We introduce a new class of data-fitting energies that couple image segmentation with image restoration. These functionals model the image intensity using the statistical framework of generalized linear models. By dua...
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We introduce a new class of data-fitting energies that couple image segmentation with image restoration. These functionals model the image intensity using the statistical framework of generalized linear models. By duality, we establish an information-theoretic interpretation using Bregman divergences. We demonstrate how this formulation couples in a principled way image restoration tasks such as denoising, deblurring (deconvolution), and inpainting with segmentation. We present an alternating minimization algorithm to solve the resulting composite photometric/geometric inverse problem. We use Fisher scoring to solve the photometric problem and to provide asymptotic uncertainty estimates. We derive the shape gradient of our data-fitting energy and investigate convex relaxation for the geometric problem. We introduce a new alternating split-Bregman strategy to solve the resulting convex problem and present experiments and comparisons on both synthetic and real-world images.
In this article, we revise the estimation of the dose response function described in Hirano and Imbens (2004, Applied Bayesian modeling and Causal Inference from Incomplete-Data Perspectives, 73-84) by proposing a fle...
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In this article, we revise the estimation of the dose response function described in Hirano and Imbens (2004, Applied Bayesian modeling and Causal Inference from Incomplete-Data Perspectives, 73-84) by proposing a flexible way to estimate the generalized propensity score when the treatment variable is not necessarily normally distributed. We also provide a set of programs that accomplish this task. To do this, in the existing doseresponse program (Bin and Mattei, 2008, Stata Journal 8: 354-373), we substitute the maximum likelihood estimator in the first step of the computation with the more flexible generalized linear model.
The problem of selecting the best treatment is studied under generalized linear models. For certain balanced designs, it is shown that simple rules are Bayes with respect to any non-informative prior on the treatment ...
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The problem of selecting the best treatment is studied under generalized linear models. For certain balanced designs, it is shown that simple rules are Bayes with respect to any non-informative prior on the treatment effects under any monotone invariant loss. When the nuisance parameters such as block effects are assumed to follow a uniform (improper) prior or a normal prior, Bayes rules are obtained for the normal linearmodel under more suitable balanced designs, keeping the generality of the loss and the generality of the non-informativeness on the prior of the treatment effects. These results are extended to certain types of informative priors on the treatment effects. When the designs are unbalanced, algorithms based on the Gibbs sampler and the Laplace method are provided to compute the Bayes rules. (c) 2005 Elsevier B.V. All rights reserved.
In this paper, we continue the development of the ideas introduced in England and Verrall (2001) by suggesting the use of a reparameterized version of the generalized linear model (GLM) which is frequently used in sto...
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In this paper, we continue the development of the ideas introduced in England and Verrall (2001) by suggesting the use of a reparameterized version of the generalized linear model (GLM) which is frequently used in stochastic claims reserving. This model enables us to smooth the origin, development and calendar year parameters in a similar way as is often done in practice, but still keep the GLM structure. Specifically, we use this model structure in order to obtain reserve estimates and to systemize the model selection procedure that arises in the smoothing process. Moreover, we provide a bootstrap procedure to achieve a full predictive distribution. (C) 2011 Elsevier B.V. All rights reserved.
We demonstrate that the efficiency of regression parameter estimates in the generalized linear model can be expressed as a function of Pearson residuals and likelihood based information. The relationship provides an e...
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We demonstrate that the efficiency of regression parameter estimates in the generalized linear model can be expressed as a function of Pearson residuals and likelihood based information. The relationship provides an easy way to derive sandwich variance estimators on (beta) over cap for a specific distribution within the exponential family. In generalized linear models, the correlation between Pearson residual and Fisher information can be used to predict the error ratio of quasi-likelihood variance versus sandwich variance when the sample size is sufficiently large. The derived theory can help to determine which conventional approach to use in the generalized linear model for certain types of data analysis, such as analyzing heteroscedastic data in linear regression;or to analyze over-dispersed data for single parameter families of distributions. The results from reanalysis of a clinical trial data set are used to illustrate issues explored in the paper. (C) 2010 Elsevier B.V. All rights reserved.
It is well known that the exponential dispersion family (EDF) of univariate distributions is closed under Bayesian revision in the presence of natural conjugate priors. However, this is not the case for the general mu...
