A fast Bayesian reconstruction algorithm for emission tomography with entropy prior converging to feasible images

The development and tests of an iterative reconstruction algorithm for emission tomography based on Bayesian statistical concepts are described. The algorithm uses the entropy of the generated image as a prior distribution, can be accelerated by the choice of an exponent, and converges uniformly to feasible images by the choice of one adjustable parameter. A feasible image has been defined as one that is consistent with the initial data (i.e. it is an image that, if truly a source of radiation in a patient, could have generated the initial data by the Poisson process that governs radioactive disintegration). The fundamental ideas of Bayesian reconstruction are discussed, along with the use of an entropy prior with an adjustable contrast parameter, the use of likelihood with data increment parameters as conditional probability, and the development of the new fast maximum a posteriori with entropy (FMAPE) Algorithm by the successive substitution method. It is shown that in the maximum likelihood estimator (MLE) and FMAPE algorithms, the only correct choice of initial image for the iterative procedure in the absence of a priori knowledge about the image configuration is a uniform field.

Bayesian image reconstruction with space-variant noise suppression

In this paper we present a Bayesian image reconstruction algorithm with entropy prior (FMAPE) that uses a space-variant hyperparameter. The spatial variation of the hyperparameter allows different degrees of resolution in areas of different statistical characteristics, thus avoiding the large residuals resulting from algorithms that use a constant hyperparameter. In the first implementation of the algorithm, we begin by segmenting a Maximum Likelihood Estimator (MLE) reconstruction. The segmentation method is based on using a wavelet decomposition and a self-organizing neural network. The result is a predetermined number of extended regions plus a small region for each star or bright object. To assign a different value of the hyperparameter to each extended region and star, we use either feasibility tests or cross-validation methods. Once the set of hyperparameters is obtained, we carried out the final Bayesian reconstruction, leading to a reconstruction with decreased bias and excellent visual characteristics. The method has been applied to data from the non-refurbished Hubble Space Telescope. The method can be also applied to ground-based images.

Image restoration in astronomy: a Bayesian perspective

When preparing an article on image restoration in astronomy, it is obvious that some topics have to be dropped to keep the work at reasonable length. We have decided to concentrate on image and noise models and on the algorithms to find the restoration. Topics like parameter estimation and stopping rules are also commented on. We start by describing the Bayesian paradigm and then proceed to study the noise and blur models used by the astronomical community. Then the prior models used to restore astronomical images are examined. We describe the algorithms used to find the restoration for the most common combinations of degradation and image models. Then we comment on important issues such as acceleration of algorithms, stopping rules, and parameter estimation. We also comment on the huge amount of information available to, and made available by, the astronomical community.

A program for the computation of power and determination of sample size in hierarchical experimental designs.

We have devised a program that allows computation of the power of F-test, and hence determination of appropriate sample and subsample sizes, in the context of the one-way hierarchical analysis of variance with fixed effects. The power at a fixed alternative is an increasing function of the sample size and of the subsample size. The program makes it easy to obtain the power of F-test for a range of values of sample and subsample sizes, and therefore the appropriate sizes based on a desired power. The program can be used for the 'ordinary' case of the one-way analysis of variance, as well as for hierarchical analysis of variance with two stages of sampling. Examples are given of the practical use of the program.

Growth, convergence and public investment : a bayesian model averaging approach

The aim of this paper is twofold. First, we study the determinants of economic growth among a wide set of potential variables for the Spanish provinces (NUTS3). Among others, we include various types of private, public and human capital in the group of growth factors. Also,we analyse whether Spanish provinces have converged in economic terms in recent decades. Thesecond objective is to obtain cross-section and panel data parameter estimates that are robustto model speci¯cation. For this purpose, we use a Bayesian Model Averaging (BMA) approach.Bayesian methodology constructs parameter estimates as a weighted average of linear regression estimates for every possible combination of included variables. The weight of each regression estimate is given by the posterior probability of each model.

