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Local dimension and finite time prediction in spatiotemporal chaotic systems.

We show how a recently introduced statistic [Patil et al., Phys. Rev. Lett. 81, 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as having high predictability and vice versa. This conclusion is reached by using methods from dynamical systems theory and Bayesian modeling. In this work we emphasize on the consequences for short time forecasting and examine the relevance for factor analysis. Although we concentrate on coupled map lattices and coupled nonlinear oscillators for convenience, any other spatially distributed system could be used instead, such as turbulent fluid flows.

Journal Article↗

Automated semantic analysis of changes in image sequences of neurons in culture.

Quantitative studies of dynamic behaviors of live neurons are currently limited by the slowness, subjectivity, and tedium of manual analysis of changes in time-lapse image sequences. Challenges to automation include the complexity of the changes of interest, the presence of obfuscating and uninteresting changes due to illumination variations and other imaging artifacts, and the sheer volume of recorded data. This paper describes a highly automated approach that not only detects the interesting changes selectively, but also generates quantitative analyses at multiple levels of detail. Detailed quantitative neuronal morphometry is generated for each frame. Frame-to-frame neuronal changes are measured and labeled as growth, shrinkage, merging, or splitting, as would be done by a human expert. Finally, events unfolding over longer durations, such as apoptosis and axonal specification, are automatically inferred from the short-term changes. The proposed method is based on a Bayesian model selection criterion that leverages a set of short-term neurite change models and takes into account additional evidence provided by an illumination-insensitive change mask. An automated neuron tracing algorithm is used to identify the objects of interest in each frame. A novel curve distance measure and weighted bipartite graph matching are used to compare and associate neurites in successive frames. A separate set of multi-image change models drives the identification of longer term events. The method achieved frame-to-frame change labeling accuracies ranging from 85% to 100% when tested on 8 representative recordings performed under varied imaging and culturing conditions, and successfully detected all higher order events of interest. Two sequences were used for training the models and tuning their parameters; the learned parameter settings can be applied to hundreds of similar image sequences, provided imaging and culturing conditions are similar to the training set. The proposed approach is a substantial innovation over manual annotation and change analysis, accomplishing in minutes what it would take an expert hours to complete.

Algorithms↗

The latent process decomposition of cDNA microarray data sets.

We present a new computational technique (a software implementation, data sets, and supplementary information are available at http://www.enm.bris.ac.uk/lpd/) which enables the probabilistic analysis of cDNA microarray data and we demonstrate its effectiveness in identifying features of biomedical importance. A hierarchical Bayesian model, called Latent Process Decomposition (LPD), is introduced in which each sample in the data set is represented as a combinatorial mixture over a finite set of latent processes, which are expected to correspond to biological processes. Parameters in the model are estimated using efficient variational methods. This type of probabilistic model is most appropriate for the interpretation of measurement data generated by cDNA microarray technology. For determining informative substructure in such data sets, the proposed model has several important advantages over the standard use of dendrograms. First, the ability to objectively assess the optimal number of sample clusters. Second, the ability to represent samples and gene expression levels using a common set of latent variables (dendrograms cluster samples and gene expression values separately which amounts to two distinct reduced space representations). Third, in constrast to standard cluster models, observations are not assigned to a single cluster and, thus, for example, gene expression levels are modeled via combinations of the latent processes identified by the algorithm. We show this new method compares favorably with alternative cluster analysis methods. To illustrate its potential, we apply the proposed technique to several microarray data sets for cancer. For these data sets it successfully decomposes the data into known subtypes and indicates possible further taxonomic subdivision in addition to highlighting, in a wholly unsupervised manner, the importance of certain genes which are known to be medically significant. To illustrate its wider applicability, we also illustrate its performance on a microarray data set for yeast.

Algorithms↗

A Bayesian approach for stochastic white matter tractography.

White matter fiber bundles in the human brain can be located by tracing the local water diffusion in diffusion weighted magnetic resonance imaging (MRI) images. In this paper, a novel Bayesian modeling approach for white matter tractography is presented. The uncertainty associated with estimated white matter fiber paths is investigated, and a method for calculating the probability of a connection between two areas in the brain is introduced. The main merits of the presented methodology are its simple implementation and its ability to handle noise in a theoretically justified way. Theory for estimating global connectivity is also presented, as well as a theorem that facilitates the estimation of the parameters in a constrained tensor model of the local water diffusion profile.

Algorithms↗

Fusion of intelligence information: a Bayesian approach.

