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.

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

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

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

Bayesian Analysis for Penalized Spline Regression Using Win BUGS

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. MCMC mixing is substantially improved from the previous versions by using low{rank thin{plate splines instead of truncated polynomial basis. Simulation time per iteration is reduced 5 to 10 times using a computational trick

Asymptotic normality and valid inference for Gaussian variational approximation

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

The translation, validity and reliability of the German version of the Fremantle Back Awareness Questionnaire

Background: The Fremantle Back Awareness Questionnaire (FreBAQ) claims to assess disrupted self-perception of the back. The aim of this study was to develop a German version of the Fre-BAQ (FreBAQ-G) and assess its test-retest reliability, its known-groups validity and its convergent validity with another purported measure of back perception. Methods: The FreBaQ-G was translated following international guidelines for the transcultural adaptation of questionnaires. Thirty-five patients with non-specific CLBP and 48 healthy participants were recruited. Assessor one administered the FreBAQ-G to each patient with CLBP on two separate days to quantify intra-observer reliability. Assessor two administered the FreBaQ-G to each patient on day 1. The scores were compared to those obtained by assessor one on day 1 to assess inter-observer reliability. Known-groups validity was quantified by comparing the FreBAQ-G score between patients and healthy controls. To assess convergent validity, patient\u27s FreBAQ-G scores were correlated to their two-point discrimination (TPD) scores. Results: Intra- and Inter-observer reliability were both moderate with ICC3.1 = 0.88 (95%CI: 0.77 to 0.94) and 0.89 (95%CI: 0.79 to 0.94), respectively. Intra- and inter-observer limits of agreement (LoA) were 6.2 (95%CI: 5.0±8.1) and 6.0 (4.8±7.8), respectively. The adjusted mean difference between patients and controls was 5.4 (95%CI: 3.0 to 7.8, p\u3c0.01). Patient\u27s FreBAQ-G scores were not associated with TPD thresholds (Pearson\u27s r = -0.05, p = 0.79). Conclusions: The FreBAQ-G demonstrated a degree of reliability and known-groups validity. Interpretation of patient level data should be performed with caution because the LoA were substantial. It did not demonstrate convergent validity against TPD. Floor effects of some items of the FreBAQ-G may have influenced the validity and reliability results. The clinimetric properties of the FreBAQ-G require further investigation as a simple measure of disrupted self-perception of the back before firm recommendations on its use can be made