The statistical mentor system incorporates a knowledge base into an educational tool for novices in statistical decision making to use in choosing a statistical technique. The novices are students in a business school curriculum who are expected to learn the basic statistical processes in business applications. The purpose of the system is to stimulate learning of the data analysis process on the part of the novice, usually a difficult task. The system acts as a consultant to the novice and approaches the task using a top-down problem solving strategy rather than the traditional bottom-up strategy used by novices. The heart of the system is the rule base for differentiating between statistics. These rules were built by gathering expertise from two experts in statistical analysis. The rules are based on five questions which the data can answer, as well as the type of data, the number of variables, and any dependent/independent relationships which exist between the variables. The knowledge base consists of five rule sets and can be represented either by condition/conclusion rules or by a set of multi-dimensional tables. Twenty-nine statistics and the rules for choosing them are in the rules sets. The knowledge base was used to define the logic incorporated in the consultant system in order to aid the user in selecting a correct technique. A dialogue mode is employed in the consultant to determine which conditions are true for the problem and data set. The rule sets are then checked to find the conclusion satisfying the conditions. The computer mentor was tested against the usual textbook mentor method (search through a textbook until one finds a statistic that looks promising) with two different groups of subjects, 25 undergraduates and 19 doctoral students. The results were that the computer-assisted students in both samples correctly solved a larger proportion of problems and had a higher average number of problems correct than did the textbook assisted groups.

Thesis (MSc)--Stellenbosch University, 2004. / ENGLISH ABSTRACT: The Bayesian approach to decision-making is considered in this thesis for reliability/survival models pertaining to a Weibull class of distributions. A generalised right censored sampling scheme has been assumed and implemented. The Jeffreys' prior for the inverse mean lifetime and the survival function of the exponential model were derived. The consequent posterior distributions of these two parameters were obtained using this non-informative prior. In addition to the Jeffreys' prior, the natural conjugate prior was considered as a prior for the parameter of the exponential model and the consequent posterior distribution was derived. In many reliability problems, overestimating a certain parameter of interest is more detrimental than underestimating it and hence, the LINEX loss function was used to estimate the parameters and their consequent risk measures. Moreover, the same analogous derivations have been carried out relative to the commonly-used symmetrical squared error loss function. The risk function, the posterior risk and the integrated risk of the estimators were obtained and are regarded in this thesis as the risk measures. The performance of the estimators have been compared relative to these risk measures. For the Jeffreys' prior under the squared error loss function, the comparison resulted in crossing-over risk functions and hence, none of these estimators are completely admissible. However, relative to the LINEX loss function, it was found that a correct Bayesian estimator outperforms an incorrectly chosen alternative. On the other hand for the conjugate prior, crossing-over of the risk functions of the estimators were evident as a result. In comparing the performance of the Bayesian estimators, whenever closed-form expressions of the risk measures do not exist, numerical techniques such as Monte Carlo procedures were used. In similar fashion were the posterior risks and integrated risks used in the performance compansons. The Weibull pdf, with its scale and shape parameter, was also considered as a reliability model. The Jeffreys' prior and the consequent posterior distribution of the scale parameter of the Weibull model have also been derived when the shape parameter is known. In this case, the estimation process of the scale parameter is analogous to the exponential model. For the case when both parameters of the Weibull model are unknown, the Jeffreys' and the reference priors have been derived and the computational difficulty of the posterior analysis has been outlined. The Jeffreys' prior for the survival function of the Weibull model has also been derived, when the shape parameter is known. In all cases, two forms of the scalar estimation error have been t:. used to compare as much risk measures as possible. The performance of the estimators were compared for acceptability in a decision-making framework. This can be seen as a type of procedure that addresses robustness of an estimator relative to a chosen loss function. / AFRIKAANSE OPSOMMING: Die Bayes-benadering tot besluitneming is in hierdie tesis beskou vir betroubaarheids- / oorlewingsmodelle wat behoort tot 'n Weibull klas van verdelings. 'n Veralgemene regs gesensoreerde steekproefnemingsplan is aanvaar en geïmplementeer. Die Jeffreyse prior vir die inverse van die gemiddelde leeftyd en die oorlewingsfunksie is afgelei vir die eksponensiële model. Die gevolglike aposteriori-verdeling van hierdie twee parameters is afgelei, indien hierdie nie-inligtingge-wende apriori gebruik word. Addisioneel tot die Jeffreyse prior, is die natuurlike toegevoegde prior beskou vir die parameter van die eksponensiële model en ooreenstemmende aposteriori-verdeling is afgelei. In baie betroubaarheidsprobleme het die oorberaming van 'n parameter meer ernstige nagevolge as die onderberaming daarvan en omgekeerd en gevolglik is die LINEX verliesfunksie gebruik om die parameters te beraam tesame met ooreenstemmende risiko maatstawwe. Soortgelyke afleidings is gedoen vir hierdie algemene simmetriese kwadratiese verliesfunksie. Die risiko funksie, die aposteriori-risiko en die integreerde risiko van die beramers is verkry en word in hierdie tesis beskou as die risiko maatstawwe. Die gedrag van die beramers is vergelyk relatief tot hierdie risiko maatstawwe. Die vergelyking vir die Jeffreyse prior onder kwadratiese verliesfunksie het op oorkruisbare risiko funksies uitgevloei en gevolglik is geeneen van hierdie beramers volkome toelaatbaar nie. Relatief tot die LINEX verliesfunksie is egter gevind dat die korrekte Bayes-beramer beter vaar as die alternatiewe beramer. Aan die ander kant is gevind dat oorkruisbare risiko funksies van die beramers verkry word vir die toegevoegde apriori-verdeling. Met hierdie gedragsvergelykings van die beramers word numeriese tegnieke toegepas, soos die Monte Carlo prosedures, indien die maatstawwe nie in geslote vorm gevind kan word nie. Op soortgelyke wyse is die aposteriori-risiko en die integreerde risiko's gebruik in die gedragsvergelykings. Die Weibull waarskynlikheidsverdeling, met skaal- en vormingsparameter, is ook beskou as 'n betroubaarheidsmodel. Die Jeffreyse prior en die gevolglike aposteriori-verdeling van die skaalparameter van die Weibull model is afgelei, indien die vormingsparameter bekend is. In hierdie geval is die beramingsproses van die skaalparameter analoog aan die afleidings van die eksponensiële model. Indien beide parameters van die Weibull modelonbekend is, is die Jeffreyse prior en die verwysingsprior afgelei en is daarop gewys wat die berekeningskomplikasies is van 'n aposteriori-analise. Die Jeffreyse prior vir die oorlewingsfunksie van die Weibull model is ook afgelei, indien die vormingsparameter bekend is. In al die gevalle is twee vorms van die skalaar beramingsfoute gebruik in die vergelykings, sodat soveel as moontlik risiko maatstawwe vergelyk kan word. Die gedrag van die beramers is vergelyk vir aanvaarbaarheid binne die besluitnemingsraamwerk. Hierdie kan gesien word as 'n prosedure om die robuustheid van 'n beramer relatief tot 'n gekose verliesfunksie aan te spreek.

