Estimating Bayesian decision problems with heterogeneous priors

In many areas of economics there is a growing interest in how expertise andpreferences drive individual and group decision making under uncertainty. Increasingly, we wish to estimate such models to quantify which of these drive decisionmaking. In this paper we propose a new channel through which we can empirically identify expertise and preference parameters by using variation in decisionsover heterogeneous priors. Relative to existing estimation approaches, our \Prior-Based Identification" extends the possible environments which can be estimated,and also substantially improves the accuracy and precision of estimates in thoseenvironments which can be estimated using existing methods.

Further insights on the French WISC-IV factor structure through Bayesian structural equation modeling

The interpretation of the Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV) is based on a 4-factor model, which is only partially compatible with the mainstream Cattell-Horn-Carroll (CHC) model of intelligence measurement. The structure of cognitive batteries is frequently analyzed via exploratory factor analysis and/or confirmatory factor analysis. With classical confirmatory factor analysis, almost all crossloadings between latent variables and measures are fixed to zero in order to allow the model to be identified. However, inappropriate zero cross-loadings can contribute to poor model fit, distorted factors, and biased factor correlations; most important, they do not necessarily faithfully reflect theory. To deal with these methodological and theoretical limitations, we used a new statistical approach, Bayesian structural equation modeling (BSEM), among a sample of 249 French-speaking Swiss children (8-12 years). With BSEM, zero-fixed cross-loadings between latent variables and measures are replaced by approximate zeros, based on informative, small-variance priors. Results indicated that a direct hierarchical CHC-based model with 5 factors plus a general intelligence factor better represented the structure of the WISC-IV than did the 4-factor structure and the higher order models. Because a direct hierarchical CHC model was more adequate, it was concluded that the general factor should be considered as a breadth rather than a superordinate factor. Because it was possible for us to estimate the influence of each of the latent variables on the 15 subtest scores, BSEM allowed improvement of the understanding of the structure of intelligence tests and the clinical interpretation of the subtest scores.

Sample size and statistical power in the hierarchical analysis of variance: applications in morphometry of the nervous system.

Analysis of variance is commonly used in morphometry in order to ascertain differences in parameters between several populations. Failure to detect significant differences between populations (type II error) may be due to suboptimal sampling and lead to erroneous conclusions; the concept of statistical power allows one to avoid such failures by means of an adequate sampling. Several examples are given in the morphometry of the nervous system, showing the use of the power of a hierarchical analysis of variance test for the choice of appropriate sample and subsample sizes. In the first case chosen, neuronal densities in the human visual cortex, we find the number of observations to be of little effect. For dendritic spine densities in the visual cortex of mice and humans, the effect is somewhat larger. A substantial effect is shown in our last example, dendritic segmental lengths in monkey lateral geniculate nucleus. It is in the nature of the hierarchical model that sample size is always more important than subsample size. The relative weight to be attributed to subsample size thus depends on the relative magnitude of the between observations variance compared to the between individuals variance.

Therapeutic Drug Monitoring (TDM) of Imatinib: Effectiveness of Bayesian dose adjustment for CML patients enrolled in the Imatinib Concentration Monitoring (I-COME) study

Introduction: As imatinib pharmacokinetics are highly variable, plasma levels differ largely between patients under the same dosage. Retrospective studies in chronic myeloid leukemia (CML) patients showed significant correlations between low levels and suboptimal response, as well as between high levels and poor tolerability. Monitoring of trough plasma levels, targeting 1000 μg/L and above, is thus increasingly advised. Our study was launched to assess prospectively the clinical usefulness of systematic imatinib TDM in CML patients. This preliminary analysis addresses the appropriateness of the dosage adjustment approach applied in this study, which targets the recommended trough level and allows an interval of 4-24 h after last drug intake for blood sampling. Methods: Blood samples from the first 15 patients undergoing 1st TDM were obtained 1.5-25 h after last dose. Imatinib plasma levels were measured by LC-MS/MS and the concentrations were extrapolated to trough based on a Bayesian approach using a population pharmacokinetic model. Trough levels were predicted to differ significantly from the target in 12 patients (10 <750 μg/L; 2 >1500 μg/L along with poor tolerance) and individual dose adjustments were proposed. 8 patients underwent a 2nd TDM cycle. Trough levels of 1st and 2nd TDM were compared, the sample drawn 1.5 h after last dose (during distribution phase) was excluded from the analysis. Results: Individual dose adjustments were applied in 6 patients. Observed concentrations extrapolated to trough ranged from 360 to 1832 μg/L (median 725; mean 810, CV 52%) on 1st TDM and from 720 to 1187 μg/L (median 950; mean 940, CV 18%) on 2nd TDM cycle. Conclusions: These preliminary results suggest that TDM of imatinib using a Bayesian interpretation is able to target the recommended trough level of 1000 μg/L and to reduce the considerable differences in trough level exposure between patients (with CV decreasing from 52% to 18%). While this may simplify blood collection in daily practice, as samples do not have to be drawn exactly at trough, the largest possible interval to last drug intake yet remains preferable to avoid sampling during distribution phase leading to biased extrapolation. This encourages the evaluation of the clinical benefit of a routine TDM intervention in CML patients, which the randomized Swiss I-COME trial aims to.

