A study of simulated annealing and a revised cascade algorithm for image reconstruction

We describe an image reconstruction problem and the computational difficulties arising in determining the maximum a posteriori (MAP) estimate. Two algorithms for tackling the problem, iterated conditional modes (ICM) and simulated annealing, are usually applied pixel by pixel. The performance of this strategy can be poor, particularly for heavily degraded images, and as a potential improvement Jubb and Jennison (1991) suggest the cascade algorithm in which ICM is initially applied to coarser images formed by blocking squares of pixels. In this paper we attempt to resolve certain criticisms of cascade and present a version of the algorithm extended in definition and implementation. As an illustration we apply our new method to a synthetic aperture radar (SAR) image. We also carry out a study of simulated annealing, with and without cascade, applied to a more tractable minimization problem from which we gain insight into the properties of cascade algorithms.     

Familial spinal shape

It has been proposed that there is a familial relationship in the shape of the spine. This paper describes a pilot study investigating familial shape in the sagittal plane (side view), using three data sets of normal Leeds schoolchildren. The study is exploratory in nature, because only small samples were available. Data acquisition was by means of the Quantec system, which obtains surface shape measurements and extracts a line representing the spinal curve. The coordinates of the spine line in the sagittal plane are then used to investigate familial correlations of spinal shape. The spine lines first undergo some preprocessing, including Procrustes rotations to remove location, rotation and size effects. Smoothed principal component analysis of the curves provides suitable shape variables, and familial correlations between curves are then investigated. The covariates of sex and height are also investigated in the analysis. It does appear that there could be some evidence for familial correlations in sagittal spinal shape, although a further large-scale study is required. Finally, a discussion of the approach and other alternatives is considered.     

Difficulties in the use of auxiliary variables in Markov chain Monte Carlo methods

Markov chain Monte Carlo (MCMC) methods are now widely used in a diverse range of application areas to tackle previously intractable problems. Difficult questions remain, however, in designing MCMC samplers for problems exhibiting severe multimodality where standard methods may exhibit prohibitively slow movement around the state space. Auxiliary variable methods, sometimes together with multigrid ideas, have been proposed as one possible way forward. Initial disappointing experiments have led to data-driven modifications of the methods. In this paper, these suggestions are investigated for lattice data such as is found in imaging and some spatial applications. The results suggest that adapting the auxiliary variables to the specific application is beneficial. However the form of adaptation needed and the extent of the resulting benefits are not always clear-cut.     

Child care in an age of family differences

The importance of understanding America's day care needs has become a major issue in society today. Understanding these needs involves more than simply providing spaces for care. The uniqueness of each family's situation requires research into differing family expectations. This paper provides some insight into differences between single mothers and fathers in their utilization of child care.     

Improving power posterior estimation of statistical evidence

The statistical evidence (or marginal likelihood) is a key quantity in Bayesian statistics, allowing one to assess the probability of the data given the model under investigation. This paper focuses on refining the power posterior approach to improve estimation of the evidence. The power posterior method involves transitioning from the prior to the posterior by powering the likelihood by an inverse temperature. In common with other tempering algorithms, the power posterior involves some degree of tuning. The main contributions of this article are twofold—we present a result from the numerical analysis literature which can reduce the bias in the estimate of the evidence by addressing the error arising from numerically integrating across the inverse temperatures. We also tackle the selection of the inverse temperature ladder, applying this approach additionally to the Stepping Stone sampler estimation of evidence. A key practical point is that both of these innovations incur virtually no extra cost.     

A Bayesian hierarchical model for photometric red shifts

Summary.  The Sloan digital sky survey is an extremely large astronomical survey that is conducted with the intention of mapping more than a quarter of the sky. Among the data that it is generating are spectroscopic and photometric measurements, both containing information about the red shift of galaxies. The former are precise and easy to interpret but expensive to gather; the latter are far cheaper but correspondingly more difficult to interpret. Recently, Csabai and co-workers have described various calibration techniques aiming to predict red shift from photometric measurements. We investigate what a structured Bayesian approach to the problem can add. In particular, we are interested in providing uncertainty bounds that are associated with the underlying red shifts and the classifications of the galaxies. We find that quite a generic statistical modelling approach, using for the most part standard model ingredients, can compete with much more specific custom-made and highly tuned techniques that are already available in the astronomical literature.     

Confocal fluorescence microscopy of leaf cells: an application of Bayesian image analysis

Confocal fluorescence microscopy is a recent and important imaging tool for visualizing three-dimensional specimens without the need for physical sectioning, so that changes in living cells can be studied over time. The application of interest here is a study of the changes in the stomatal guard cells of plant leaves during their opening and closing response sequences. Quantitative estimates of the size and shape of these cells rely on accurate classification (or segmentation) of the images into areas which are parts of cells and areas which are background. This segmentation is complicated in confocal microscopy because the images appear to be 'smudged' or 'dirty'; this degradation is due largely to diffraction and attenuation of the recorded signal caused by the specimen itself. Correcting for this degradation is difficult without knowing the specimen-dependent parameters involved in the degradation process. A fully Bayesian approach is proposed for tackling this problem of blind deconvolution, i.e. of concurrently estimating the degradation parameters while segmenting two-dimensional sections. The end-products are interval estimates of size and shape which acknowledge some of the uncertainty involved in the segmentation. The results are promising, generating credible intervals which are sufficiently narrow to be useful in practice.     

Building Multinational Teams: The Challenge

Using experience from running courses for British and overseas companies at the Centre for International Briefing in the U.K., and his own training consultancy, the author examines the challenge presented to management in building multinational teams in the current climate. Concentrates on need to balance cultural values and practices, maximising cultural synergy. Considers problem areas of perception, team selection, choice of common language, building trust, use of humour, attitude to time, critical success factors in conducting meetings, training and sustaining multi-cultural teams. Offers a checklist of principles to follow. This revised version was published online in August 2006 with corrections to the Cover Date.     

Estimating the Parameters of Stochastic Volatility Models Using Option Price Data

This article describes a maximum likelihood method for estimating the parameters of the standard square-root stochastic volatility model and a variant of the model that includes jumps in equity prices. The model is fitted to data on the S&P 500 Index and the prices of vanilla options written on the index, for the period 1990 to 2011. The method is able to estimate both the parameters of the physical measure (associated with the index) and the parameters of the risk-neutral measure (associated with the options), including the volatility and jump risk premia. The estimation is implemented using a particle filter whose efficacy is demonstrated under simulation. The computational load of this estimation method, which previously has been prohibitive, is managed by the effective use of parallel computing using graphics processing units (GPUs). The empirical results indicate that the parameters of the models are reliably estimated and consistent with values reported in previous work. In particular, both the volatility risk premium and the jump risk premium are found to be significant.