Mathematical prerequisites for learning statistics in Psychology: Assessing core skills of numeracy and mathematical reasoning among undergraduates.

This study sought to extend earlier work by Mulhern and Wylie (2004) to investigate a UK-wide sample of psychology undergraduates. A total of 890 participants from eight universities across the UK were tested on six broadly defined components of mathematical thinking relevant to the teaching of statistics in psychology - calculation, algebraic reasoning, graphical interpretation, proportionality and ratio, probability and sampling, and estimation. Results were consistent with Mulhern and Wylie's (2004) previously reported findings. Overall, participants across institutions exhibited marked deficiencies in many aspects of mathematical thinking. Results also revealed significant gender differences on calculation, proportionality and ratio, and estimation. Level of qualification in mathematics was found to predict overall performance. Analysis of the nature and content of errors revealed consistent patterns of misconceptions in core mathematical knowledge , likely to hamper the learning of statistics.

Review of Aerospace Engineering Cost Modelling: The Genetic Causal Approach

The primary intention of this paper is to review the current state of the art in engineering cost modelling as applied to aerospace. This is a topic of current interest and in addressing the literature, the presented work also sets out some of the recognised definitions of cost that relate to the engineering domain. The paper does not attempt to address the higher-level financial sector but rather focuses on the costing issues directly relevant to the engineering process, primarily those of design and manufacture. This is of more contemporary interest as there is now a shift towards the analysis of the influence of cost, as defined in more engineering related terms; in an attempt to link into integrated product and process development (IPPD) within a concurrent engineering environment. Consequently, the cost definitions are reviewed in the context of the nature of cost as applicable to the engineering process stages: from bidding through to design, to manufacture, to procurement and ultimately, to operation. The linkage and integration of design and manufacture is addressed in some detail. This leads naturally to the concept of engineers influencing and controlling cost within their own domain rather than trusting this to financers who have little control over the cause of cost. In terms of influence, the engineer creates the potential for cost and in a concurrent environment this requires models that integrate cost into the decision making process.

Aircraft Cost Modelling using the Genetic Causal Technique within a Systems Engineering Approach

The paper is primarily concerned with the modelling of aircraft manufacturing cost. The aim is to establish an integrated life cycle balanced design process through a systems engineering approach to interdisciplinary analysis and control. The cost modelling is achieved using the genetic causal approach that enforces product family categorisation and the subsequent generation of causal relationships between deterministic cost components and their design source. This utilises causal parametric cost drivers and the definition of the physical architecture from the Work Breakdown Structure (WBS) to identify product families. The paper presents applications to the overall aircraft design with a particular focus on the fuselage as a subsystem of the aircraft, including fuselage panels and localised detail, as well as engine nacelles. The higher level application to aircraft requirements and functional analysis is investigated and verified relative to life cycle design issues for the relationship between acquisition cost and Direct Operational Cost (DOC), for a range of both metal and composite subsystems. Maintenance is considered in some detail as an important contributor to DOC and life cycle cost. The lower level application to aircraft physical architecture is investigated and verified for the WBS of an engine nacelle, including a sequential build stage investigation of the materials, fabrication and assembly costs. The studies are then extended by investigating the acquisition cost of aircraft fuselages, including the recurring unit cost and the non-recurring design cost of the airframe sub-system. The systems costing methodology is facilitated by the genetic causal cost modeling technique as the latter is highly generic, interdisciplinary, flexible, multilevel and recursive in nature, and can be applied at the various analysis levels required of systems engineering. Therefore, the main contribution of paper is a methodology for applying systems engineering costing, supported by the genetic causal cost modeling approach, whether at a requirements, functional or physical level.

Risk assessment of E-Commerce projects using evidential reasoning

The purpose of this study is to develop a decision making system to evaluate the risks in E-Commerce (EC) projects. Competitive software businesses have the critical task of assessing the risk in the software system development life cycle. This can be conducted on the basis of conventional probabilities, but limited appropriate information is available and so a complete set of probabilities is not available. In such problems, where the analysis is highly subjective and related to vague, incomplete, uncertain or inexact information, the Dempster-Shafer (DS) theory of evidence offers a potential advantage. We use a direct way of reasoning in a single step (i.e., extended DS theory) to develop a decision making system to evaluate the risk in EC projects. This consists of five stages 1) establishing knowledge base and setting rule strengths, 2) collecting evidence and data, 3) determining evidence and rule strength to a mass distribution for each rule; i.e., the first half of a single step reasoning process, 4) combining prior mass and different rules; i.e., the second half of the single step reasoning process, 5) finally, evaluating the belief interval for the best support decision of EC project. We test the system by using potential risk factors associated with EC development and the results indicate that the system is promising way of assisting an EC project manager in identifying potential risk factors and the corresponding project risks.

The Combination of Multiple Classifiers Using an Evidential Reasoning Approach

In many domains when we have several competing classifiers available we want to synthesize them or some of them to get a more accurate classifier by a combination function. In this paper we propose a ‘class-indifferent’ method for combining classifier decisions represented by evidential structures called triplet and quartet, using Dempster's rule of combination. This method is unique in that it distinguishes important elements from the trivial ones in representing classifier decisions, makes use of more information than others in calculating the support for class labels and provides a practical way to apply the theoretically appealing Dempster–Shafer theory of evidence to the problem of ensemble learning. We present a formalism for modelling classifier decisions as triplet mass functions and we establish a range of formulae for combining these mass functions in order to arrive at a consensus decision. In addition we carry out a comparative study with the alternatives of simplet and dichotomous structure and also compare two combination methods, Dempster's rule and majority voting, over the UCI benchmark data, to demonstrate the advantage our approach offers. (A continuation of the work in this area that was published in IEEE Trans on KDE, and conferences)

An extended framework for evidential reasoning systems.

Use of the Dempster-Shafer (D-S) theory of evidence to deal with uncertainty in knowledge-based systems has been widely addressed. Several AI implementations have been undertaken based on the D-S theory of evidence or the extended theory. But the representation of uncertain relationships between evidence and hypothesis groups (heuristic knowledge) is still a major problem. This paper presents an approach to representing such knowledge, in which Yen’s probabilistic multi-set mappings have been extended to evidential mappings, and Shafer’s partition technique is used to get the mass function in a complex evidence space. Then, a new graphic method for describing the knowledge is introduced which is an extension of the graphic model by Lowrance et al. Finally, an extended framework for evidential reasoning systems is specified.