This dissertation work is part of a larger research effort involving soil-aquifer treatment (SAT). The dissertation's focus was to investigate meta-heuristic (global) optimization methods suitable for developing water resources decision support system (DSS), particularly to optimally design and operate groundwater storage and recovery projects. The effort included developing an integrated simulation-optimization management model for complex aquifer recharge/extraction operation considering water quality transformation. The research demonstrated successful integration of three-dimensional hydraulic, water quality, and particle tracking models with shuffled complex evolution (SCE) optimization algorithm. It also included developing the shuffled frog leaping algorithm (SFLA), a meta-heuristic optimization technique for solving discrete/combinatorial problems, and its application to aid decision making in water supply and distribution system optimization issues. SFLA is a memetic, meta-heuristic population-based cooperative search metaphor inspired by natural memetics. SFLA was developed by extending the logic of two existing global optimization techniques for continuous optimization problems. The local search is completed using an extension of the particle swami optimization (PSO) method, and the global exploration is performed by a technique similar to that used in the shuffled complex evolution (SCE) algorithm. SFLA was tested favorably on several literature test functions and engineering problems that present difficulties to many global optimization problems. The effectiveness and suitability of this algorithm has also been demonstrated by applying it to a groundwater model calibration problem and several water distribution system design problems that are considered as benchmark problems in the literature. The comparison of SFLA with other existing global optimization methods, such as genetic algorithms (GA), in terms of the likelihood and efficiency of converging to a global optimal solution, suggests that SFLA can be an effective algorithm for solving discrete/combinatorial optimization problems.

Thesis (MTech (Business Administration))--Cape Peninsula University of Technology, 2016. / This mixed methods study examined specific influences on low usage of analytics among level 4 managers in a selected public sector organisation, based on SAP Business Intelligence (SAP BI) log on statistics collected between July 2012 and June 2016. Analytics provides an organisation the ability to enable its management team to make decisions based on facts, rather than assumption. The aim of this interpretivist research, grounded in a subjectivist epistemological position, was to gain an in-depth understanding of the manager’s environment and how it influences the usage and adoption of analytics in strategic decision making. Human beings change all the time and the environment in which they find themselves constantly influences them. The main research question was: what specific factors inhibit managers’ use of analytics in organisations? A case study approach was deemed the most appropriate for this kind of study because specific environmental factors influence analytics usage. Themes identified as possible factors influencing different dimensions included: individual characteristics, business intelligence systems quality, organisational factors, macro-environment factors, behavioural beliefs and attitudes, effort perceptions, social influence, facilitating conditions and other. For the qualitative component, eight level 4 public sector managers within the selected organisation were interviewed in order to experience the work environment and their interactions with colleagues, while an electronic survey questionnaire yielded data from 211 level 4 managers. The rationale for selecting this category of managers was that they not only manage staff, but also control a budget, and would find it useful to utilise analytics to aid the decision making process. Qualitative and quantitative data analysis methods were used to analyse the data. Dominant themes that emerged from interviews with eight level 4 managers were: organisational factors and system quality characteristics. Daily log on statistics collected from the electronic survey questionnaire yielded quantitative results on usage of analytics within the organisation. Overall, it was found that managers’ use of analytics is low. Given the importance of analytics for informed decision-making, recommendations are made to increase usage.

Decision makers have long relied on experts to inform their decision making. Expert judgment analysis is a way to elicit and combine the opinions of a group of experts to facilitate decision making. The use of expert judgment is most appropriate when there is a lack of data for obtaining reasonable statistical results. The experts are asked for advice by one or more decision makers who face a specific real decision problem. The decision makers are outside the group of experts and are jointly responsible and accountable for the decision and committed to finding solutions that everyone can live with. The emphasis is on the decision makers learning from the experts. The focus of this thesis is an overview and comparison of the various elicitation and combination methods available. These include the traditional committee method, the Delphi method, the paired comparisons method, the negative exponential model, Cooke’s classical model, the histogram technique, using the Dirichlet distribution in the case of a set of uncertain proportions which must sum to one, and the employment of overfitting. The supra Bayes approach, the determination of weights for the experts, and combining the opinions of experts where each opinion is associated with a confidence level that represents the expert’s conviction of his own judgment are also considered.