. Delaying corrections can lead to higher costs. In this research, the classification Bayesian Networks modelling technique was used to predict the software quality by classifying program modules either as fault-prone or not fault-prone. A general classification rule was applied to yield classification Bayesian Belief Network models. Six classification Bayesian Belief Network models were developed based on quality metrics data records of two very large window application systems. The fit data set was used to build the model and the test data set was used to evaluate the model. The first two models used median based data cluster technique, the second two models used median as critical value to cluster metrics using Generalized Boolean Discriminant Function and the third two models used Kolniogorov-Smirnov test to select the critical value to cluster metrics using Generalized Boolean Discriminant Function; All six models used the product metrics (FAULT or CDCHURN) as predictors.

The focus of this thesis is to statistically model violent crime rates against population over the years 1960-2009 for the United States. We approach this question as to be of interest since the trend of population for individual states follows different patterns. We propose here a method which employs cubic spline regression modeling. First we introduce a minimum/maximum algorithm that will identify potential knots. Then we employ least squares estimation to find potential regression coefficients based upon the cubic spline model and the knots chosen by the minimum/maximum algorithm. We then utilize the best subsets regression method to aid in model selection in which we find the minimum value of the Bayesian Information Criteria. Finally, we preent the R2adj as a measure of overall goodness of fit of our selected model. We have found among the fifty states and Washington D.C., 42 out of 51 showed an R2adj value that was greater than 90%. We also present an overall model of the United States. Also, we show additional applications our algorithm for data which show a non linear association. It is hoped that our method can serve as a unified model for violent crime rate over future years.