ABCtoolbox: a versatile toolkit for approximate Bayesian computations.

BACKGROUND: The estimation of demographic parameters from genetic data often requires the computation of likelihoods. However, the likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has therefore been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations. RESULTS: Here we present ABCtoolbox, a series of open source programs to perform Approximate Bayesian Computations (ABC). It implements various ABC algorithms including rejection sampling, MCMC without likelihood, a Particle-based sampler and ABC-GLM. ABCtoolbox is bundled with, but not limited to, a program that allows parameter inference in a population genetics context and the simultaneous use of different types of markers with different ploidy levels. In addition, ABCtoolbox can also interact with most simulation and summary statistics computation programs. The usability of the ABCtoolbox is demonstrated by inferring the evolutionary history of two evolutionary lineages of Microtus arvalis. Using nuclear microsatellites and mitochondrial sequence data in the same estimation procedure enabled us to infer sex-specific population sizes and migration rates and to find that males show smaller population sizes but much higher levels of migration than females. CONCLUSION: ABCtoolbox allows a user to perform all the necessary steps of a full ABC analysis, from parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results.

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.

Phylogenetics of Olea (Oleaceae) based on plastid and nuclear ribosomal DNA sequences: tertiary climatic shifts and lineage differentiation times.

BACKGROUND AND AIMS: The genus Olea (Oleaceae) includes approx. 40 taxa of evergreen shrubs and trees classified in three subgenera, Olea, Paniculatae and Tetrapilus, the first of which has two sections (Olea and Ligustroides). Olive trees (the O. europaea complex) have been the subject of intensive research, whereas little is known about the phylogenetic relationships among the other species. To clarify the biogeographical history of this group, a molecular analysis of Olea and related genera of Oleaceae is thus necessary. METHODS: A phylogeny was built of Olea and related genera based on sequences of the nuclear ribosomal internal transcribed spacer-1 and four plastid regions. Lineage divergence and the evolution of abaxial peltate scales, the latter character linked to drought adaptation, were dated using a Bayesian method. KEY RESULTS: Olea is polyphyletic, with O. ambrensis and subgenus Tetrapilus not sharing a most recent common ancestor with the main Olea clade. Partial incongruence between nuclear and plastid phylogenetic reconstructions suggests a reticulation process in the evolution of subgenus Olea. Estimates of divergence times for major groups of Olea during the Tertiary were obtained. CONCLUSIONS: This study indicates the necessity of revising current taxonomic boundaries in Olea. The results also suggest that main lines of evolution were promoted by major Tertiary climatic shifts: (1) the split between subgenera Olea and Paniculatae appears to have taken place at the Miocene-Oligocene boundary; (2) the separation of sections Ligustroides and Olea may have occurred during the Early Miocene following the Mi-1 glaciation; and (3) the diversification within these sections (and the origin of dense abaxial indumentum in section Olea) was concomitant with the aridification of Africa in the Late Miocene.

Computational problems in perfect phylogeny haplotyping: Typing without calling the allele

A haplotype is an m-long binary vector. The XOR-genotype of two haplotypes is the m-vector of their coordinate-wise XOR. We study the following problem: Given a set of XOR-genotypes, reconstruct their haplotypes so that the set of resulting haplotypes can be mapped onto a perfect phylogeny (PP) tree. The question is motivated by studying population evolution in human genetics and is a variant of the PP haplotyping problem that has received intensive attention recently. Unlike the latter problem, in which the input is '' full '' genotypes, here, we assume less informative input and so may be more economical to obtain experimentally. Building on ideas of Gusfield, we show how to solve the problem in polynomial time by a reduction to the graph realization problem. The actual haplotypes are not uniquely determined by the tree they map onto and the tree itself may or may not be unique. We show that tree uniqueness implies uniquely determined haplotypes, up to inherent degrees of freedom, and give a sufficient condition for the uniqueness. To actually determine the haplotypes given the tree, additional information is necessary. We show that two or three full genotypes suffice to reconstruct all the haplotypes and present a linear algorithm for identifying those genotypes.

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.

