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First-price sealed-bid (FPSB) auctions have mostly been modelled in auction theory using the decision-theoretic and Bayesian game-theoretic approaches. From a practical point of view, each approach has its limitations. To overcome those limitations, Rios Insua et al. (2009) introduced an approach, called adversarial risk analysis (ARA) that provides an optimal solution for one of the intervening agents, based on a decision making problem in hand and treating the intelligent adversaries' decisions as uncertainties. ARA solutions for FPSB auctions have previously been found but only under strong assumptions which make the model somewhat unrealistic. In this thesis, we use ARA methodology and model bidders' behaviours in FPSB auctions using more realistic assumptions. First, we model bidders' behaviours by defining a new utility function that considers bidders' wealth which is assumed to be different for each bidder. We consider bidders' wealth since it is a significant determinant of their bidding behaviour in these auctions. Also, we define new risk behaviour parameters that change with the relative change in circumstances of bidders' wealth. In our modelling, we assume that the auctioned item is normal and has a reserve price which is known in advance to each bidder. We find ARA solutions not only for risk-neutral but also for risk-averse as well as risk-seeking bidders. We model these auctions by ARA framework using non-strategic play, level-k thinking, mirror equilibrium (ME) and Bayes Nash equilibrium (BNE) solution concepts. Finding ARA solutions using non-strategic play and level-k thinking, ME and BNE (asymmetric case) solution concepts, we assume two bidders. Whereas, we assume n bidders while finding ARA solutions using BNE symmetric case. Second, we use ARA methodology and model bidders' behaviours using the utility function that takes into account bidders' winning and losing regret for the auctioned item. We define new winning and losing regret parameters

The Integrated Nested Laplace Approximation (INLA) provides fast and accurate Bayesian inference for complex hierarchical models. For INLA, and other deterministic methods, the hyperparameter space is explored and points are laid out in a grid structure. These points are used in some numerical integration scheme for which marginal posterior distributions are computed. The main drawback is that the number of points increase exponentially with the number of hyperparameters. The grid is a type of quasi-Monte Carlo (QMC) point set. Low discrepancy sequences (LDS) are QMC point sets that are well known to have significant advantages over grids in terms of convergence and accuracy, and suffer less from the so-called curse of dimensionality. This work makes several important contributions. We introduce a new method using LDS to compute marginal posterior distributions for hyperparameters, discuss the convergence properties of the approximations and show that they converge to the true posterior. We also show how these methods can be incorporated into the INLA inference framework, and we outline important extensions that improve the accuracy of our approximations with little extra computational effort needed. Lastly, we build a unique spatio-temporal model of residential crime in Hamilton, using INLA’s stochastic partial differential equation approach to a Log-Gaussian Cox Process, and use an LDS to approximate the latent parameters of the model. Our results show that for a fixed number of points or computational time, LDS methods can outperform general grid-based methods, leading to better marginal posterior approximations. Modifying the method for the purposes of incorporation to INLA, we show that we can outperform INLA’s grid with respect to computational speed, and obtain accurate and flexible approximations to the model hyperparameters.

The foremost vital action in applying Business Process Re-engineering (BPR) is that the company’s strategic goal to supply customer minded services. BPR could be a technique wont to implement this sort of structure. Having the management commitment for modification, another vital issue for implementing BPR, is that the facultative role of knowledge technology. This working paper stresses the need of re-vamping the organizational structure in order to bring more efficiency in its operations. For this purpose, the BPR is identified as an optimum solution. The paper suggests a re-vamped course of action to improvise the operational effectiveness of the organization.

Lattice rules are equal-weight quadrature rules which are used in the approximation of multidimensional integrands over the s-dimensional unit cube [0,1]ˢ. One of the problems encountered in the study of such rules is the unavailability of a unique representation. It is known that any lattice rule may be expressed in a canonical D - Z form in which D is a diagonal matrix whose diagonal entries are known as the invariants and Z is an integer matrix. Although D is unique in this canonical form, Z may be chosen in many different ways. Except for the case of so-called projection-regular and prime-power rules, no such unique Z is available. In the latter case of prime-power rules, the unique D - Z form developed is known as an ultratriangular form. Associated with each ultratriangular form is a set of column indices. Any lattice rule may be decomposed into prime-power components. In this thesis, a unique D - Z form is defined for a special class of lattice rules for which the component prime-power rules have a consistent set of column indices. This new unique form includes the known unique forms for projection-regular and prime-power rules as special cases. We also use the ultratriangular form for prime-power lattice rules to derive a formula to calculate the number of prime-power rules having a given set of invariants and column indices. The existing theory of lattice rules that is based on the generator matrix of the dual lattice has made the assumption that its representation in the so-called Hermite normal form is upper triangular. However, since projection-regular rules have a unique Z-matrix which is unit upper triangular, the corresponding generator matrix for the dual lattice is lower triangular. This suggests that a lower triangular Hermite normal form might be appropriate for study. We consider this situation and give the conditions on the lower triangular Hermite normal form which allow a projection-regular rule to be easily recognized. Number-theoretic rules