An Auxiliary Variable Method for Markov Chain Monte Carlo Algorithms in High Dimension

A Monte Carlo framework for missing wedge restoration and noise removal in cryo-electron tomography

We propose a statistical method to address an important issue in cryo-electron tomography image analysis: reduction of a high amount of noise and artifacts due to the presence of a missing wedge (MW) in the spectral domain. The method takes as an input a 3D tomogram derived from limited-angle tomography, and gives as an output a 3D denoised and artifact compensated volume. The artifact compensation is achieved by filling up the MW with meaningful information. To address this inverse problem, we compute a Minimum Mean Square Error (MMSE) estimator of the uncorrupted image. The underlying high-dimensional integral is computed by applying a dedicated Markov Chain Monte-Carlo (MCMC) sampling procedure based on the Metropolis-Hasting (MH) algorithm. The proposed MWR (Missing Wedge Restoration) algorithm can be used to enhance visualization or as a pre-processing step for image analysis, including segmentation and classification of macromolecules. Results are presented for both synthetic data and real 3D cryo-electron images.

Gaussian Mixture and Kernel Density-Based Hybrid Model for Volatility Behavior Extraction From Public Financial Data

This paper carried out a hybrid clustering model for foreign exchange market volatility clustering. The proposed model is built using a Gaussian Mixture Model and the inference is done using an Expectation Maximization algorithm. A mono-dimensional kernel density estimator is used in order to build a probability density based on all historical observations. That allows us to evaluate the behavior’s probability of each symbol of interest. The computation result shows that the approach is able to pinpoint risky and safe hours to trade a given currency pair.