Adapting data processing to compare model and experiment accurately: A discrete element model and magnetic resonance measurements of a 3d cylindrical fluidized bed

Discrete element modeling is being used increasingly to simulate flow in fluidized beds. These models require complex measurement techniques to provide validation for the approximations inherent in the model. This paper introduces the idea of modeling the experiment to ensure that the validation is accurate. Specifically, a 3D, cylindrical gas-fluidized bed was simulated using a discrete element model (DEM) for particle motion coupled with computational fluid dynamics (CFD) to describe the flow of gas. The results for time-averaged, axial velocity during bubbling fluidization were compared with those from magnetic resonance (MR) experiments made on the bed. The DEM-CFD data were postprocessed with various methods to produce time-averaged velocity maps for comparison with the MR results, including a method which closely matched the pulse sequence and data processing procedure used in the MR experiments. The DEM-CFD results processed with the MR-type time-averaging closely matched experimental MR results, validating the DEM-CFD model. Analysis of different averaging procedures confirmed that MR time-averages of dynamic systems correspond to particle-weighted averaging, rather than frame-weighted averaging, and also demonstrated that the use of Gaussian slices in MR imaging of dynamic systems is valid. © 2013 American Chemical Society.

Dynamic Covariance Models for Multivariate Financial Time Series

The accurate prediction of time-changing covariances is an important problem in the modeling of multivariate financial data. However, some of the most popular models suffer from a) overfitting problems and multiple local optima, b) failure to capture shifts in market conditions and c) large computational costs. To address these problems we introduce a novel dynamic model for time-changing covariances. Over-fitting and local optima are avoided by following a Bayesian approach instead of computing point estimates. Changes in market conditions are captured by assuming a diffusion process in parameter values, and finally computationally efficient and scalable inference is performed using particle filters. Experiments with financial data show excellent performance of the proposed method with respect to current standard models.

Gaussian process volatility model

The prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the evolution of the variance. Moreover, functional parameters are usually learned by maximum likelihood, which can lead to over-fitting. To address these problems we introduce GP-Vol, a novel non-parametric model for time-changing variances based on Gaussian Processes. This new model can capture highly flexible functional relationships for the variances. Furthermore, we introduce a new online algorithm for fast inference in GP-Vol. This method is much faster than current offline inference procedures and it avoids overfitting problems by following a fully Bayesian approach. Experiments with financial data show that GP-Vol performs significantly better than current standard alternatives.

Anisotropy preserving DTI processing

Statistical analysis of diffusion tensor imaging (DTI) data requires a computational framework that is both numerically tractable (to account for the high dimensional nature of the data) and geometric (to account for the nonlinear nature of diffusion tensors). Building upon earlier studies exploiting a Riemannian framework to address these challenges, the present paper proposes a novel metric and an accompanying computational framework for DTI data processing. The proposed approach grounds the signal processing operations in interpolating curves. Well-chosen interpolating curves are shown to provide a computational framework that is at the same time tractable and information relevant for DTI processing. In addition, and in contrast to earlier methods, it provides an interpolation method which preserves anisotropy, a central information carried by diffusion tensor data. © 2013 Springer Science+Business Media New York.

Copula Processes

We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility (GCPV), to predict the latent standard deviations of a sequence of random variables. To make predictions we use Bayesian inference, with the Laplace approximation, and with Markov chain Monte Carlo as an alternative. We find both methods comparable. We also find our model can outperform GARCH on simulated and financial data. And unlike GARCH, GCPV can easily handle missing data, incorporate covariates other than time, and model a rich class of covariance structures.

Generalised Wishart Processes

We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time varying) covariance matrices. Unlike existing models, it can capture a diverse class of covariance structures, it can easily handle missing data, the dependent variable can readily include covariates other than time, and it scales well with dimension; there is no need for free parameters, and optional parameters are easy to interpret. We describe how to construct the GWP, introduce general procedures for inference and predictions, and show that it outperforms its main competitor, multivariate GARCH, even on financial data that especially suits GARCH. We also show how to predict the mean of a multivariate process while accounting for dynamic correlations.

Distributed optical fiber strain sensing in a secant piled wall

An optical fiber strain sensing technique, based on Brillouin Optical Time Domain Reflectometry (BOTDR), was used to obtain the full deformation profile of a secant pile wall during construction of an adjacent basement in London. Details of the installation of sensors as well as data processing are described. By installing optical fiber down opposite sides of the pile, the distributed strain profiles obtained can be used to give both the axial and lateral movements along the pile. Measurements obtained from the BOTDR were found in good agreement with inclinometer data from the adjacent piles. The relative merits of the two different techniques are discussed. © 2007 ASCE.