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Adaptive designs in the time to event setting: The potential for benefit and risk

Thesis (Ph.D.)--University of Washington, 2016-06

Aspects of Markov Chains and Particle Systems

Thesis (Ph.D.)--University of Washington, 2016-06

Finite mixture regression model with random effects: application to neonatal hospital length of stay

A two-component mixture regression model that allows simultaneously for heterogeneity and dependency among observations is proposed. By specifying random effects explicitly in the linear predictor of the mixture probability and the mixture components, parameter estimation is achieved by maximising the corresponding best linear unbiased prediction type log-likelihood. Approximate residual maximum likelihood estimates are obtained via an EM algorithm in the manner of generalised linear mixed model (GLMM). The method can be extended to a g-component mixture regression model with the component density from the exponential family, leading to the development of the class of finite mixture GLMM. For illustration, the method is applied to analyse neonatal length of stay (LOS). It is shown that identification of pertinent factors that influence hospital LOS can provide important information for health care planning and resource allocation. (C) 2002 Elsevier Science B.V. All rights reserved.

Mixed model formulations for multi-environment trials

When studying genotype X environment interaction in multi-environment trials, plant breeders and geneticists often consider one of the effects, environments or genotypes, to be fixed and the other to be random. However, there are two main formulations for variance component estimation for the mixed model situation, referred to as the unconstrained-parameters (UP) and constrained-parameters (CP) formulations. These formulations give different estimates of genetic correlation and heritability as well as different tests of significance for the random effects factor. The definition of main effects and interactions and the consequences of such definitions should be clearly understood, and the selected formulation should be consistent for both fixed and random effects. A discussion of the practical outcomes of using the two formulations in the analysis of balanced data from multi-environment trials is presented. It is recommended that the CP formulation be used because of the meaning of its parameters and the corresponding variance components. When managed (fixed) environments are considered, users will have more confidence in prediction for them but will not be overconfident in prediction in the target (random) environments. Genetic gain (predicted response to selection in the target environments from the managed environments) is independent of formulation.

Assessing the impacts of grazing levels on bird density in woodland habitat: a Bayesian approach using expert opinion

Many studies on birds focus on the collection of data through an experimental design, suitable for investigation in a classical analysis of variance (ANOVA) framework. Although many findings are confirmed by one or more experts, expert information is rarely used in conjunction with the survey data to enhance the explanatory and predictive power of the model. We explore this neglected aspect of ecological modelling through a study on Australian woodland birds, focusing on the potential impact of different intensities of commercial cattle grazing on bird density in woodland habitat. We examine a number of Bayesian hierarchical random effects models, which cater for overdispersion and a high frequency of zeros in the data using WinBUGS and explore the variation between and within different grazing regimes and species. The impact and value of expert information is investigated through the inclusion of priors that reflect the experience of 20 experts in the field of bird responses to disturbance. Results indicate that expert information moderates the survey data, especially in situations where there are little or no data. When experts agreed, credible intervals for predictions were tightened considerably. When experts failed to agree, results were similar to those evaluated in the absence of expert information. Overall, we found that without expert opinion our knowledge was quite weak. The fact that the survey data is quite consistent, in general, with expert opinion shows that we do know something about birds and grazing and we could learn a lot faster if we used this approach more in ecology, where data are scarce. Copyright (c) 2005 John Wiley & Sons, Ltd.

Nonclassicality of a photon-subtracted Gaussian field

We investigate the nonclassicality of a photon-subtracted Gaussian field, which was produced in a recent experiment, using negativity of the Wigner function and the nonexistence of well-behaved positive P function. We obtain the condition to see negativity of the Wigner function for the case including the mixed Gaussian incoming field, the threshold photodetection and the inefficient homodyne measurement. We show how similar the photon-subtracted state is to a superposition of coherent states.

Searching for convergence in phylogenetic Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a methodology that is gaining widespread use in the phylogenetics community and is central to phylogenetic software packages such as MrBayes. An important issue for users of MCMC methods is how to select appropriate values for adjustable parameters such as the length of the Markov chain or chains, the sampling density, the proposal mechanism, and, if Metropolis-coupled MCMC is being used, the number of heated chains and their temperatures. Although some parameter settings have been examined in detail in the literature, others are frequently chosen with more regard to computational time or personal experience with other data sets. Such choices may lead to inadequate sampling of tree space or an inefficient use of computational resources. We performed a detailed study of convergence and mixing for 70 randomly selected, putatively orthologous protein sets with different sizes and taxonomic compositions. Replicated runs from multiple random starting points permit a more rigorous assessment of convergence, and we developed two novel statistics, delta and epsilon, for this purpose. Although likelihood values invariably stabilized quickly, adequate sampling of the posterior distribution of tree topologies took considerably longer. Our results suggest that multimodality is common for data sets with 30 or more taxa and that this results in slow convergence and mixing. However, we also found that the pragmatic approach of combining data from several short, replicated runs into a metachain to estimate bipartition posterior probabilities provided good approximations, and that such estimates were no worse in approximating a reference posterior distribution than those obtained using a single long run of the same length as the metachain. Precision appears to be best when heated Markov chains have low temperatures, whereas chains with high temperatures appear to sample trees with high posterior probabilities only rarely. [Bayesian phylogenetic inference; heating parameter; Markov chain Monte Carlo; replicated chains.]

The displacement and strain field of three-dimensional rheologic model of earthquake preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.

A scalarization technique for computing the power and exponential moments of gaussian random matrices

We consider the problems of computing the power and exponential moments EXs and EetX of square Gaussian random matrices X=A+BWC for positive integer s and real t, where W is a standard normal random vector and A, B, C are appropriately dimensioned constant matrices. We solve the problems by a matrix product scalarization technique and interpret the solutions in system-theoretic terms. The results of the paper are applicable to Bayesian prediction in multivariate autoregressive time series and mean-reverting diffusion processes.

Energy forward price prediction with a hybrid adaptive model

This paper presents a forecasting technique for forward electricity/gas prices, one day ahead. This technique combines a Kalman filter (KF) and a generalised autoregressive conditional heteroschedasticity (GARCH) model (often used in financial forecasting). The GARCH model is used to compute next value of a time series. The KF updates parameters of the GARCH model when the new observation is available. This technique is applied to real data from the UK energy markets to evaluate its performance. The results show that the forecasting accuracy is improved significantly by using this hybrid model. The methodology can be also applied to forecasting market clearing prices and electricity/gas loads.