Multiple Criteria Decision Analysis: Classification Problems and Solutions

Multiple criteria decision analysis (MCDA) techniques are developed to address challenging classification problems arising in engineering management and elsewhere. MCDA consists of a set of principles and tools to assist a decision maker (DM) to solve a decision problem with a finite set of alternatives compared according to two or more criteria, which are usually conflicting. The three types of classification problems to which original research contributions are made are Screening: Reduce a large set of alternatives to a smaller set that most likely contains the best choice. Sorting: Arrange the alternatives into a few groups in preference order, so that the DM can manage them more effectively. Nominal classification: Assign alternatives to nominal groups structured by the DM, so that the number of groups, and the characteristics of each group, seem appropriate to the DM. Research on screening is divided into two parts: the design of a sequential screening procedure that is then applied to water resource planning in the Region of Waterloo, Ontario, Canada; and the development of a case-based distance method for screening that is then demonstrated using a numerical example. Sorting problems are studied extensively under three headings. Case-based distance sorting is carried out with Model I, which is optimized for use with cardinal criteria only, and Model II, which is designed for both cardinal and ordinal criteria; both sorting approaches are applied to a case study in Canadian municipal water usage analysis. Sorting in inventory management is studied using a case-based distance method designed for multiple criteria ABC analysis, and then applied to a case study involving hospital inventory management. Finally sorting is applied to bilateral negotiation using a case-based distance model to assist negotiators that is then demonstrated on a negotiation regarding the supply of bicycle components. A new kind of decision analysis problem, called multiple criteria nominal classification (MCNC), is addressed. Traditional classification methods in MCDA focus on sorting alternatives into groups ordered by preference. MCNC is the classification of alternatives into nominal groups, structured by the DM, who specifies multiple characteristics for each group. The features, definitions and structures of MCNC are presented, emphasizing criterion and alternative flexibility. An analysis procedure is proposed to solve MCNC problems systematically and applied to a water resources planning problem

Approximate Bayesian Computation in State Space Models

A new approach to inference in state space models is proposed, based on approximate Bayesian computation (ABC). ABC avoids evaluation of the likelihood function by matching observed summary statistics with statistics computed from data simulated from the true process; exact inference being feasible only if the statistics are sufficient. With finite sample sufficiency unattainable in the state space setting, we seek asymptotic sufficiency via the maximum likelihood estimator (MLE) of the parameters of an auxiliary model. We prove that this auxiliary model-based approach achieves Bayesian consistency, and that - in a precise limiting sense - the proximity to (asymptotic) sufficiency yielded by the MLE is replicated by the score. In multiple parameter settings a separate treatment of scalar parameters, based on integrated likelihood techniques, is advocated as a way of avoiding the curse of dimensionality. Some attention is given to a structure in which the state variable is driven by a continuous time process, with exact inference typically infeasible in this case as a result of intractable transitions. The ABC method is demonstrated using the unscented Kalman filter as a fast and simple way of producing an approximation in this setting, with a stochastic volatility model for financial returns used for illustration

A Comparison of Nature Inspired Algorithms for Multi-threshold Image Segmentation

In the field of image analysis, segmentation is one of the most important preprocessing steps. One way to achieve segmentation is by mean of threshold selection, where each pixel that belongs to a determined class islabeled according to the selected threshold, giving as a result pixel groups that share visual characteristics in the image. Several methods have been proposed in order to solve threshold selectionproblems; in this work, it is used the method based on the mixture of Gaussian functions to approximate the 1D histogram of a gray level image and whose parameters are calculated using three nature inspired algorithms (Particle Swarm Optimization, Artificial Bee Colony Optimization and Differential Evolution). Each Gaussian function approximates thehistogram, representing a pixel class and therefore a threshold point. Experimental results are shown, comparing in quantitative and qualitative fashion as well as the main advantages and drawbacks of each algorithm, applied to multi-threshold problem.Comment: 16 pages, this is a draft of the final version of the article sent to the Journa

Considerate Approaches to Achieving Sufficiency for ABC model selection

For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations from a model, but cannot evaluate the likelihood directly. When summary statistics of real and simulated data are compared --- rather than the data directly --- information is lost, unless the summary statistics are sufficient. Here we employ an information-theoretical framework that can be used to construct (approximately) sufficient statistics by combining different statistics until the loss of information is minimized. Such sufficient sets of statistics are constructed for both parameter estimation and model selection problems. We apply our approach to a range of illustrative and real-world model selection problems