2,079 research outputs found

    Asymptotics and optimal bandwidth selection for highest density region estimation

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    We study kernel estimation of highest-density regions (HDR). Our main contributions are two-fold. First, we derive a uniform-in-bandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then used to derive a bandwidth selection rule for HDR estimation possessing attractive asymptotic properties. We also present the results of numerical studies that illustrate the benefits of our theory and methodology.Comment: Published in at http://dx.doi.org/10.1214/09-AOS766 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    General Design Bayesian Generalized Linear Mixed Models

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    Linear mixed models are able to handle an extraordinary range of complications in regression-type analyses. Their most common use is to account for within-subject correlation in longitudinal data analysis. They are also the standard vehicle for smoothing spatial count data. However, when treated in full generality, mixed models can also handle spline-type smoothing and closely approximate kriging. This allows for nonparametric regression models (e.g., additive models and varying coefficient models) to be handled within the mixed model framework. The key is to allow the random effects design matrix to have general structure; hence our label general design. For continuous response data, particularly when Gaussianity of the response is reasonably assumed, computation is now quite mature and supported by the R, SAS and S-PLUS packages. Such is not the case for binary and count responses, where generalized linear mixed models (GLMMs) are required, but are hindered by the presence of intractable multivariate integrals. Software known to us supports special cases of the GLMM (e.g., PROC NLMIXED in SAS or glmmML in R) or relies on the sometimes crude Laplace-type approximation of integrals (e.g., the SAS macro glimmix or glmmPQL in R). This paper describes the fitting of general design generalized linear mixed models. A Bayesian approach is taken and Markov chain Monte Carlo (MCMC) is used for estimation and inference. In this generalized setting, MCMC requires sampling from nonstandard distributions. In this article, we demonstrate that the MCMC package WinBUGS facilitates sound fitting of general design Bayesian generalized linear mixed models in practice.Comment: Published at http://dx.doi.org/10.1214/088342306000000015 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Prevalence, characteristics and management of headache experienced by people with schizophrenia and schizoaffective disorder: a cross sectional cohort study

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    Objective: Headache is the most common type of pain reported by people with schizophrenia. This study aimed to establish prevalence, characteristics and management of these headache. Method: One-hundred participants with schizophrenia/schizoaffective disorder completed a reliable and valid headache questionnaire. Two clinicians independently classified each headache as migraine (MH), tension-type (TTH), cervicogenic (CGH) or other (OH). Results: The twelve-month prevalence of headache (57%) was higher than the general population (46%) with no evidence of a relationship between psychiatric clinical characteristics and presence of headache. Prevalence of CGH (5%) and MH (18%) was comparable to the general population. TTH (16%) had a lower prevalence and 19% of participant’s experienced OH. No-one with MH was prescribed migraine specific medication, no-one with CGH and TTH received best-practice treatment Conclusion: Headache is a common complaint in people with schizophrenia/schizoaffective disorder with most fitting recognised diagnostic criteria for which effective interventions are available. No-one in this sample was receiving best-practice care for their headache

    Variational inference for count response semiparametric regression

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    © 2015 International Society for Bayesian Analysis. Fast variational approximate algorithms are developed for Bayesian semiparametric regression when the response variable is a count, i.e., a nonnegative integer. We treat both the Poisson and Negative Binomial families as models for the response variable. Our approach utilizes recently developed methodology known as non-conjugate variational message passing. For concreteness, we focus on generalized additive mixed models, although our variational approximation approach extends to a wide class of semiparametric regression models such as those containing interactions and elaborate random effect structure

    Self reported aggravating activities do not demonstrate a consistent directional pattern in chronic non specific low back pain patients: An observational study

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    Question: Do the self-reported aggravating activities of chronic non-specific low back pain patients demonstrate a consistent directional pattern? Design: Cross-sectional observational study. Participants: 240 chronic non specific low back pain patients. Outcome measure: We invited experienced clinicians to classify each of the three self-nominated aggravating activities from the Patient Specific Functional Scale by the direction of lumbar spine movement. Patients were described as demonstrating a directional pattern if all nominated activities moved the spine into the same direction. Analyses were undertaken to determine if the proportion of patients demonstrating a directional pattern was greater than would be expected by chance. Results: In some patients, all tasks did move the spine into the same direction, but this proportion did not differ from chance (p = 0.328). There were no clinical or demographic differences between those who displayed a directional pattern and those who did not (all p > 0.05). Conclusion: Using patient self-reported aggravating activities we were unable to demonstrate the existence of a consistent pattern of adverse movement in patients with chronic non-specific low back pain

    Functional regression via variational bayes

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    We introduce variational Bayes methods for fast approximate inference in functional regression analysis. Both the standard cross-sectional and the increasingly common longitudinal settings are treated. The method- ology allows Bayesian functional regression analyses to be conducted with- out the computational overhead of Monte Carlo methods. Confidence in- tervals of the model parameters are obtained both using the approximate variational approach and nonparametric resampling of clusters. The latter approach is possible because our variational Bayes functional regression ap- proach is computationally efficient. A simulation study indicates that varia- tional Bayes is highly accurate in estimating the parameters of interest and in approximating the Markov chain Monte Carlo-sampled joint posterior distribution of the model parameters. The methods apply generally, but are motivated by a longitudinal neuroimaging study of multiple sclerosis patients. Code used in simulations is made available as a web-supplement

    More SPASS with Isabelle: superposition with hard sorts and configurable simplification

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    Sledgehammer for Isabelle/HOL integrates automatic theorem provers to discharge interactive proof obligations. This paper considers a tighter integration of the superposition prover SPASS to increase Sledgehammer’s success rate. The main enhancements are native support for hard sorts (simple types) in SPASS, simplification that honors the orientation of Isabelle simp rules, and a pair of clause-selection strategies targeted at large lemma libraries. The usefulness of this integration is confirmed by an evaluation on a vast benchmark suite and by a case study featuring a formalization of language-based security

    Asymptotic normality and valid inference for Gaussian variational approximation

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    We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical properties of a variational approximation method. Moreover, they give rise to asymptotically valid statistical inference. A simulation study demonstrates that Gaussian variational approximate confidence intervals possess good to excellent coverage properties, and have a similar precision to their exact likelihood counterparts
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