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Companies and organizations must make decisions concerning capital budgeting. Capital budgeting is a decision-making process that determines whether a firm should purchase equipment to be used on a long-term basis. The initial investment in the equipment is predicted to be returned through revenue gained by the use of the equipment over its lifetime. However, there is inherent risk associated with these investment decisions. Therefore, potential purchasers must decide whether the risk involved with investing in the equipment is justified. This dissertation addresses risk-based technology assessment for capital equipment acquisition decisions in small firms. Technology assessment, here, is concerned with understanding the uncertainty associated with assessing the value predicted in the capital budgeting process. When analyzing the risk for a given technology, we assign a probability law to its net present value. Our primary research contribution is providing an analytical framework together with a computational strategy to support capital equipment budgeting in firms where the value of candidate technologies can represent nearly all the firm’s value. Since small firms typically have limited budgets, spending for technology is always a difficult budgeting decision. The organization’s administration must decide which, if any, among the available technologies will be best for their operation. The process for acquiring technology in many small firms can be filled with challenges. Most important among them is that capital budgeting is typically a “one-off” decision. These decisions are difficult since the candidate technologies may not have operational data available. Thus, decision makers need some means to predict how the proposed technology (e.g., equipment or machinery) will be used. Hence, firms should follow techniques and procedures based on appropriate normative principles and well-established theory. Senior company executives and/or governance boards are often authorized to approve capital equipment purchases. However, these company leaders may not have adequate expertise in the operations of candidate technologies or may lack the understanding necessary to determine how new technologies may impact other company operations. Appropriate financial evaluation measures and selection criteria that incorporate risk are critical to making sound, quantitative acquisition decisions. The research reported here offers an analytical framework for comparing different technology alternatives in capital budgeting decisions. Comparison is based on the expected net present value and the risk (i.e., probability law on net present value) associated with each decision alternative. To this end, the operational characteristics of each technology alternative are connected to their potential revenue and cost streams. The framework is embedded within a computational architecture that can be customized to account for operations and technologies in specific application scenarios. One major barrier addressed by this research is overcoming the fact that new technologies typically have no historical operational data. Therefore, characterizing the uncertainty of operations (e.g., distribution of the equipment lifetime) can be very difficult. Discrete- event simulation is used to generate potential revenue and cost estimates. We demonstrate the tractability and practicality of the analytical framework and computational architecture via a healthcare technology assessment decision. Data extracted from a published journal article detailing a hospital’s technology assessment decision are used to find the risk of the medical technology using the computational architecture developed. Widely-available, no-cost software tools are employed. Results of the health care example suggest that the financial analysis in the original technology assessment was in- adequate and simplistic. Small firms may find this research particularly beneficial because potential investments can be a significant portion of a small firm’s value.

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In this thesis, we present a strongly coupled data fusion architecture within a Bayesian framework for modeling the bi-directional influences between the scene and object classification mechanisms. A number of psychophysical studies provide experimental evidence that the object and the scene perception mechanisms are not functionally separate in the human visual system. Object recognition facilitates the recognition of the scene background and also knowledge of the scene context facilitates the recognition of the individual objects in the scene. The evidence indicating a bi-directional exchange between the two processes has motivated us to build a computational model where object and scene classification proceed in an interdependent manner, while no hierarchical relationship is imposed between the two processes. We propose a strongly coupled data fusion model for implementing the feedback relationship between the scene and object classification processes. We present novel schemes for modifying the Bayesian solutions for the scene and object classification tasks which allow data fusion between the two modules based on the constraining of the priors or the likelihoods. We have implemented and tested the two proposed models using a database of natural images created for this purpose. The Receiver Operator Curves (ROC) depicting the scene classification performance of the likelihood coupling and the prior coupling models show that scene classification performance improves significantly in both models as a result of the strong coupling of the scene and object modules. / ROC curves depicting the scene classification performance of the two models also show that the likelihood coupling model achieves a higher detection rate compared to the prior coupling model. We have also computed the average rise times of the models' outputs as a measure of comparing the speed of the two models. The results show that the likelihood coupling model outputs have a shorter rise time. Based on these experimental findings one can conclude that imposing constraints on the likelihood models provides better solutions to the scene classification problems compared to imposing constraints on the prior models. / We have also proposed an attentional feature modulation scheme, which consists of tuning the input image responses to the bank of Gabor filters based on the scene class probabilities estimated by the model and the energy profiles of the Gabor filters for different scene categories. Experimental results based on combining the attentional feature tuning scheme with the likelihood coupling and the prior coupling methods show a significant improvement in the scene classification performances of both models.