Learning about Bayesian networks for forensic interpretation : An example based on the "the problem of multiple propositions"

Both, Bayesian networks and probabilistic evaluation are gaining more and more widespread use within many professional branches, including forensic science. Notwithstanding, they constitute subtle topics with definitional details that require careful study. While many sophisticated developments of probabilistic approaches to evaluation of forensic findings may readily be found in published literature, there remains a gap with respect to writings that focus on foundational aspects and on how these may be acquired by interested scientists new to these topics. This paper takes this as a starting point to report on the learning about Bayesian networks for likelihood ratio based, probabilistic inference procedures in a class of master students in forensic science. The presentation uses an example that relies on a casework scenario drawn from published literature, involving a questioned signature. A complicating aspect of that case study - proposed to students in a teaching scenario - is due to the need of considering multiple competing propositions, which is an outset that may not readily be approached within a likelihood ratio based framework without drawing attention to some additional technical details. Using generic Bayesian networks fragments from existing literature on the topic, course participants were able to track the probabilistic underpinnings of the proposed scenario correctly both in terms of likelihood ratios and of posterior probabilities. In addition, further study of the example by students allowed them to derive an alternative Bayesian network structure with a computational output that is equivalent to existing probabilistic solutions. This practical experience underlines the potential of Bayesian networks to support and clarify foundational principles of probabilistic procedures for forensic evaluation.

A non-linear Bayesian approach for upscaling local-scale hydraulic conductivity measurements based on local- and regional-scale geophysical data

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the regional scale represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed an upscaling procedure based on a Bayesian sequential simulation approach. This method is then applied to the stochastic integration of low-resolution, regional-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities. Finally, the overall viability of this upscaling approach is tested and verified by performing and comparing flow and transport simulation through the original and the upscaled hydraulic conductivity fields. Our results indicate that the proposed procedure does indeed allow for obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.

Web Services for Bayesian Learning

In this demonstration we present our web services to perform Bayesian learning for classification tasks.

Clustering of HCV coinfections on HIV phylogeny indicates domestic and sexual transmission of HCV.

BACKGROUND: HCV coinfection remains a major cause of morbidity and mortality among HIV-infected individuals and its incidence has increased dramatically in HIV-infected men who have sex with men(MSM). METHODS: Hepatitis C virus (HCV) coinfection in the Swiss HIV Cohort Study(SHCS) was studied by combining clinical data with HIV-1 pol-sequences from the SHCS Drug Resistance Database(DRDB). We inferred maximum-likelihood phylogenetic trees, determined Swiss HIV-transmission pairs as monophyletic patient pairs, and then considered the distribution of HCV on those pairs. RESULTS: Among the 9748 patients in the SHCS-DRDB with known HCV status, 2768(28%) were HCV-positive. Focusing on subtype B(7644 patients), we identified 1555 potential HIV-1 transmission pairs. There, we found that, even after controlling for transmission group, calendar year, age and sex, the odds for an HCV coinfection were increased by an odds ratio (OR) of 3.2 [95% confidence interval (CI) 2.2, 4.7) if a patient clustered with another HCV-positive case. This strong association persisted if transmission groups of intravenous drug users (IDUs), MSMs and heterosexuals (HETs) were considered separately(in all cases OR>2). Finally we found that HCV incidence was increased by a hazard ratio of 2.1 (1.1, 3.8) for individuals paired with an HCV-positive partner. CONCLUSIONS: Patients whose HIV virus is closely related to the HIV virus of HIV/HCV-coinfected patients have a higher risk for carrying or acquiring HCV themselves. This indicates the occurrence of domestic and sexual HCV transmission and allows the identification of patients with a high HCV-infection risk.

Bayesian networks and the evaluation of scientific evidence in forensic science

Résumé Ce travail de thèse étudie des moyens de formalisation permettant d'assister l'expert forensique dans la gestion des facteurs influençant l'évaluation des indices scientifiques, tout en respectant des procédures d'inférence établies et acceptables. Selon une vue préconisée par une partie majoritaire de la littérature forensique et juridique - adoptée ici sans réserve comme point de départ - la conceptualisation d'une procédure évaluative est dite 'cohérente' lors qu'elle repose sur une implémentation systématique de la théorie des probabilités. Souvent, par contre, la mise en oeuvre du raisonnement probabiliste ne découle pas de manière automatique et peut se heurter à des problèmes de complexité, dus, par exemple, à des connaissances limitées du domaine en question ou encore au nombre important de facteurs pouvant entrer en ligne de compte. En vue de gérer ce genre de complications, le présent travail propose d'investiguer une formalisation de la théorie des probabilités au moyen d'un environment graphique, connu sous le nom de Réseaux bayesiens (Bayesian networks). L'hypothèse principale que cette recherche envisage d'examiner considère que les Réseaux bayesiens, en concert avec certains concepts accessoires (tels que des analyses qualitatives et de sensitivité), constituent une ressource clé dont dispose l'expert forensique pour approcher des problèmes d'inférence de manière cohérente, tant sur un plan conceptuel que pratique. De cette hypothèse de travail, des problèmes individuels ont été extraits, articulés et abordés dans une série de recherches distinctes, mais interconnectées, et dont les résultats - publiés dans des revues à comité de lecture - sont présentés sous forme d'annexes. D'un point de vue général, ce travail apporte trois catégories de résultats. Un premier groupe de résultats met en évidence, sur la base de nombreux exemples touchant à des domaines forensiques divers, l'adéquation en termes de compatibilité et complémentarité entre des modèles de Réseaux bayesiens et des procédures d'évaluation probabilistes existantes. Sur la base de ces indications, les deux autres catégories de résultats montrent, respectivement, que les Réseaux bayesiens permettent également d'aborder des domaines auparavant largement inexplorés d'un point de vue probabiliste et que la disponibilité de données numériques dites 'dures' n'est pas une condition indispensable pour permettre l'implémentation des approches proposées dans ce travail. Le présent ouvrage discute ces résultats par rapport à la littérature actuelle et conclut en proposant les Réseaux bayesiens comme moyen d'explorer des nouvelles voies de recherche, telles que l'étude de diverses formes de combinaison d'indices ainsi que l'analyse de la prise de décision. Pour ce dernier aspect, l'évaluation des probabilités constitue, dans la façon dont elle est préconisée dans ce travail, une étape préliminaire fondamentale de même qu'un moyen opérationnel.

