5,405 research outputs found
Design of experiments with mixed effects and discrete responses plus related topics
No full textFor certain types of experiment, the response cannot be adequately modelled using a normal distribution. When this is the case, it is common to use a Generalised Linear Model (GLM) to analyse the data. Such models allow us to fit a wide range of response distributions including Bernoulli and Poisson.If responses in the same block are correlated, it may be appropriate to model the impact of blocking using random effects. The GLM can be extended in several ways to include random effects; both Generalised Linear Mixed Models (GLMMs) and Hierarchical Generalised Linear Models (HGLMs) are common examples of such extensions. Another example is a random intercept model for a binary response bioassay study with repeated measurements on heterogeneous individuals. The latter model is related to a GLMM but not strictly within that class.Obtaining designs for non-normal models with random effects is complicated by the fact that the information matrix, on which most optimality criteria are based, is computationally expensive to evaluate. Indeed, if one computes naively, the search for a typical optimal GLMM design is likely to take several months.When estimating GLMMs, it is common to use analytical approximations such as marginal quasi-likelihood (MQL) and penalised quasi-likelihood (PQL) in place of full maximum likelihood estimation. In Chapters 2 and 3, we consider the use of such computationally cheap approximations to construct surrogates for the information matrix when producing optimal designs. These reduce the computational burden substantially, enabling us to obtain designs within a practical time frame. The accuracy of the analytical approximations is explored through the use of a detailed computational approximation, which enables us to compute the optimal maximum likelihood design in the case where there are at most two points per block. It is found that one of the analytical approximations appears to perform consistently better than the others for the purposes of producing designs.In Chapters 4 and 5, designs for an individual variation bioassay model are obtained in the cases where (i) there is a single observation, or (ii) there are multiple observations, per individual. In the former case, designs on the basis of both maximum likelihood and analytical approximations are found and compared. In the multiple observation case, a restriction on the design space enables optimal designs to be computed using a computational approximation related to that for GLMMs. This involves extensive precomputation of numerical integrals.In Chapter 6 designs for HGLMs are studied using a computationally inexpensive asymptotic approximation to the variance-covariance matrix of the parameter estimators. This allows us to derive designs which are also efficient for the estimation of the random effects.Throughout, the dependence of the optimal design on the unknown values of the model parameters is addressed through the use of Bayesian methods, which codify uncertainty about the parameter values using a prior distribution. We often assess the performance of the designs obtained from the optimisation of a Bayesian objective function in terms of the distribution on the local efficiencies which is induced by the prior distribution.When the parameter space contains degenerate values, there is a problem with potential non-convergence of the Bayesian objective function used to select designs. This issue is explored in depth in Chapter 7, and results are obtained for a number of standard models
Singular prior distributions in Bayesian D-optimal design for nonlinear models
No full textFor Bayesian D-optimal design, we define a singular prior distribution to be a prior distribution such that the determinant of the Fisher information matrix has a prior geometric mean of zero for all designs. For such a prior distribution, the Bayesian D-optimality criterion fails to select a design. For the exponential decay model, we characterize singularity of the prior distribution in terms of the expectations of a few elementary transformations of the parameter. For a compartmental model and multi-parameter logistic regression we establish sufficient conditions for singularity of a prior distribution. For logistic regression we also obtain sufficient conditions for non-singularity. The results are applied to show that the weakly informative prior distribution proposed as a default for inference by Gelman, Jakulin, Pittau and Su (2008) should not be used for Bayesian D-optimal design. Additionally, we develop methods to derive and assess Bayesian D-efficient designs for logistic regression when numerical evaluation of the objective function fails due to ill-conditioning
Minimax-efficient random experimental design strategies with application to model-robust design for prediction
No full textIn game theory and statistical decision theory, a random (i.e., mixed) decision strategy often outperforms a deterministic strategy in minimax expected loss. As experimental design can be viewed as a game pitting the Statistician against Nature, the use of a random strategy to choose a design will often be beneficial. However, the topic of minimax-efficient random strategies for design selection is mostly unexplored, with consideration limited to Fisherian randomization of the allocation of a predetermined set of treatments to experimental units. Here, for the first time, novel and more flexible random design strategies are shown to have better properties than their deterministic counterparts in linear model estimation and prediction, including stronger bounds on both the expectation and survivor function of the loss distribution. Design strategies are considered for three important statistical problems: (i) parameter estimation in linear potential outcomes models, (ii) point prediction from a correct linear model, and (iii) global prediction from a linear model taking into account an L
2-class of possible model discrepancy functions. The new random design strategies proposed for (iii) give a finite bound on the expected loss, a dramatic improvement compared to existing deterministic exact designs for which the expected loss is unbounded. Supplementary materials for this article are available online.