Growth, convergence and public investment : a bayesian model averaging approach

The aim of this paper is twofold. First, we study the determinants of economic growth among a wide set of potential variables for the Spanish provinces (NUTS3). Among others, we include various types of private, public and human capital in the group of growth factors. Also,we analyse whether Spanish provinces have converged in economic terms in recent decades. Thesecond objective is to obtain cross-section and panel data parameter estimates that are robustto model speci¯cation. For this purpose, we use a Bayesian Model Averaging (BMA) approach.Bayesian methodology constructs parameter estimates as a weighted average of linear regression estimates for every possible combination of included variables. The weight of each regression estimate is given by the posterior probability of each model.

Communication in networks with hierarchical branching

We present a simple model of communication in networks with hierarchical branching. We analyze the behavior of the model from the viewpoint of critical systems under different situations. For certain values of the parameters, a continuous phase transition between a sparse and a congested regime is observed and accurately described by an order parameter and the power spectra. At the critical point the behavior of the model is totally independent of the number of hierarchical levels. Also scaling properties are observed when the size of the system varies. The presence of noise in the communication is shown to break the transition. The analytical results are a useful guide to forecasting the main features of real networks.

Hierarchical neural network with high storage capacity

A recent method used to optimize biased neural networks with low levels of activity is applied to a hierarchical model. As a consequence, the performance of the system is strongly enhanced. The steps to achieve optimization are analyzed in detail.

From Empirical Bayes to Full Bayes: Methods for Analysing Traffice Safety Data, October 25, 2004

Traffic safety engineers are among the early adopters of Bayesian statistical tools for analyzing crash data. As in many other areas of application, empirical Bayes methods were their first choice, perhaps because they represent an intuitively appealing, yet relatively easy to implement alternative to purely classical approaches. With the enormous progress in numerical methods made in recent years and with the availability of free, easy to use software that permits implementing a fully Bayesian approach, however, there is now ample justification to progress towards fully Bayesian analyses of crash data. The fully Bayesian approach, in particular as implemented via multi-level hierarchical models, has many advantages over the empirical Bayes approach. In a full Bayesian analysis, prior information and all available data are seamlessly integrated into posterior distributions on which practitioners can base their inferences. All uncertainties are thus accounted for in the analyses and there is no need to pre-process data to obtain Safety Performance Functions and other such prior estimates of the effect of covariates on the outcome of interest. In this slight, fully Bayesian methods may well be less costly to implement and may result in safety estimates with more realistic standard errors. In this manuscript, we present the full Bayesian approach to analyzing traffic safety data and focus on highlighting the differences between the empirical Bayes and the full Bayes approaches. We use an illustrative example to discuss a step-by-step Bayesian analysis of the data and to show some of the types of inferences that are possible within the full Bayesian framework.

From Empirical Bayes to Full Bayes: Methods for Analyzubg Traffic Safey Data, October 25, 2004

Traffic safety engineers are among the early adopters of Bayesian statistical tools for analyzing crash data. As in many other areas of application, empirical Bayes methods were their first choice, perhaps because they represent an intuitively appealing, yet relatively easy to implement alternative to purely classical approaches. With the enormous progress in numerical methods made in recent years and with the availability of free, easy to use software that permits implementing a fully Bayesian approach, however, there is now ample justification to progress towards fully Bayesian analyses of crash data. The fully Bayesian approach, in particular as implemented via multi-level hierarchical models, has many advantages over the empirical Bayes approach. In a full Bayesian analysis, prior information and all available data are seamlessly integrated into posterior distributions on which practitioners can base their inferences. All uncertainties are thus accounted for in the analyses and there is no need to pre-process data to obtain Safety Performance Functions and other such prior estimates of the effect of covariates on the outcome of interest. In this light, fully Bayesian methods may well be less costly to implement and may result in safety estimates with more realistic standard errors. In this manuscript, we present the full Bayesian approach to analyzing traffic safety data and focus on highlighting the differences between the empirical Bayes and the full Bayes approaches. We use an illustrative example to discuss a step-by-step Bayesian analysis of the data and to show some of the types of inferences that are possible within the full Bayesian framework.

Density-based hierarchical clustering of pyro-sequences on a large scale--the case of fungal ITS1.