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It is well known that the exponential dispersion family (EDF) of univariate distributions is closed under Bayesian revision in the presence of natural conjugate priors. However, this is not the case for the general multivariate EDF. This paper derives a second-order approximation to the posterior likelihood of a naturally conjugated generalized linear model (GLM), i.e., multivariate EDF subject to a link function (Section 5.5). It is not the same as a normal approximation. It does, however, lead to second-order Bayes estimators of parameters of the posterior. The family of second-order approximations is found to be closed under Bayesian revision. This generates a recursion for repeated Bayesian revision of the GLM with the acquisition of additional data. The recursion simplifies greatly for a canonical link. The resulting structure is easily extended to a filter for estimation of the parameters of a dynamic generalized linear model (DGLM) (Section 6.2). The Kalman filter emerges as a special case. A second type of link function, related to the canonical link, and with similar properties, is identified. This is called here the companion canonical link. For a given GLM with canonical link, the companion to that link generates a companion GLM (Section 4). The recursive form of the Bayesian revision of this GLM is also obtained (Section 5.5.3). There is a perfect parallel between the development of the GLM recursion and its companion. A dictionary for translation between the two is given so that one is readily derived from the other (Table 5.1). The companion canonical link also generates a companion DGLM. A filter for this is obtained (Section 6.3). Section 1.2 provides an indication of how the theory developed here might be applied to loss reserving. A sequel paper, providing numerical illustrations of this, is planned.
We consider the problem of fitting a generalized linear model to overdispersed data, focussing on a quasilikelihood approach in which the variance is assumed to be proportional to that specified by the model, and the ...
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We consider the problem of fitting a generalized linear model to overdispersed data, focussing on a quasilikelihood approach in which the variance is assumed to be proportional to that specified by the model, and the constant of proportionality, phi, is used to obtain appropriate standard errors and model comparisons. It is common practice to base an estimate of phi on Pearson's lack-of-fit statistic, with or without Farrington's modification. We propose a new estimator that has a smaller variance, subject to a condition on the third moment of the response variable. We conjecture that this condition is likely to be achieved for the important special cases of count and binomial data. We illustrate the benefits of the new estimator using simulations for both count and binomial data.
In toxicological and pharmaceutical experiments, a type of quantal bioassay experiment is designed in which a response, such as mortality, in a group of animals is recorded over time points under different dose levels...
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In toxicological and pharmaceutical experiments, a type of quantal bioassay experiment is designed in which a response, such as mortality, in a group of animals is recorded over time points under different dose levels in the course of the experiment. The application of the typical logit and probit analyses is no longer valid in this situation because it neglects the dependency on time and also the possible interaction of time and dose concentration on the response in the experiment. In this paper, a dose-time-response model is proposed for this type of experiment and a cumulative multinomial generalized linear model that incorporates time and the other experimental conditions as covariates is developed by the theory of maximum likelihood estimation. Both the point estimator and confidence bands for ED50(t), the concentration of a toxicant that will kill 50% of the animals by a specific time, t;as well as LT50 (d), the time to 50% mortalities for a specific concentration, d, is then formulated in closed form from the newly proposed dose-time-response model. Finally, the newly proposed model is considered for a real data set to demonstrate the application.
Over the last 20-30 years, there has been a significant amount of tools and statistical methods that have been proposed for analyzing crash data. Yet, the Poisson-gamma (PG) is still the most commonly used and widely ...
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Over the last 20-30 years, there has been a significant amount of tools and statistical methods that have been proposed for analyzing crash data. Yet, the Poisson-gamma (PG) is still the most commonly used and widely acceptable model. This paper documents the application of the Poisson-Weibull (PW) generalized linear model (GLM) for modeling motor vehicle crashes. The objectives of this study were to evaluate the application of the PW GLM for analyzing this kind of dataset and compare the results with the traditional PG model. To accomplish the objectives of the study, the modeling performance of the PW model was first examined using a simulated dataset and then several PW and PG GLMs were developed and compared using two observed crash datasets. The results of this study show that the PW GLM performs as well as the PG GLM in terms of goodness-of-fit statistics. (C) 2012 Elsevier Ltd. All rights reserved.
For censored response variable against projected co-variable, a generalized linear model with an unknown link function can cover almost all existing models under censorship. Its special cases include the accelerated f...
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For censored response variable against projected co-variable, a generalized linear model with an unknown link function can cover almost all existing models under censorship. Its special cases include the accelerated failure time model with censored data. Such a model in the uncensored case is called the single-index model in econometrics. In this paper, we systematically study the asymptotic properties. We derive the central limit theorem and the law of the iterated logarithm for an estimator of the direction parameter. We also obtain the optimal convergence rate of an estimator of the unknown link function in the model.
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