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.

Portable, Fiber-Based, Diffuse Reflection Spectroscopy (DRS) Systems for Estimating Tissue Optical Properties.

Steady-state diffuse reflection spectroscopy is a well-studied optical technique that can provide a noninvasive and quantitative method for characterizing the absorption and scattering properties of biological tissues. Here, we compare three fiber-based diffuse reflection spectroscopy systems that were assembled to create a light-weight, portable, and robust optical spectrometer that could be easily translated for repeated and reliable use in mobile settings. The three systems were built using a broadband light source and a compact, commercially available spectrograph. We tested two different light sources and two spectrographs (manufactured by two different vendors). The assembled systems were characterized by their signal-to-noise ratios, the source-intensity drifts, and detector linearity. We quantified the performance of these instruments in extracting optical properties from diffuse reflectance spectra in tissue-mimicking liquid phantoms with well-controlled optical absorption and scattering coefficients. We show that all assembled systems were able to extract the optical absorption and scattering properties with errors less than 10%, while providing greater than ten-fold decrease in footprint and cost (relative to a previously well-characterized and widely used commercial system). Finally, we demonstrate the use of these small systems to measure optical biomarkers in vivo in a small-animal model cancer therapy study. We show that optical measurements from the simple portable system provide estimates of tumor oxygen saturation similar to those detected using the commercial system in murine tumor models of head and neck cancer.