</p
Variations on the Author
No full text“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Designs for generalized linear models with random block effects via information matrix approximations
No full textThe selection of optimal designs for generalized linear mixed models is complicated by the fact that the Fisher information matrix, on which most optimality criteria depend, is computationally expensive to evaluate. Our focus is on the design of experiments for likelihood estimation of parameters in the conditional model. We provide two novel approximations that substantially reduce the computational cost of evaluating the information matrix by complete enumeration of response outcomes, or Monte Carlo approximations thereof: (i) an asymptotic approximation which is accurate when there is strong dependence between observations in the same block; (ii) an approximation via Kriging interpolators. For logistic random intercept models, we show how interpolation can be especially effective for finding pseudo-Bayesian designs that incorporate uncertainty in the values of the model parameters. The new results are used to provide the first evaluation of the efficiency, for estimating conditional models, of optimal designs from closed-form approximations to the information matrix derived from marginal models. It is found that correcting for the marginal attenuation of parameters in binary-response models yields much improved designs, typically with very high efficiencies. However, in some experiments exhibiting strong dependence, designs for marginal models may still be inefficient for conditional modelling. Our asymptotic results provide some theoretical insights into why such inefficiencies occur
Approximate Laplace importance sampling for the estimation of expected Shannon information gain in high-dimensional Bayesian design for nonlinear models
No full textOne of the major challenges in Bayesian optimal design is to approximate the expected utility function in an accurate and computationally efficient manner. We focus on Shannon information gain, one of the most widely used utilities when the experimental goal is parameter inference. We compare the performance of various methods for approximating expected Shannon information gain in common nonlinear models from the statistics literature, with a particular emphasis on Laplace importance sampling (LIS) and approximate Laplace importance sampling (ALIS), a new method that aims to reduce the computational cost of LIS. Specifically, in order to centre the importance distributions LIS requires computation of the posterior mode for each of a large number of simulated possibilities for the response vector. ALIS substantially reduces the amount of numerical optimization that is required, in some cases eliminating all optimization, by centering the importance distributions on the data-generating parameter values wherever possible. Both methods are thoroughly compared with existing approximations including Double Loop Monte Carlo, nested importance sampling, and Laplace approximation. It is found that LIS and ALIS both give an efficient trade-off between mean squared error and computational cost for utility estimation, and ALIS can be up to 70% cheaper than LIS. Usually ALIS gives an approximation that is cheaper but less accurate than LIS, while still being efficient, giving a useful addition to the suite of efficient methods. However, we observed one case where ALIS is both cheaper and more accurate. In addition, for the first time we show that LIS and ALIS yield superior designs to existing methods in problems with large numbers of model parameters when combined with the approximate co-ordinate exchange algorithm for design optimization
Bayesian design of experiments for generalised linear models and dimensional analysis with industrial and scientific application
No full textThe design of an experiment can always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the explanatory variables and measured responses. Bayesian methods allow uncertainty in these decisions to be incorporated into design selection through prior distributions that encapsulate information available from scientific knowledge or previous experimentation. Further, a design may be explicitly tailored to the aim of the experiment through a decision-theoretic approach using an appropriate loss function. We review the area of decision-theoretic Bayesian design, with particular emphasis on recent advances in computational methods. For many problems arising in industry and science, experiments result in a discrete response that is well described by a member of the class of generalized linear models. Bayesian design for such nonlinear models is often seen as impractical as the expected loss is analytically intractable and numerical approximations are usually computationally expensive. We describe how Gaussian process emulation, commonly used in computer experiments, can play an important role in facilitating Bayesian design for realistic problems. A main focus is the combination of Gaussian process regression to approximate the expected loss with cyclic descent (coordinate exchange) optimization algorithms to allow optimal designs to be found for previously infeasible problems. We also present the first optimal design results for statistical models formed from dimensional analysis, a methodology widely employed in the engineering and physical sciences to produce parsimonious and interpretable models. Using the famous paper helicopter experiment, we show the potential for the combination of Bayesian design, generalized linear models, and dimensional analysis to produce small but informative experiments
Money piece by Timothy P. Agnew, chief executive officer of the Finance Author
No full textMoney piece by Timothy P. Agnew, chief executive officer of the Finance Authority of Maine, about the increased availability of credit for Maine\u27s small businesses
Timothy Meyer serves as a contributing author for UN report
No full textAssistant Professor Timothy Meyer served as a contributing author for the United Nations Industrial Development Organization\u27s report titled Networks for Prosperity: Connecting Development Knowledge Beyond 2015. The document, which was released during November, analyzes the nexus between the global connectedness of a country and its economic success, sustainability and government effectiveness. Meyer was one of only approximately 20 academic and practical experts from around the world selected to serve as a contributor after a global call for proposals.
Learn more View the full repor
Selected Contributions of Sister Mary Berenice Beck, O.S.F. to Nursing in the United States, 1923-1956
No full textby Sister M. Timothy Costello.Typescript.Thesis (M.S.N.)--Catholic University of America.Bibliography: leaves 44-47.Also available in microfilm
- …