The attack that occurred on September 11, 2001 was, in the end, the result of a failure to detect and prevent the terrorist operations that hit the United States. The U.S. government thus faces at this time the daunting tasks of first, drastically increasing its ability to obtain and interpret different types of signals of impending terrorist attacks with sufficient lead time and accuracy, and second, improving its ability to react effectively. One of the main challenges is the fusion of information, from different sources (U.S. or foreign), and of different types (electronic signals, human intelligence. etc.). Fusion thus involves two very distinct and separate issues: communications, i.e., ensuring that the different U.S. and foreign intelligence agencies communicate all relevant and accurate information in a timely fashion and, perhaps more difficult, merging the content of signals, some "sharp" and some "fuzzy," some dependent and some independent into useful information. The focus of this article is on the latter issue, and on the use of the results. In this article, I present a classic probabilistic Bayesian model sometimes used in engineering risk analysis, which can be helpful in the fusion of information because it allows computation of the posterior probability of an event given its prior probability (before the signal is observed) and the quality of the signal characterized by the probabilities of false positive and false negative. Experience suggests that the nature of these errors has been sometimes misunderstood; therefore, I discuss the validity of several possible definitions.

Journal Article↗

Bayesian latent variable models for median regression on multiple outcomes.

Often a response of interest cannot be measured directly and it is necessary to rely on multiple surrogates, which can be assumed to be conditionally independent given the latent response and observed covariates. Latent response models typically assume that residual densities are Gaussian. This article proposes a Bayesian median regression modeling approach, which avoids parametric assumptions about residual densities by relying on an approximation based on quantiles. To accommodate within-subject dependency, the quantile response categories of the surrogate outcomes are related to underlying normal variables, which depend on a latent normal response. This underlying Gaussian covariance structure simplifies interpretation and model fitting, without restricting the marginal densities of the surrogate outcomes. A Markov chain Monte Carlo algorithm is proposed for posterior computation, and the methods are applied to single-cell electrophoresis (comet assay) data from a genetic toxicology study.

Algorithms↗

Multivariate survival analysis with positive stable frailties.

In this paper, we describe Bayesian modeling of dependent multivariate survival data using positive stable frailty distributions. A flexible baseline hazard formulation using a piecewise exponential model with a correlated prior process is used. The estimation of the stable law parameter together with the parameters of the (conditional) proportional hazards model is facilitated by a modified Gibbs sampling procedure. The methodology is illustrated on kidney infection data (McGilchrist and Aisbett, 1991).

Algorithms↗

Bayesian point estimation of quantitative trait loci.

In this article, we consider the problem of the estimation of quantitative trait loci (QTL), those chromosomal regions at which genetic information affecting some quantitative trait is encoded. Generally the number of such encoding sites is unknown, and associations between neutral molecular marker genotypes and observed trait phenotypes are sought to locate them. We consider a Bayesian model for simple experimental designs, and discuss the existing approaches to inference for this problem. In particular, we focus on locating positions of the best candidate markers segregating for the trait, a situation which is of primary interest in comparative mapping. We introduce a loss function for estimating both the number of QTL and their location, and we illustrate its application via simulated and real data.

Animals↗

Genetic diversity, population structure, effective population size and demographic history of the Finnish wolf population.

The Finnish wolf population (Canis lupus) was sampled during three different periods (1996-1998, 1999-2001 and 2002-2004), and 118 individuals were genotyped with 10 microsatellite markers. Large genetic variation was found in the population despite a recent demographic bottleneck. No spatial population subdivision was found even though a significant negative relationship between genetic relatedness and geographic distance suggested isolation by distance. Very few individuals did not belong to the local wolf population as determined by assignment analyses, suggesting a low level of immigration in the population. We used the temporal approach and several statistical methods to estimate the variance effective size of the population. All methods gave similar estimates of effective population size, approximately 40 wolves. These estimates were slightly larger than the estimated census size of breeding individuals. A Bayesian model based on Markov chain Monte Carlo simulations indicated strong evidence for a long-term population decline. These results suggest that the contemporary wolf population size is roughly 8% of its historical size, and that the population decline dates back to late 19th century or early 20th century. Despite an increase of over 50% in the census size of the population during the whole study period, there was only weak evidence that the effective population size during the last period was higher than during the first. This may be caused by increased inbreeding, diminished dispersal within the population, and decreased immigration to the population during the last study period.

Animal Migration↗

Zinc and nitrate in the ground water and the incidence of Type 1 diabetes in Finland.

AIMS: In Finland, the risk of childhood Type 1 diabetes varies geographically. Therefore we investigated the association between spatial variation of Type 1 diabetes and its putative environmental risk factors, zinc and nitrates. METHODS: The association was evaluated using Bayesian modelling and the geo-referenced data on diabetes cases and population. RESULTS: Neither zinc nor nitrate nor the urban/rural status of the area had a significant effect on the variation in incidence of childhood Type 1 diabetes. CONCLUSIONS: The results showed that although there was no significant difference in incidence between rural and urban areas, there was a tendency to increasing risk of Type 1 diabetes with the increasing concentration of NO3 in drinking water. The fact that no significant effect was found may stem from the aggregated data being too crude to detect it.

