Linear gaussian computations for near-exact Bayesian Monte Carlo inference in skewed alpha-stable time series models

In this paper we study parameter estimation for time series with asymmetric α-stable innovations. The proposed methods use a Poisson sum series representation (PSSR) for the asymmetric α-stable noise to express the process in a conditionally Gaussian framework. That allows us to implement Bayesian parameter estimation using Markov chain Monte Carlo (MCMC) methods. We further enhance the series representation by introducing a novel approximation of the series residual terms in which we are able to characterise the mean and variance of the approximation. Simulations illustrate the proposed framework applied to linear time series, estimating the model parameter values and model order P for an autoregressive (AR(P)) model driven by asymmetric α-stable innovations. © 2012 IEEE.

Bayesian non-parametrics and the probabilistic approach to modelling.

Modelling is fundamental to many fields of science and engineering. A model can be thought of as a representation of possible data one could predict from a system. The probabilistic approach to modelling uses probability theory to express all aspects of uncertainty in the model. The probabilistic approach is synonymous with Bayesian modelling, which simply uses the rules of probability theory in order to make predictions, compare alternative models, and learn model parameters and structure from data. This simple and elegant framework is most powerful when coupled with flexible probabilistic models. Flexibility is achieved through the use of Bayesian non-parametrics. This article provides an overview of probabilistic modelling and an accessible survey of some of the main tools in Bayesian non-parametrics. The survey covers the use of Bayesian non-parametrics for modelling unknown functions, density estimation, clustering, time-series modelling, and representing sparsity, hierarchies, and covariance structure. More specifically, it gives brief non-technical overviews of Gaussian processes, Dirichlet processes, infinite hidden Markov models, Indian buffet processes, Kingman's coalescent, Dirichlet diffusion trees and Wishart processes.

Probing the electronic structure of multi-walled carbon nanotubes by transient optical transmittivity

High-resolution time resolved transmittivity measurements on horizontally aligned free-standing multi-walled carbon nanotubes reveal a different electronic transient behavior from that of graphite. This difference is ascribed to the presence of discrete energy states in the multishell carbon nanotube electronic structure. Probe polarization dependence suggests that the optical transitions involve definite selection rules. The origin of these states is discussed and a rate equation model is proposed to rationalize our findings. © 2013 Elsevier Ltd. All rights reserved.

Probing the location of displayed cytochrome b562 on amyloid by scanning tunnelling microscopy.

Amyloid fibres displaying cytochrome b562 were probed using scanning tunnelling microscopy (STM) in vacuo. The cytochromes are electron transfer proteins containing a haem cofactor and could, in principle, mediate electron transfer between the tip and the gold substrate. If the core fibres were insulating and electron transfer within the 3D haem network was detected, then the electron transport properties of the fibre could be controlled by genetic engineering. Three kinds of STM images were obtained. At a low bias (<1.5 V) the fibres appeared as regions of low conductivity with no evidence of cytochrome mediated electron transfer. At a high bias, stable peaks in tunnelling current were observed for all three fibre species containing haem and one species of fibre that did not contain haem. In images of this kind, some of the current peaks were collinear and spaced around 10 nm apart over ranges longer than 100 nm, but background monomers complicate interpretation. Images of the third kind were rare (1 in 150 fibres); in these, fully conducting structures with the approximate dimensions of fibres were observed, suggesting the possibility of an intermittent conduction mechanism, for which a precedent exists in DNA. To test the conductivity, some fibres were immobilized with sputtered gold, and no evidence of conduction between the grains of gold was seen. In control experiments, a variation of monomeric cytochrome b562 was not detected by STM, which was attributed to low adhesion, whereas a monomeric multi-haem protein, GSU1996, was readily imaged. We conclude that the fibre superstructure may be intermittently conducting, that the cytochromes have been seen within the fibres and that they are too far apart for detectable current flow between sites to occur. We predict that GSU1996, being 10 nm long, is more likely to mediate successful electron transfer along the fibre as well as being more readily detectable when displayed from amyloid.

Accelerating Bayesian hierarchical clustering of time series data with a randomised algorithm.

We live in an era of abundant data. This has necessitated the development of new and innovative statistical algorithms to get the most from experimental data. For example, faster algorithms make practical the analysis of larger genomic data sets, allowing us to extend the utility of cutting-edge statistical methods. We present a randomised algorithm that accelerates the clustering of time series data using the Bayesian Hierarchical Clustering (BHC) statistical method. BHC is a general method for clustering any discretely sampled time series data. In this paper we focus on a particular application to microarray gene expression data. We define and analyse the randomised algorithm, before presenting results on both synthetic and real biological data sets. We show that the randomised algorithm leads to substantial gains in speed with minimal loss in clustering quality. The randomised time series BHC algorithm is available as part of the R package BHC, which is available for download from Bioconductor (version 2.10 and above) via http://bioconductor.org/packages/2.10/bioc/html/BHC.html. We have also made available a set of R scripts which can be used to reproduce the analyses carried out in this paper. These are available from the following URL. https://sites.google.com/site/randomisedbhc/.

Approximate Bayesian Computation for Smoothing

We consider a method for approximate inference in hidden Markov models (HMMs). The method circumvents the need to evaluate conditional densities of observations given the hidden states. It may be considered an instance of Approximate Bayesian Computation (ABC) and it involves the introduction of auxiliary variables valued in the same space as the observations. The quality of the approximation may be controlled to arbitrary precision through a parameter ε > 0. We provide theoretical results which quantify, in terms of ε, the ABC error in approximation of expectations of additive functionals with respect to the smoothing distributions. Under regularity assumptions, this error is, where n is the number of time steps over which smoothing is performed. For numerical implementation, we adopt the forward-only sequential Monte Carlo (SMC) scheme of [14] and quantify the combined error from the ABC and SMC approximations. This forms some of the first quantitative results for ABC methods which jointly treat the ABC and simulation errors, with a finite number of data and simulated samples. © Taylor & Francis Group, LLC.

Active learning of model evidence using Bayesian quadrature

Numerical integration is a key component of many problems in scientific computing, statistical modelling, and machine learning. Bayesian Quadrature is a modelbased method for numerical integration which, relative to standard Monte Carlo methods, offers increased sample efficiency and a more robust estimate of the uncertainty in the estimated integral. We propose a novel Bayesian Quadrature approach for numerical integration when the integrand is non-negative, such as the case of computing the marginal likelihood, predictive distribution, or normalising constant of a probabilistic model. Our approach approximately marginalises the quadrature model's hyperparameters in closed form, and introduces an active learning scheme to optimally select function evaluations, as opposed to using Monte Carlo samples. We demonstrate our method on both a number of synthetic benchmarks and a real scientific problem from astronomy.

A Bayesian framework to predict deformations during supported excavations based on a semi-empirical method

The ground movements induced by the construction of supported excavation systems are generally predicted by empirical/semi-empirical methods in the design stage. However, these methods cannot account for the site-specific conditions and for information that becomes available as an excavation proceeds. A Bayesian updating methodology is proposed to update the predictions of ground movements in the later stages of excavation based on recorded deformation measurements. As an application, the proposed framework is used to predict the three-dimensional deformation shapes at four incremental excavation stages of an actual supported excavation project. © 2011 Taylor & Francis Group, London.