Prior Information in Linear Models

The predictive accuracy of a Rainfall–Runoff Neural Network (RRNN) model depends largely on the suitability of its structure. Unfortunately, the procedures for selecting an appropriate structure for the RRNN have not been thoroughly examined. Inclusion of too many input neurons in the RRNN may complicate its structure, and thereby decrease its generalization performance. The objective of this study is to evaluate the potential of a Principal Component Analysis (PCA) method, i.e. by extracting the principal components from lagged input hydrometeorological data, in improving the predictive accuracy of the RRNN. The Darong River watershed located in Guangxi Province of China, with a drainage area of 722 km 2 , has been selected to demonstrate the PCA method for modeling the hourly Rainfall–Runoff (RR) relationship. Comparative tests on the forecasting accuracy were conducted among the RRNNs configured with both basin-averaged and spatially distributed rainfall information. Experimental results revealed that, when calibrating the RRNNs with spatially distributed rainfall, the RRNNs using the PCA as an input data-preprocessing tool were found to provide a generally better representation of the RR relationship for the Darong River watershed. However, variable results were observed if the neural networks had been calibrated with basin-averaged rainfall.

Rainfall–runoff modeling using principal component analysis and neural network

‘Being church’ in today’s world is frought with challenges to traditional practice and contemporaneous opportunities. These challenges, differences, dilemmas and paradoxes, when not handled effectively, have the propensity to escalate into and along a conflict continuum. Conflict can arise at any time within a congregation and needs to be understood and handled theologically. This article addresses some areas within congregations that attract or incubate conflict and provides an overview of related theory of conflict. The research explores current perceptions, understandings and behavioural responses to conflict, personal and corporate experiences and observed outcomes of conflict within congregations. The exploratory study reveals certain disconnects between individual and corporate practice. Congregations in general are biased towards conflict avoidance, peacekeeping and reconciliatory measures – frequently at the expense of long-term resolution. Attaining both resolution and reconciliation appears to be a luxury and not the natural outcome one may expect within Christian fellowship. The perception, understanding and views of most congregants are not aligned to good theological principles and practice. The resultant behaviour mostly observed within congregations does not lead to reconciliation and to a lesser extent resolution. Despite the seemingly high presence of conflict within congregations, no specified education on the understanding, appreciation and handling of conflict in commonly used discipleship resources or dedicated programme was found. The article concludes with a view towards a future praxis of discipleship and leadership, which incorporates the theological understanding and handling of conflict. Broader means of assisting congregations in or post conflict to recovery are also presented.

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Conflict resolution and reconciliation within congregations

The properties of the estimators of population mean arising from the ratio and product methods of estimation in the context of sample surveys have been analyzed in this paper when the observations on both the study and auxiliary variables are contaminated with measurement errors. The measurement errors in both the variables are also correlated. The properties of the ratio and product estimators along with the sample mean under the influence of measurement errors are derived and studied. The properties of the estimators in finite samples are studied through Monte-Carlo simulation and its findings are reported.

Ratio and product methods of estimation of population mean in the presence of correlated measurement errors

Projector Quantum Monte Carlo Methods for Linear and Non-linear Wavefunction Ansatzes Lauretta Rebecca Schwarz This thesis is concerned with the development of a Projector Quantum Monte Carlo method for non-linear wavefunction ansatzes and its application to strongly correlated materials. This new approach is partially inspired by a prior application of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method to the threeband (p− d) Hubbard model. Through repeated stochastic application of a projector FCIQMC projects out a stochastic description of the Full Configuration Interaction (FCI) ground state wavefunction, a linear combination of Slater determinants spanning the full Hilbert space. The study of the p− d Hubbard model demonstrates that the nature of this FCI expansion is profoundly affected by the choice of single-particle basis. In a counterintuitive manner, the effectiveness of a one-particle basis to produce a sparse, compact and rapidly converging FCI expansion is not necessarily paralleled by its ability to describe the physics of the system within a single determinant. The results suggest that with an appropriate basis, single-reference quantum chemical approaches may be able to describe many-body wavefunctions of strongly correlated materials. Furthermore, this thesis presents a reformulation of the projected imaginary time evolution of FCIQMC as a Lagrangian minimisation. This naturally allows for the optimisation of polynomial complex wavefunction ansatzes with a polynomial rather than exponential scaling with system size. The proposed approach blurs the line between traditional Variational and Projector Quantum Monte Carlo approaches whilst involving developments from the field of deep-learning neural networks which can be expressed as a modification of the projector. The ability of the developed approach to sample and optimise arbitrary non-linear wavefunctions is demonstrated with several classes of Tensor Network States all of which involve controlled approximations but still retain systematic improvability towards exactness. Thus, by applying the method to strongly-correlated Hubbard models, as well as ab-initio systems, including a fully periodic ab-initio graphene sheet, many-body wavefunctions and their oneand two-body static properties are obtained. The proposed approach can handle and simultaneously optimise large numbers of variational parameters, greatly exceeding those of alternative Variational Monte Carlo approaches.

Projector Quantum Monte Carlo Methods for Linear and Non-linear Wavefunction Ansatzes

Simple Random Sampling Sampling with Varying Probabilities of Selection Stratified Sampling Systematic Sampling Ratio Method of Estimation Regression Method of Estimation Cluster Sampling Sub-Sampling Two-Stage and Three-Stage Sampling Double Sampling Non-Sampling Errors.

Theory of sample surveys

Razzaghi (1987) conjectures that a wrong choice of covariance matrix in a restricted linear model results in loss of efficiency, This conjecture is proved to be correct.

On a superiority problem in misspecified restricted linear models

Multivariate Statistical Inference

When a sample of size n is available from a mixture of two normal populations with different mean vectors and a common covariance matrix, SRIVASTAVA and AWAN (1982) develop one-way ANOVA analysis for testing a certain composite linear hypothesis. They show that the error and hypothesis sum of products matrices have independent noncentral Wishart densities of rank unity each. However, they do not obtain the necessary Wilks' λ for testing the desired hypothesis. The present paper obtains the density of λ. This density is doubly noncentral multivariate beta density. The derivation is based on generalized Sverdrup's lemmas, KABE (1965), (1974).

D. G. Kabe

Papers

Theory of sample surveys

On a superiority problem in misspecified restricted linear models

Multivariate Statistical Inference

Multivariate Statistical Inference

One‐Way Classification ANOVA Model for the Mixture of Two Multivariate Normal Populations