Bayesian approach to signal modelling

In this paper, an introduction to Bayesian methods in signal processing will be given. The paper starts by considering the important issues of model selection and parameter estimation and derives analytic expressions for the model probabilities of two simple models. The idea of marginal estimation of certain model parameter is then introduced and expressions are derived for the marginal probability densities for frequencies in white Gaussian noise and a Bayesian approach to general changepoint analysis is given. Numerical integration methods are introduced based on Markov chain Monte Carlo techniques and the Gibbs sampler in particular.

The Bayesian Approach to Signal Modelling

In this paper, an introduction to Bayesian methods in signal processing will be given. The paper starts by considering the important issues of model selection and parameter estimation and derives analytic expressions for the model probabilities of two simple models. The idea of marginal estimation of certain model parameter is then introduced and expressions are derived for the marginal probabilitiy densities for frequencies in white Gaussian noise and a Bayesian approach to general changepoint analysis is given. Numerical integration methods are introduced based on Markov chain Monte Carlo techniques and the Gibbs sampler in particular.

Fourier analysis and gabor filtering for texture analysis and local reconstruction of general shapes

Since the pioneering work of Gibson in 1950, Shape- From-Texture has been considered by researchers as a hard problem, mainly due to restrictive assumptions which often limit its applicability. We assume a very general stochastic homogeneity and perspective camera model, for both deterministic and stochastic textures. A multi-scale distortion is efficiently estimated with a previously presented method based on Fourier analysis and Gabor filters. The novel 3D reconstruction method that we propose applies to general shapes, and includes non-developable and extensive surfaces. Our algorithm is accurate, robust and compares favorably to the present state of the art of Shape-From- Texture. Results show its application to non-invasively study shape changes with laid-on textures, while rendering and retexturing of cloth is suggested for future work. © 2009 IEEE.

Random function priors for exchangeable arrays with applications to graphs and relational data

A fundamental problem in the analysis of structured relational data like graphs, networks, databases, and matrices is to extract a summary of the common structure underlying relations between individual entities. Relational data are typically encoded in the form of arrays; invariance to the ordering of rows and columns corresponds to exchangeable arrays. Results in probability theory due to Aldous, Hoover and Kallenberg show that exchangeable arrays can be represented in terms of a random measurable function which constitutes the natural model parameter in a Bayesian model. We obtain a flexible yet simple Bayesian nonparametric model by placing a Gaussian process prior on the parameter function. Efficient inference utilises elliptical slice sampling combined with a random sparse approximation to the Gaussian process. We demonstrate applications of the model to network data and clarify its relation to models in the literature, several of which emerge as special cases.

Probability-Matching Predictors for Extreme Extremes

A location- and scale-invariant predictor is constructed which exhibits good probability matching for extreme predictions outside the span of data drawn from a variety of (stationary) general distributions. It is constructed via the three-parameter {\mu, \sigma, \xi} Generalized Pareto Distribution (GPD). The predictor is designed to provide matching probability exactly for the GPD in both the extreme heavy-tailed limit and the extreme bounded-tail limit, whilst giving a good approximation to probability matching at all intermediate values of the tail parameter \xi. The predictor is valid even for small sample sizes N, even as small as N = 3. The main purpose of this paper is to present the somewhat lengthy derivations which draw heavily on the theory of hypergeometric functions, particularly the Lauricella functions. Whilst the construction is inspired by the Bayesian approach to the prediction problem, it considers the case of vague prior information about both parameters and model, and all derivations are undertaken using sampling theory.

Evaluation of live-attenuated Salmonella vaccines expressing Campylobacter antigens for control of C. jejuni in poultry

