The Inverse G-Wishart Distribution and Variational Message Passing

Message passing on a factor graph is a powerful paradigm for the coding of approximate inference algorithms for arbitrarily graphical large models. The notion of a factor graph fragment allows for compartmentalization of algebra and computer code. We show that the Inverse G-Wishart family of distributions enables fundamental variational message passing factor graph fragments to be expressed elegantly and succinctly. Such fragments arise in models for which approximate inference concerning covariance matrix or variance parameters is made, and are ubiquitous in contemporary statistics and machine learning

Asymptotics and optimal bandwidth selection for highest density region estimation

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

A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

Bayesian Analysis for Penalized Spline Regression Using WinBUGS

Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact inference provided by the Bayesian inferential machinery. This paper provides a simple, yet comprehensive, set of programs for the implementation of nonparametric Bayesian analysis in WinBUGS. Good mixing properties of the MCMC chains are obtained by using low-rank thin-plate splines, while simulation times per iteration are reduced employing WinBUGS specific computational tricks.

General Design Bayesian Generalized Linear Mixed Models

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

Grip and muscle strength dynamometry in acute burn injury: Evaluation of an updated assessment protocol

External stabilization is reported to improve reliability of hand held dynamometry, yet this has not been tested in burns. We aimed to assess the reliability of dynamometry using an external system of stabilization in people with moderate burn injury and explore construct validity of strength assessment using dynamometry. Participants were assessed on muscle and grip strength three times on each side. Assessment occurred three times per week for up to four weeks. Within session reliability was assessed using intraclass correlations calculated for within session data grouped prior to surgery, immediately after surgery and in the sub-acute phase of injury. Minimum detectable differences were also calculated. In the same timeframe categories, construct validity was explored using regression analysis incorporating burn severity and demographic characteristics. Thirty-eight participants with total burn surface area 5 – 40% were recruited. Reliability was determined to be clinically applicable for the assessment method (intraclass correlation coefficient \u3e0.75) at all phases after injury. Muscle strength was associated with sex and burn location during injury and wound healing. Burn size in the immediate period after surgery and age in the sub-acute phase of injury were also associated with muscle strength assessment results. Hand held dynamometry is a reliable assessment tool for evaluating within session muscle strength in the acute and sub-acute phase of injury in burns up to 40% total burn surface area. External stabilization may assist to eliminate reliability issues related to patient and assessor strength

Predicting outcome in acute low back pain using different models of patient profiling

Study Design: Prospective observational study of prognostic indicators, utilising data from a randomised, controlled trial of physiotherapy care of acute low back pain (ALBP) with follow up at 6 weeks, 3 months and 6 months. Objective: To evaluate which patient profile offers the most useful guide to long-term outcome in ALBP. Summary of Background Data: The evidence used to inform prognostic decision-making is derived largely from studies where baseline data is used to predict future status. Clinicians often see patients on multiple occasions so may profile patients in a variety of ways. It is worth considering if better prognostic decisions can be made from alternative profiles. Methods: Clinical, psychological and demographic data were collected from a sample of 54 ALBP patients. Three clinical profiles were developed from information collected at baseline, information collected at 6 weeks, and the change in status between these two time points. A series of regression models were used to determine the independent and relative contributions of these profiles to the prediction of chronic pain and disability. Results: The baseline profile predicted long-term pain only. The 6-week profile predicted both long-term pain and disability. The change profile only predicted long-term disability (p \u3c 0.01). When predicting long-term pain, after the baseline profile had been added to the model, the 6-week profile did not add significantly when forced in at the second step (p \u3e 0.05). A similar result was obtained when the order of entry was reversed. When predicting long-term disability, after the 6-week profile was entered at the first step, the change profile was not significant when forced in at the second step. However, when the change profile was entered at the first step and the 6-week clinical profile was forced in at the second step, a significant contribution of the 6-week profile was found. Conclusions: The profile derived from information collected at 6 weeks provided the best guide to long-term pain and disability. The baseline profile and change in status offered less predictive value

Tactile Thresholds are Preserved yet Cortical Sensory Function is Impaired in Chronic Non-Specific Low Back Pain Patients

Introduction: A substantial amount of evidence points to an alteration in brain structure and function patients with chronic non-specific low back pain (CNSLBP) [1-6]. One interpretation of these findings is that the observed brain changes may represent a disruption of the brain’s representations of the body part and the resultant body perception disturbance may underpin this clinical problem. The current study aimed to investigate sensory dysfunction in CNSLBP. Specifically we aimed to distinguish cortically mediated sensory dysfunction from peripheral dysfunction by comparing simple tactile thresholds with more complex cortically mediated sensory tests Methods: We investigated tactile thresholds (TTH), two point discrimination (TPD) and graphaesthesia over the lumbar spine of 19 CLBP patients and 19 age and sex matched healthy controls as a way of investigating whether CLBP patients present with a perceptual disturbance of their lumbar spine. Differences in performance of the sensory tests was explored using the Mann Whitney U Test and one-way between groups multivariate analysis of variance. Results: We found no difference in tactile threshold between the two groups (P=.0.751). There was a statistically significant difference between controls and LBP for TPD: F(1,36)=10.15, p=.003 and letter error rate: F(1, 36)=6.54 p=0.015. The data indicate that LBP patients had a larger lumbar TPD distance and a greater letter recognition error rate. Discussion: Both TPD and graphaesthesia are dependant on the integrity of the primary sensory cortex [7]. These data support existing findings of perceptual abnormality in chronic back pain [8] and the preservation of tactile thresholds is suggestive of cortical rather than peripheral sensory dysfunction. Amelioration of these abnormalities may present a target for therapeutic intervention

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

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

Adversarial reverse mapping of equilibrated condensed-phase molecular structures

A tight and consistent link between resolutions is crucial to further expand the impact of multiscale modeling for complex materials. We herein tackle the generation of condensed molecular structures as a refinement—backmapping—of a coarse-grained (CG) structure. Traditional schemes start from a rough coarse-to-fine mapping and perform further energy minimization and molecular dynamics simulations to equilibrate the system. In this study we introduce DeepBackmap: A deep neural network based approach to directly predict equilibrated molecular structures for condensed-phase systems. We use generative adversarial networks to learn the Boltzmann distribution from training data and realize reverse mapping by using the CG structure as a conditional input. We apply our method to a challenging condensed-phase polymeric system. We observe that the model trained in a melt has remarkable transferability to the crystalline phase. The combination of data-driven and physics-based aspects of our architecture help reach temperature transferability with only limited training data