Adolescent↗

State regulation and the delivery of physical therapy services.

OBJECTIVE: The study purpose was to examine the relationship between state regulations of physical therapists (PT) and three dependent variables: physical therapist assistant (PTA) utilization more than 50 percent of the time during the treatment episode (high PTA utilization), number of visits, and patient self-reported functional health status (FHS) at discharge. We evaluated regulations governing licensure of PTAs, PT/PTA ratio, frequency of PT re-evaluation, and PTA supervision. DATA SOURCE: The analytic sample included 63,900 patients from 38 states drawn from 395 clinics who participated in the Focus on Therapeutic Outcomes Inc. (Knoxville, TN) database in 2000 and 2001. STUDY DESIGN: Using a Bayesian modeling approach with the Markov Chain Monte Carlo estimation method, we fitted separate multilevel multivariate regression models predicting high PTA utilization, number of visits, and discharge FHS. DATA COLLECTION METHODS: Patients completed FHS surveys at intake and discharge. Clinicians recorded the number of visits and percentage of time a patient spent with each provider. PRINCIPAL FINDINGS: After controlling for patient, therapist, and clinic characteristics, the presence of state regulations regarding PTA supervision was not associated with the likelihood of high PTA utilization. High PTA utilization and regulations requiring full-time onsite supervision were associated with more visits, whereas regulation of PT/PTA ratio was associated with fewer visits. Supervisory regulations were associated with better discharge FHS. High PTA utilization and use of therapy aides were associated with more visits per episode and lower discharge FHS. CONCLUSIONS: The use of care extenders in place of PTs is likely to result in less efficient and lower quality care in outpatient rehabilitation.

Adult↗

Dose response for infectivity of several strains of Campylobacter jejuni in chickens.

Although some major risk studies have been done for Campylobacter jejuni, its dose response is not well characterized. Only a single human study is available, providing dose-response information for only a single isolate. As substantial heterogeneity in infectivity has been acknowledged for other pathogens, it remains unknown how well this single study represents the dose-response relation for this pathogen. As future human challenge studies with Campylobacter are unlikely, we have to find other means of studying its infectivity. Several dose-response studies have been done using chickens as host organisms. These studies may be used to obtain quantitative information on the variation in infectivity among different isolates of this pathogen. A hierarchical Bayesian model is well suited to describe heterogeneity, and we demonstrate how the beta-Poisson model of microbial infection may be adapted to allow for within- and between-isolate variation. Isolates tested in chickens can be categorized into two distinct groups: lab-adapted and fresh isolates, and we show how the hierarchical dose-response model can be used to quantitatively describe their differences. Fresh isolates show higher colonization potential and less within-isolate variation than lab isolates. The results indicate that Campylobacter jejuni is highly infectious in chickens. Different isolates show great variation in infectivity, especially between lab and fresh isolates, indicating that human clinical (volunteer) studies on infectivity must be interpreted cautiously.

Animals↗

Bias adjustment in Bayesian estimation of bird nest age-specific survival rates.

The populations of many North American landbirds are showing signs of declining. Gathering information on breeding productivity allows early detection of unhealthy populations and helps develop good habitat-management practices. In this paper, we study the performance of the Bayesian model (He, 2003, Biometrics 59, 962-973) for age-specific nest survival rates with irregular visits. We find that the estimates are satisfactory except for the age-one survival rate. Usually the more days skipped between two visits, the more serious the underestimation of the age-one survival rate. We investigated the problem and developed three approaches to adjust for the underestimation bias. The simulation results show that the three approaches can significantly improve the estimation of the age-one survival rate.

Age Factors↗

Chronic diffuse infiltrative lung disease: determination of the diagnostic value of clinical data, chest radiography, and CT and Bayesian analysis.

PURPOSE: To assess the value of clinical, chest radiographic, and computed tomographic (CT) findings in classifying chronic diffuse infiltrative lung disease (CDILD) MATERIALS AND METHODS: Two samples from the same population were consecutively studied: the training set (group A, n = 208) for the development of the decision aid and the test set (group B, n = 100) for validation. Computer-aided diagnoses were made with a Bayesian model that assigned to each patient diagnostic probabilities based on clinical, radiographic, or CT variables. RESULTS: In group A, a correct diagnosis based on clinical data was obtained in 29% of cases; radiography, 9%; and CT, 36%. This increased to 54% when clinical and radiographic variables were combined (P < .0001) and to 80% when data from all three were analyzed together (P < .0001). With prior and conditional probabilities determined from group A, the frequency of correct diagnosis in group B was 27% with clinical data, which increased to 53% (P < .0001) with radiographic findings and 61% after including CT data (P = .07). CONCLUSION: CT can help determine the specific diagnosis in patients with CDILD.

Bayes Theorem↗

Bayesian integration in force estimation.