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.

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.

Rapid radiation in spiny lobsters (Palinurus spp) as revealed by classic and ABC methods using mtDNA and microsatellite data

Background: Molecular tools may help to uncover closely related and still diverging species from a wide variety of taxa and provide insight into the mechanisms, pace and geography of marine speciation. There is a certain controversy on the phylogeography and speciation modes of species-groups with an Eastern Atlantic-Western Indian Ocean distribution, with previous studies suggesting that older events (Miocene) and/or more recent (Pleistocene) oceanographic processes could have influenced the phylogeny of marine taxa. The spiny lobster genus Palinurus allows for testing among speciation hypotheses, since it has a particular distribution with two groups of three species each in the Northeastern Atlantic (P. elephas, P. mauritanicus and P. charlestoni) and Southeastern Atlantic and Southwestern Indian Oceans (P. gilchristi, P. delagoae and P. barbarae). In the present study, we obtain a more complete understanding of the phylogenetic relationships among these species through a combined dataset with both nuclear and mitochondrial markers, by testing alternative hypotheses on both the mutation rate and tree topology under the recently developed approximate Bayesian computation (ABC) methods. Results Our analyses support a North-to-South speciation pattern in Palinurus with all the South-African species forming a monophyletic clade nested within the Northern Hemisphere species. Coalescent-based ABC methods allowed us to reject the previously proposed hypothesis of a Middle Miocene speciation event related with the closure of the Tethyan Seaway. Instead, divergence times obtained for Palinurus species using the combined mtDNA-microsatellite dataset and standard mutation rates for mtDNA agree with known glaciation-related processes occurring during the last 2 my. Conclusion The Palinurus speciation pattern is a typical example of a series of rapid speciation events occurring within a group, with very short branches separating different species. Our results support the hypothesis that recent climate change-related oceanographic processes have influenced the phylogeny of marine taxa, with most Palinurus species originating during the last two million years. The present study highlights the value of new coalescent-based statistical methods such as ABC for testing different speciation hypotheses using molecular data.

MBIS: multivariate Bayesian image segmentation tool.

We present MBIS (Multivariate Bayesian Image Segmentation tool), a clustering tool based on the mixture of multivariate normal distributions model. MBIS supports multichannel bias field correction based on a B-spline model. A second methodological novelty is the inclusion of graph-cuts optimization for the stationary anisotropic hidden Markov random field model. Along with MBIS, we release an evaluation framework that contains three different experiments on multi-site data. We first validate the accuracy of segmentation and the estimated bias field for each channel. MBIS outperforms a widely used segmentation tool in a cross-comparison evaluation. The second experiment demonstrates the robustness of results on atlas-free segmentation of two image sets from scan-rescan protocols on 21 healthy subjects. Multivariate segmentation is more replicable than the monospectral counterpart on T1-weighted images. Finally, we provide a third experiment to illustrate how MBIS can be used in a large-scale study of tissue volume change with increasing age in 584 healthy subjects. This last result is meaningful as multivariate segmentation performs robustly without the need for prior knowledge.

Improvement of therapeutic drug monitoring of imatinib by Bayesian prediction of trough levels. Personalized drug dosage

Aims: Plasma concentrations of imatinib differ largely between patients despite same dosage, owing to large inter-individual variability in pharmacokinetic (PK) parameters. As the drug concentration at the end of the dosage interval (Cmin) correlates with treatment response and tolerability, monitoring of Cmin is suggested for therapeutic drug monitoring (TDM) of imatinib. Due to logistic difficulties, random sampling during the dosage interval is however often performed in clinical practice, thus rendering the respective results not informative regarding Cmin values.Objectives: (I) To extrapolate randomly measured imatinib concentrations to more informative Cmin using classical Bayesian forecasting. (II) To extend the classical Bayesian method to account for correlation between PK parameters. (III) To evaluate the predictive performance of both methods.Methods: 31 paired blood samples (random and trough levels) were obtained from 19 cancer patients under imatinib. Two Bayesian maximum a posteriori (MAP) methods were implemented: (A) a classical method ignoring correlation between PK parameters, and (B) an extended one accounting for correlation. Both methods were applied to estimate individual PK parameters, conditional on random observations and covariate-adjusted priors from a population PK model. The PK parameter estimates were used to calculate trough levels. Relative prediction errors (PE) were analyzed to evaluate accuracy (one-sample t-test) and to compare precision between the methods (F-test to compare variances).Results: Both Bayesian MAP methods allowed non-biased predictions of individual Cmin compared to observations: (A) - 7% mean PE (CI95% - 18 to 4 %, p = 0.15) and (B) - 4% mean PE (CI95% - 18 to 10 %, p = 0.69). Relative standard deviations of actual observations from predictions were 22% (A) and 30% (B), i.e. comparable to the intraindividual variability reported. Precision was not improved by taking into account correlation between PK parameters (p = 0.22).Conclusion: Clinical interpretation of randomly measured imatinib concentrations can be assisted by Bayesian extrapolation to maximum likelihood Cmin. Classical Bayesian estimation can be applied for TDM without the need to include correlation between PK parameters. Both methods could be adapted in the future to evaluate other individual pharmacokinetic measures correlated to clinical outcomes, such as area under the curve(AUC).

