Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.

Are component positioning and prosthesis size associated with hip resurfacing failure?

BACKGROUND: Recent studies suggest that there is a learning curve for metal-on-metal hip resurfacing. The purpose of this study was to assess whether implant positioning changed with surgeon experience and whether positioning and component sizing were associated with implant longevity. METHODS: We evaluated the first 361 consecutive hip resurfacings performed by a single surgeon, which had a mean follow-up of 59 months (range, 28 to 87 months). Pre and post-operative radiographs were assessed to determine the inclination of the acetabular component, as well as the sagittal and coronal femoral stem-neck angles. Changes in the precision of component placement were determined by assessing changes in the standard deviation of each measurement using variance ratio and linear regression analysis. Additionally, the cup and stem-shaft angles as well as component sizes were compared between the 31 hips that failed over the follow-up period and the surviving components to assess for any differences that might have been associated with an increased risk for failure. RESULTS: Surgeon experience was correlated with improved precision of the antero-posterior and lateral positioning of the femoral component. However, femoral and acetabular radiographic implant positioning angles were not different between the surviving hips and failures. The failures had smaller mean femoral component diameters as compared to the non-failure group (44 versus 47 millimeters). CONCLUSIONS: These results suggest that there may be differences in implant positioning in early versus late learning curve procedures, but that in the absence of recognized risk factors such as intra-operative notching of the femoral neck and cup inclination in excess of 50 degrees, component positioning does not appear to be associated with failure. Nevertheless, surgeons should exercise caution in operating patients with small femoral necks, especially when they are early in the learning curve.