In this thesis, we utilise the framework of Bayesian statistics to discriminate between models of the cosmological mass function. We first review the cosmological model and the formation and distribution of galaxy clusters before formulating a statistic within the Bayesian framework, namely the Bayesian razor, that allows model testing of probability distributions. The Bayesian razor is used to discriminate between three popular mass functions, namely the Press-Schechter, Sheth-Tormen and normalisable Tinker models. With a small number of particles in the simulation, we find that the simpler model is preferred due to the Occam’s razor effect, but as the size of the simulation increases the more complex model, if taken to be the true model, is preferred. We establish criteria on the size of the simulation that is required to decisively favour a given model and investigate the dependence of the simulation size on the threshold mass for clusters, and prior probability distributions. Finally we outline how our method can be extended to consider more realistic N-body simulations or be applied to observational data. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2010.

Bayesian variable selection approaches are more powerful in discriminating among models regardless of whether these models under investigation are hierarchical or not. Although Bayesian approaches require complex computation, use of theMarkov Chain Monte Carlo (MCMC) methods, such as, Gibbs sampler and Metropolis-Hastings algorithm make computations easier. In this study we investigated the e↵ectiveness of Bayesian variable selection approaches in comparison to other non-Bayesian or classical approaches. For this purpose, we compared the performance of Bayesian versus non-Bayesian variable selection approaches for linear models. Among these approaches, we studied Conditional Predictive Ordinate (CPO) and Bayes factor. Among the non-Bayesian or classical approaches, we implemented adjusted R-square, Akaike Information Criterion (AIC) and Bayes Information Criterion (BIC) for model selection. We performed a simulation study to examine how Bayesian and non- Bayesian approaches perform in selecting variables. We also applied these methods to real data and compared their performances. We observed that for linear models, Bayesian variable selection approaches perform consistently as that of non-Bayesian approaches. / Bayesian inference -- Bayesian inference for normally distributed likekilhood -- Model adequacy -- Simulation approach -- Application to wage data. / Department of Mathematical Sciences

One employs the mathematical analysis of decision making when the state of nature is uncertain but further information about it can be obtained by experimentation. Bayesian Decision Theory concerns practical problems of decision making under conditions of uncertainty and also requires the use of statistical and mathematical methods.In this thesis, some basic risk sharing and group decision concepts are provided. Risk is the expected value of the Loss Function of Bayesian Estimators. Group decisions consider situations in which the individuals need to agree both on utilities for consequences and on conditional probability assessments for different experimental outcomes. / Department of Mathematical Sciences

The thesis is based on the notion that a person's behaviour is largely a result of the interplay between his beliefs and values. A model is described which ccmbines Personal Construct Theo~J (as a means of describing beliefs) and Multi-Attributed Utility Theory (as a means of describing values) in order to predict purposive choice behaviour. The model is applied to choice of records, books, clothes and role behaviours and is found to predict choices with a high degree of accuracy. Prediction using personal constructs is shown to be superior to that using supplied dimensions. Furthermore, construct weights elicited by a lottery tech~que are shown generally to be purposespecific and to give better predictions of behaviour than UIUt weights. The model is then used to investigate the sentencing of offenders by magistrates and is again found to predict behaviour with a high degree of accuracy. The data also indicate the problems inherent in using verbal measures of construct similarity since the same words may be used differently and different words may be used similarly. Claims for the model's broad applicability are illustrated by using the model to reformulate the concepts of 'attention' and 'role' and a means of operationally defining role conflict is suggested.

For reasoning under uncertainty the Bayesian network has become the representation of choice. However, except where models are considered 'simple' the task of construction and inference are provably NP-hard. For modelling larger 'real' world problems this computational complexity has been addressed by methods that approximate the model. The Naive Bayes classifier, which has strong assumptions of independence among features, is a common approach, whilst the class of trees is another less extreme example. In this thesis we propose the use of an information theory based technique as a mechanism for inference in Singly Connected Networks. We call this a Mutual Information Measure classifier, as it corresponds to the restricted class of trees built from mutual information. We show that the new approach provides for both an efficient and localised method of classification, with performance accuracies comparable with the less restricted general Bayesian networks. To improve the performance of the classifier, we additionally investigate the possibility of expanding the class Markov blanket by use of a Wrapper approach and further show that the performance can be improved by focusing on the class Markov blanket and that the improvement is not at the expense of increased complexity. Finally, the two methods are applied to the task of diagnosing the 'real' world medical domain, Acute Abdominal Pain. Known to be both a different and challenging domain to classify, the objective was to investigate the optiniality claims, in respect of the Naive Bayes classifier, that some researchers have argued, for classifying in this domain. Despite some loss of representation capabilities we show that the Mutual Information Measure classifier can be effectively applied to the domain and also provides a recognisable qualitative structure without violating 'real' world assertions. In respect of its 'selective' variant we further show that the improvement achieves a comparable predictive accuracy to the Naive Bayes classifier and that the Naive Bayes classifier's 'overall' performance is largely due the contribution of the majority group Non-Specific Abdominal Pain, a group of exclusion.