Bayesian-MCMC inversion of time-lapse geophysical data to characterize vadose zone hydraulic behaviour

Geophysical methods have the potential to provide valuable information on hydrological properties in the unsaturated zone. In particular, time-lapse geophysical data, when coupled with a hydrological model and inverted stochastically, may allow for the effective estimation of subsurface hydraulic parameters and their corresponding uncertainties. In this study, we use a Bayesian Markov-chain-Monte-Carlo (MCMC) inversion approach to investigate how much information regarding vadose zone hydraulic properties can be retrieved from time-lapse crosshole GPR data collected at the Arrenaes field site in Denmark during a forced infiltration experiment.

Application of Multi-SNP Approaches Bayesian LASSO and AUC-RF to Detect Main Effects of Inflammatory-Gene Variants Associated with Bladder Cancer Risk

The relationship between inflammation and cancer is well established in several tumor types, including bladder cancer. We performed an association study between 886 inflammatory-gene variants and bladder cancer risk in 1,047 cases and 988 controls from the Spanish Bladder Cancer (SBC)/EPICURO Study. A preliminary exploration with the widely used univariate logistic regression approach did not identify any significant SNP after correcting for multiple testing. We further applied two more comprehensive methods to capture the complexity of bladder cancer genetic susceptibility: Bayesian Threshold LASSO (BTL), a regularized regression method, and AUC-Random Forest, a machine-learning algorithm. Both approaches explore the joint effect of markers. BTL analysis identified a signature of 37 SNPs in 34 genes showing an association with bladder cancer. AUC-RF detected an optimal predictive subset of 56 SNPs. 13 SNPs were identified by both methods in the total population. Using resources from the Texas Bladder Cancer study we were able to replicate 30% of the SNPs assessed. The associations between inflammatory SNPs and bladder cancer were reexamined among non-smokers to eliminate the effect of tobacco, one of the strongest and most prevalent environmental risk factor for this tumor. A 9 SNP-signature was detected by BTL. Here we report, for the first time, a set of SNP in inflammatory genes jointly associated with bladder cancer risk. These results highlight the importance of the complex structure of genetic susceptibility associated with cancer risk.

Methods for Estimating Annual Exceedance-Probability Discharges for Streams in Iowa, Based on Data through Water Year 2010, TR-519, 2013

A statewide study was performed to develop regional regression equations for estimating selected annual exceedance- probability statistics for ungaged stream sites in Iowa. The study area comprises streamgages located within Iowa and 50 miles beyond the State’s borders. Annual exceedanceprobability estimates were computed for 518 streamgages by using the expected moments algorithm to fit a Pearson Type III distribution to the logarithms of annual peak discharges for each streamgage using annual peak-discharge data through 2010. The estimation of the selected statistics included a Bayesian weighted least-squares/generalized least-squares regression analysis to update regional skew coefficients for the 518 streamgages. Low-outlier and historic information were incorporated into the annual exceedance-probability analyses, and a generalized Grubbs-Beck test was used to detect multiple potentially influential low flows. Also, geographic information system software was used to measure 59 selected basin characteristics for each streamgage. Regional regression analysis, using generalized leastsquares regression, was used to develop a set of equations for each flood region in Iowa for estimating discharges for ungaged stream sites with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities, which are equivalent to annual flood-frequency recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively. A total of 394 streamgages were included in the development of regional regression equations for three flood regions (regions 1, 2, and 3) that were defined for Iowa based on landform regions and soil regions. Average standard errors of prediction range from 31.8 to 45.2 percent for flood region 1, 19.4 to 46.8 percent for flood region 2, and 26.5 to 43.1 percent for flood region 3. The pseudo coefficients of determination for the generalized leastsquares equations range from 90.8 to 96.2 percent for flood region 1, 91.5 to 97.9 percent for flood region 2, and 92.4 to 96.0 percent for flood region 3. The regression equations are applicable only to stream sites in Iowa with flows not significantly affected by regulation, diversion, channelization, backwater, or urbanization and with basin characteristics within the range of those used to develop the equations. These regression equations will be implemented within the U.S. Geological Survey StreamStats Web-based geographic information system tool. StreamStats allows users to click on any ungaged site on a river and compute estimates of the eight selected statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged sites also are provided by the Web-based tool. StreamStats also allows users to click on any streamgage in Iowa and estimates computed for these eight selected statistics are provided for the streamgage.