When we interact with objects in the world, the forces we exert are finely tuned to the dynamics of the situation. As our sensors do not provide perfect knowledge about the environment, a key problem is how to estimate the appropriate forces. Two sources of information can be used to generate such an estimate: sensory inputs about the object and knowledge about previously experienced objects, termed prior information. Bayesian integration defines the way in which these two sources of information should be combined to produce an optimal estimate. To investigate whether subjects use such a strategy in force estimation, we designed a novel sensorimotor estimation task. We controlled the distribution of forces experienced over the course of an experiment thereby defining the prior. We show that subjects integrate sensory information with their prior experience to generate an estimate. Moreover, subjects could learn different prior distributions. These results suggest that the CNS uses Bayesian models when estimating force requirements.

Bayes Theorem↗

[Probability of developing and dying of cancer in Catalonia during the period 1998-2001].

BACKGROUND AND OBJECTIVE: We intended to estimate the probability of developing and dying from cancer in Catalonia during the period 1998-2001. PATIENTS AND METHOD: We used a Bayesian model which incorporates data from the Tarragona and Girona Cancer Registries and from the Catalonia Mortality Registry. The probability of developing and dying from cancer has been calculated using a competitive risk-based methodology. RESULTS: Lifetime probability of developing cancer in Catalonia is almost 1 out of 2 (43.7%) for men and 1 out of 3 (32.1%) in women. The probability of dying from cancer is 29.1% for men and 17.9% in women. 67% of men and 56% of women diagnosed with cancer will die from this disease. One out of 14 men will develop a lung cancer during his life and 1 out of 11 women will develop breast cancer. CONCLUSIONS: The observed rising in the probability of developing cancer in Catalonia over the last ten years highlights even more than ever the importance of this health problem.

Adolescent↗

Coronary artery pattern and outcome of arterial switch operation for transposition of the great arteries: a meta-analysis.

BACKGROUND: Prior studies of coronary pattern and outcome after arterial switch operation (ASO) for transposition of the great arteries (TGA) have been hindered by limited statistical power. This meta-analysis assesses the effect of coronary anatomy on post-ASO mortality, both overall and adjusted for time. METHODS AND RESULTS: A literature search revealed 9 independent series that reported post-ASO mortality by coronary pattern in a total of 1942 patients. Odds ratios comparing all-cause mortality in patients with usual versus variant coronary patterns were calculated and combined by use of an empirical Bayesian model. Single coronary patterns, both of which loop around the great vessels, were associated with significant mortality (OR 2.9, 95% CI 1.3 to 6.8), whereas looping patterns that arose from 2 separate ostia were not (OR 1.2, 95% CI 0.8 to 1.9). This latter group includes patients with the most common variant, circumflex from right coronary artery. Patients with an intramural coronary artery had the greatest mortality (OR 6.5, 95% CI 2.9 to 14.2). Overall, patients with any variant coronary pattern had nearly twice the mortality seen in those with the usual pattern (OR 1.7, 95% CI 1.3 to 2.4). Single ostium patterns and intramural coronary arteries remained associated with significant added mortality after adjustment for time-trend effects. CONCLUSIONS: Over the past 2 decades, patients with common coronary variants have undergone ASO without added mortality compared with those with the usual coronary pattern. Those with intramural or single coronary arteries have significant added mortality that has persisted over time.

Coronary Vessel Anomalies↗

Dictionary learning algorithms for sparse representation.

Algorithms for data-driven learning of domain-specific overcomplete dictionaries are developed to obtain maximum likelihood and maximum a posteriori dictionary estimates based on the use of Bayesian models with concave/Schur-concave (CSC) negative log priors. Such priors are appropriate for obtaining sparse representations of environmental signals within an appropriately chosen (environmentally matched) dictionary. The elements of the dictionary can be interpreted as concepts, features, or words capable of succinct expression of events encountered in the environment (the source of the measured signals). This is a generalization of vector quantization in that one is interested in a description involving a few dictionary entries (the proverbial "25 words or less"), but not necessarily as succinct as one entry. To learn an environmentally adapted dictionary capable of concise expression of signals generated by the environment, we develop algorithms that iterate between a representative set of sparse representations found by variants of FOCUSS and an update of the dictionary using these sparse representations. Experiments were performed using synthetic data and natural images. For complete dictionaries, we demonstrate that our algorithms have improved performance over other independent component analysis (ICA) methods, measured in terms of signal-to-noise ratios of separated sources. In the overcomplete case, we show that the true underlying dictionary and sparse sources can be accurately recovered. In tests with natural images, learned overcomplete dictionaries are shown to have higher coding efficiency than complete dictionaries; that is, images encoded with an overcomplete dictionary have both higher compression (fewer bits per pixel) and higher accuracy (lower mean square error).

Algorithms↗