Probabilistic evidential assessment of gunshot residue particle evidence (Part I): likelihood ratio calculation and case pre-assessment using Bayesian networks

Well developed experimental procedures currently exist for retrieving and analyzing particle evidence from hands of individuals suspected of being associated with the discharge of a firearm. Although analytical approaches (e.g. automated Scanning Electron Microscopy with Energy Dispersive X-ray (SEM-EDS) microanalysis) allow the determination of the presence of elements typically found in gunshot residue (GSR) particles, such analyses provide no information about a given particle's actual source. Possible origins for which scientists may need to account for are a primary exposure to the discharge of a firearm or a secondary transfer due to a contaminated environment. In order to approach such sources of uncertainty in the context of evidential assessment, this paper studies the construction and practical implementation of graphical probability models (i.e. Bayesian networks). These can assist forensic scientists in making the issue tractable within a probabilistic perspective. The proposed models focus on likelihood ratio calculations at various levels of detail as well as case pre-assessment.

Wave-height hazard analysis in Eastern Coast of Spain : Bayesian approach using generalized Pareto distribution

Standard practice of wave-height hazard analysis often pays little attention to the uncertainty of assessed return periods and occurrence probabilities. This fact favors the opinion that, when large events happen, the hazard assessment should change accordingly. However, uncertainty of the hazard estimates is normally able to hide the effect of those large events. This is illustrated using data from the Mediterranean coast of Spain, where the last years have been extremely disastrous. Thus, it is possible to compare the hazard assessment based on data previous to those years with the analysis including them. With our approach, no significant change is detected when the statistical uncertainty is taken into account. The hazard analysis is carried out with a standard model. Time-occurrence of events is assumed Poisson distributed. The wave-height of each event is modelled as a random variable which upper tail follows a Generalized Pareto Distribution (GPD). Moreover, wave-heights are assumed independent from event to event and also independent of their occurrence in time. A threshold for excesses is assessed empirically. The other three parameters (Poisson rate, shape and scale parameters of GPD) are jointly estimated using Bayes' theorem. Prior distribution accounts for physical features of ocean waves in the Mediterranean sea and experience with these phenomena. Posterior distribution of the parameters allows to obtain posterior distributions of other derived parameters like occurrence probabilities and return periods. Predictives are also available. Computations are carried out using the program BGPE v2.0

Phylogeography and recolonization of the Swiss Alps by the Valais shrew (Sorex antinorii), inferred with autosomal and sex-specific markers.

Using one male-inherited, one female-inherited and eight biparentally inherited markers, we investigate the population genetic structure of the Valais shrew (Sorex antinorii) in the Swiss Alps. Bayesian analysis on autosomal microsatellites suggests a clear genetic differentiation between two groups of populations. This geographically based structure is consistent with two separate postglacial recolonization routes of the species into Switzerland from Italian refugia after the last Pleistocene glaciations. Sex-specific markers also confirm genetic structuring among western and eastern areas, since very few haplotypes for either Y chromosome or mtDNA genome are shared between the two regions. Overall, these results suggest that two already well-differentiated genetic lineages colonized the Swiss Alps and came into secondary contact in the Rhône Valley. Low level of admixture between the two lineages is likely explained by the mountainous landscape structure of lateral valleys orthogonal to the main Rhône valley.