Campylobacter jejuni is a zoonotic bacterial pathogen of worldwide importance. It is estimated that 460,000 human infections occur in the United Kingdom per annum and these involve acute enteritis and may be complicated by severe systemic sequelae. Such infections are frequently associated with the consumption of contaminated poultry meat and strategies to control C. jejuni in poultry are expected to limit pathogen entry into the food chain and the incidence of human disease. Toward this aim, a total of 840 Light Sussex chickens were used to evaluate a Salmonella enterica serovar Typhimurium ΔaroA vaccine expressing the C. jejuni amino acid binding protein CjaA as a plasmid-borne fusion to the C-terminus of fragment C of tetanus toxin. Chickens were given the vaccine at 1-day-old and two weeks later by oral gavage, then challenged after a further two weeks with C. jejuni. Across six biological replicates, statistically significant reductions in caecal C. jejuni of c. 1.4 log10 colony-forming units/g were observed at three and four weeks post-challenge relative to age-matched unvaccinated birds. Protection was associated with the induction of CjaA-specific serum IgY and biliary IgA. Protection was not observed using a vaccine strain containing the empty plasmid. Vaccination with recombinant CjaA subcutaneously at the same intervals significantly reduced the caecal load of C. jejuni at three and four weeks post-challenge. Taken together these data imply that responses directed against CjaA, rather than competitive or cross-protective effects mediated by the carrier, confer protection. The impact of varying parameters on the efficacy of the S. Typhimurium ΔaroA vaccine expressing TetC-CjaA was also tested. Delaying the age at primary vaccination had little impact on protection or humoral responses to CjaA. The use of the parent strain as carrier or changing the attenuating mutation of the carrier to ΔspaS or ΔssaU enhanced the protective effect, consistent with increased invasion and persistence of the vaccine strains relative to the ΔaroA mutant. Expression in the ΔaroA strain of a TetC fusion to Peb1A, but not TetC fusions to GlnH or ChuA, elicited protection against intestinal colonisation by C. jejuni that was comparable to that observed with the TetC-CjaA fusion. Our data are rendered highly relevant by use of the target host in large numbers and support the potential of CjaA- and Peb1A-based vaccines for control of C. jejuni in poultry. © 2009 Elsevier Ltd. All rights reserved.

Temporally adaptive estimation of logistic classifiers on data streams

Modern technology has allowed real-time data collection in a variety of domains, ranging from environmental monitoring to healthcare. Consequently, there is a growing need for algorithms capable of performing inferential tasks in an online manner, continuously revising their estimates to reflect the current status of the underlying process. In particular, we are interested in constructing online and temporally adaptive classifiers capable of handling the possibly drifting decision boundaries arising in streaming environments. We first make a quadratic approximation to the log-likelihood that yields a recursive algorithm for fitting logistic regression online. We then suggest a novel way of equipping this framework with self-tuning forgetting factors. The resulting scheme is capable of tracking changes in the underlying probability distribution, adapting the decision boundary appropriately and hence maintaining high classification accuracy in dynamic or unstable environments. We demonstrate the scheme's effectiveness in both real and simulated streaming environments. © Springer-Verlag 2009.

Extended VTS for noise-robust speech recognition

Model compensation is a standard way of improving the robustness of speech recognition systems to noise. A number of popular schemes are based on vector Taylor series (VTS) compensation, which uses a linear approximation to represent the influence of noise on the clean speech. To compensate the dynamic parameters, the continuous time approximation is often used. This approximation uses a point estimate of the gradient, which fails to take into account that dynamic coefficients are a function of a number of consecutive static coefficients. In this paper, the accuracy of dynamic parameter compensation is improved by representing the dynamic features as a linear transformation of a window of static features. A modified version of VTS compensation is applied to the distribution of the window of static features and, importantly, their correlations. These compensated distributions are then transformed to distributions over standard static and dynamic features. With this improved approximation, it is also possible to obtain full-covariance corrupted speech distributions. This addresses the correlation changes that occur in noise. The proposed scheme outperformed the standard VTS scheme by 10% to 20% relative on a range of tasks. © 2006 IEEE.

RNA processing and Arabidopsis flowering time control.

Plants control their flowering time in order to ensure that they reproduce under favourable conditions. The components involved in this complex process have been identified using a molecular genetic approach in Arabidopsis and classified into genetically separable pathways. The autonomous pathway controls the level of mRNA encoding a floral repressor, FLC, and comprises three RNA-binding proteins, FCA, FPA and FLK. FCA interacts with the 3'-end RNA-processing factor FY to autoregulate its own expression post-transcriptionally and to control FLC. Other components of the autonomous pathway, FVE and FLD, regulate FLC epigenetically. This combination of epigenetic and post-transcriptional control gives precision to the control of FLC expression and flowering time.

Performance prediction of graphene nanoribbon and carbon nanotube transistors

Carbon nanotubes (CNTs) and graphene nanoribbons (GNRs) field-effect transistor (FET) can be the basis for a quasi-one- dimensional (Q1D) transistor technology. Recent experiments show that the on-off ratio for GNR devices can be improved to level exploration of transistor action is justified. Here we use the tight-binding energy dipersion approximation, to assess the performance of semiconducting CNT and GNR is qualitatively in terms of drain current drive strength, bandgap and density of states for a specified device. By reducing the maximum conductance 4e2/h by half, we observed that our model has a particularly good fit with 50 nm channel single walled carbon nanotube (SWCNT) experimental data. Given the same bandgap, CNTs outperform GNRs due to valley degeneracy. Nevertheless, the variation of the device contacts will decide which transistor will exhibit better conductivity and thus higher ON currents. © 2011 American Institute of Physics.