MOTIVATION: Analysis of millions of pyro-sequences is currently playing a crucial role in the advance of environmental microbiology. Taxonomy-independent, i.e. unsupervised, clustering of these sequences is essential for the definition of Operational Taxonomic Units. For this application, reproducibility and robustness should be the most sought after qualities, but have thus far largely been overlooked. RESULTS: More than 1 million hyper-variable internal transcribed spacer 1 (ITS1) sequences of fungal origin have been analyzed. The ITS1 sequences were first properly extracted from 454 reads using generalized profiles. Then, otupipe, cd-hit-454, ESPRIT-Tree and DBC454, a new algorithm presented here, were used to analyze the sequences. A numerical assay was developed to measure the reproducibility and robustness of these algorithms. DBC454 was the most robust, closely followed by ESPRIT-Tree. DBC454 features density-based hierarchical clustering, which complements the other methods by providing insights into the structure of the data. AVAILABILITY: An executable is freely available for non-commercial users at ftp://ftp.vital-it.ch/tools/dbc454. It is designed to run under MPI on a cluster of 64-bit Linux machines running Red Hat 4.x, or on a multi-core OSX system. CONTACT: dbc454@vital-it.ch or nicolas.guex@isb-sib.ch.

Recent misconceptions about the "database search problem": a probabilistic analysis using Bayesian networks

This paper analyses and discusses arguments that emerge from a recent discussion about the proper assessment of the evidential value of correspondences observed between the characteristics of a crime stain and those of a sample from a suspect when (i) this latter individual is found as a result of a database search and (ii) remaining database members are excluded as potential sources (because of different analytical characteristics). Using a graphical probability approach (i.e., Bayesian networks), the paper here intends to clarify that there is no need to (i) introduce a correction factor equal to the size of the searched database (i.e., to reduce a likelihood ratio), nor to (ii) adopt a propositional level not directly related to the suspect matching the crime stain (i.e., a proposition of the kind 'some person in (outside) the database is the source of the crime stain' rather than 'the suspect (some other person) is the source of the crime stain'). The present research thus confirms existing literature on the topic that has repeatedly demonstrated that the latter two requirements (i) and (ii) should not be a cause of concern.

Evidential relevance in scene to offender transfer cases: development and analysis of a likelihood ratio for offence level propositions

The present paper focuses on the analysis and discussion of a likelihood ratio (LR) development for propositions at a hierarchical level known in the context as 'offence level'. Existing literature on the topic has considered LR developments for so-called offender to scene transfer cases. These settings involve-in their simplest form-a single stain found on a crime scene, but with possible uncertainty about the degree to which that stain is relevant (i.e. that it has been left by the offender). Extensions to multiple stains or multiple offenders have also been reported. The purpose of this paper is to discuss a development of a LR for offence level propositions when case settings involve potential transfer in the opposite direction, i.e. victim/scene to offender transfer. This setting has previously not yet been considered. The rationale behind the proposed LR is illustrated through graphical probability models (i.e. Bayesian networks). The role of various uncertain parameters is investigated through sensitivity analyses as well as simulations.

Bayesian estimation of speciation and extinction from incomplete fossil occurrence data.

The temporal dynamics of species diversity are shaped by variations in the rates of speciation and extinction, and there is a long history of inferring these rates using first and last appearances of taxa in the fossil record. Understanding diversity dynamics critically depends on unbiased estimates of the unobserved times of speciation and extinction for all lineages, but the inference of these parameters is challenging due to the complex nature of the available data. Here, we present a new probabilistic framework to jointly estimate species-specific times of speciation and extinction and the rates of the underlying birth-death process based on the fossil record. The rates are allowed to vary through time independently of each other, and the probability of preservation and sampling is explicitly incorporated in the model to estimate the true lifespan of each lineage. We implement a Bayesian algorithm to assess the presence of rate shifts by exploring alternative diversification models. Tests on a range of simulated data sets reveal the accuracy and robustness of our approach against violations of the underlying assumptions and various degrees of data incompleteness. Finally, we demonstrate the application of our method with the diversification of the mammal family Rhinocerotidae and reveal a complex history of repeated and independent temporal shifts of both speciation and extinction rates, leading to the expansion and subsequent decline of the group. The estimated parameters of the birth-death process implemented here are directly comparable with those obtained from dated molecular phylogenies. Thus, our model represents a step towards integrating phylogenetic and fossil information to infer macroevolutionary processes.