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.

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.

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.

Toxic substances in blood: an analysis of current recommendations under a Bayesian (decision) approach

This article extends existing discussion in literature on probabilistic inference and decision making with respect to continuous hypotheses that are prevalent in forensic toxicology. As a main aim, this research investigates the properties of a widely followed approach for quantifying the level of toxic substances in blood samples, and to compare this procedure with a Bayesian probabilistic approach. As an example, attention is confined to the presence of toxic substances, such as THC, in blood from car drivers. In this context, the interpretation of results from laboratory analyses needs to take into account legal requirements for establishing the 'presence' of target substances in blood. In a first part, the performance of the proposed Bayesian model for the estimation of an unknown parameter (here, the amount of a toxic substance) is illustrated and compared with the currently used method. The model is then used in a second part to approach-in a rational way-the decision component of the problem, that is judicial questions of the kind 'Is the quantity of THC measured in the blood over the legal threshold of 1.5 μg/l?'. This is pointed out through a practical example.

Integration of local-scale hydrological and regional-scale geophysical based on a nonlinear Bayesian sequential simulation approach

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 a downscaling procedure based on a non-linear Bayesian sequential simulation approach. The basic objective of this algorithm is to estimate the value of the sparsely sampled hydraulic conductivity at non-sampled locations based on its relation to the electrical conductivity, which is available throughout the model space. The in situ relationship between the hydraulic and electrical conductivities is described through a non-parametric multivariate kernel density function. This method is then applied to the stochastic integration of low-resolution, re- gional-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 downscaling approach is tested and verified by performing and comparing flow and transport simulation through the original and the downscaled 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.

Implementing statistical learning methods through Bayesian networks. Part 1: a guide to Bayesian parameter estimation using forensic science data

As a thorough aggregation of probability and graph theory, Bayesian networks currently enjoy widespread interest as a means for studying factors that affect the coherent evaluation of scientific evidence in forensic science. Paper I of this series of papers intends to contribute to the discussion of Bayesian networks as a framework that is helpful for both illustrating and implementing statistical procedures that are commonly employed for the study of uncertainties (e.g. the estimation of unknown quantities). While the respective statistical procedures are widely described in literature, the primary aim of this paper is to offer an essentially non-technical introduction on how interested readers may use these analytical approaches - with the help of Bayesian networks - for processing their own forensic science data. Attention is mainly drawn to the structure and underlying rationale of a series of basic and context-independent network fragments that users may incorporate as building blocs while constructing larger inference models. As an example of how this may be done, the proposed concepts will be used in a second paper (Part II) for specifying graphical probability networks whose purpose is to assist forensic scientists in the evaluation of scientific evidence encountered in the context of forensic document examination (i.e. results of the analysis of black toners present on printed or copied documents).

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.

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.