Verifying stability of approximate explicit MPC

Several authors have proposed algorithms for approximate explicit MPC [1],[2],[3]. These algorithms have in common that they develop a stability criterion for approximate explicit MPC that require the approximate cost function to be within a certain distance from the optimal cost function. In this paper, stability is instead ascertained by considering only the cost function of the approximate MPC. If a region of the state space is found where the cost function is not decreasing, this indicates that an improved approximation (to the optimal control) is required in that region. If the approximate cost function is decreasing everywhere, no further refinement of the approximate MPC is necessary, since stability is guaranteed. ©2009 IEEE.

An investigation of the kinetics of CO2 uptake by a synthetic calcium based sorbent

This study examines the kinetics of carbonation by CO2 at temperatures of ca. 750 °C of a synthetic sorbent composed of 15 wt% mayenite (Ca12Al14O33) and CaO, designated HA-85-850, and draws comparisons with the carbonation of a calcined limestone. In-situ XRD has verified the inertness of mayenite, which neither interacts with the active CaO nor does it significantly alter the CaO carbonation–calcination equilibrium. An overlapping grain model was developed to predict the rate and extent of carbonation of HA-85-850 and limestone. In the model, the initial microstructure of the sorbent was defined by a discretised grain size distribution, assuming spherical grains. The initial input to the model – the size distribution of grains – was a fitted parameter, which was in good agreement with measurements made with mercury porosimetry and by the analysis of SEM images of sectioned particles. It was found that the randomly overlapping spherical grain assumption offered great simplicity to the model, despite its approximation to the actual porous structure within a particle. The model was able to predict the performance of the materials well and, particularly, was able to account for changes in rate and extent of reaction as the structure evolved after various numbers of cycles of calcination and carbonation.

An investigation of the kinetics of CO 2 uptake by a synthetic calcium based sorbent

This study examines the kinetics of carbonation by CO 2 at temperatures of ca. 750°C of a synthetic sorbent composed of 15wt% mayenite (Ca 12Al 14O 33) and CaO, designated HA-85-850, and draws comparisons with the carbonation of a calcined limestone. In-situ XRD has verified the inertness of mayenite, which neither interacts with the active CaO nor does it significantly alter the CaO carbonation-calcination equilibrium. An overlapping grain model was developed to predict the rate and extent of carbonation of HA-85-850 and limestone. In the model, the initial microstructure of the sorbent was defined by a discretised grain size distribution, assuming spherical grains. The initial input to the model - the size distribution of grains - was a fitted parameter, which was in good agreement with measurements made with mercury porosimetry and by the analysis of SEM images of sectioned particles. It was found that the randomly overlapping spherical grain assumption offered great simplicity to the model, despite its approximation to the actual porous structure within a particle. The model was able to predict the performance of the materials well and, particularly, was able to account for changes in rate and extent of reaction as the structure evolved after various numbers of cycles of calcination and carbonation. © 2011 Elsevier Ltd.

Syllable language models for Mandarin speech recognition: exploiting character language models.

Mandarin Chinese is based on characters which are syllabic in nature and morphological in meaning. All spoken languages have syllabiotactic rules which govern the construction of syllables and their allowed sequences. These constraints are not as restrictive as those learned from word sequences, but they can provide additional useful linguistic information. Hence, it is possible to improve speech recognition performance by appropriately combining these two types of constraints. For the Chinese language considered in this paper, character level language models (LMs) can be used as a first level approximation to allowed syllable sequences. To test this idea, word and character level n-gram LMs were trained on 2.8 billion words (equivalent to 4.3 billion characters) of texts from a wide collection of text sources. Both hypothesis and model based combination techniques were investigated to combine word and character level LMs. Significant character error rate reductions up to 7.3% relative were obtained on a state-of-the-art Mandarin Chinese broadcast audio recognition task using an adapted history dependent multi-level LM that performs a log-linearly combination of character and word level LMs. This supports the hypothesis that character or syllable sequence models are useful for improving Mandarin speech recognition performance.

Optimal constraint tightening policies for robust variable horizon model predictive control

This paper develops a technique for improving the region of attraction of a robust variable horizon model predictive controller. It considers a constrained discrete-time linear system acted upon by a bounded, but unknown time-varying state disturbance. Using constraint tightening for robustness, it is shown how the tightening policy, parameterised as direct feedback on the disturbance, can be optimised to increase the volume of an inner approximation to the controller's true region of attraction. Numerical examples demonstrate the benefits of the policy in increasing region of attraction volume and decreasing the maximum prediction horizon length. © 2012 IEEE.