Bayesian tools for zero counts in compositional data

The log-ratio methodology makes available powerful tools for analyzing compositionaldata. Nevertheless, the use of this methodology is only possible for those data setswithout null values. Consequently, in those data sets where the zeros are present, aprevious treatment becomes necessary. Last advances in the treatment of compositionalzeros have been centered especially in the zeros of structural nature and in the roundedzeros. These tools do not contemplate the particular case of count compositional datasets with null values. In this work we deal with \count zeros" and we introduce atreatment based on a mixed Bayesian-multiplicative estimation. We use the Dirichletprobability distribution as a prior and we estimate the posterior probabilities. Then weapply a multiplicative modi¯cation for the non-zero values. We present a case studywhere this new methodology is applied.Key words: count data, multiplicative replacement, composition, log-ratio analysis

Efficacy of prescribed injectable diacetylmorphine in the Andalusian trial: Bayesian analysis of responders and non-responders according to a multi domain outcome index.

BACKGROUND The objective of this research was to evaluate data from a randomized clinical trial that tested injectable diacetylmorphine (DAM) and oral methadone (MMT) for substitution treatment, using a multi-domain dichotomous index, with a Bayesian approach. METHODS Sixty two long-term, socially-excluded heroin injectors, not benefiting from available treatments were randomized to receive either DAM or MMT for 9 months in Granada, Spain. Completers were 44 and data at the end of the study period was obtained for 50. Participants were determined to be responders or non responders using a multi-domain outcome index accounting for their physical and mental health and psychosocial integration, used in a previous trial. Data was analyzed with Bayesian methods, using information from a similar study conducted in The Netherlands to select a priori distributions. On adding the data from the present study to update the a priori information, the distribution of the difference in response rates were obtained and used to build credibility intervals and relevant probability computations. RESULTS In the experimental group (n = 27), the rate of responders to treatment was 70.4% (95% CI 53.287.6), and in the control group (n = 23), it was 34.8% (95% CI 15.354.3). The probability of success in the experimental group using the a posteriori distributions was higher after a proper sensitivity analysis. Almost the whole distribution of the rates difference (the one for diacetylmorphine minus methadone) was located to the right of the zero, indicating the superiority of the experimental treatment. CONCLUSION The present analysis suggests a clinical superiority of injectable diacetylmorphine compared to oral methadone in the treatment of severely affected heroin injectors not benefiting sufficiently from the available treatments. TRIAL REGISTRATION Current Controlled Trials ISRCTN52023186.

Implementing statistical learning methods through Bayesian networks (Part 2): bayesian evaluations for results of black toner analyses in forensic document examination

This paper presents and discusses the use of Bayesian procedures - introduced through the use of Bayesian networks in Part I of this series of papers - for 'learning' probabilities from data. The discussion will relate to a set of real data on characteristics of black toners commonly used in printing and copying devices. Particular attention is drawn to the incorporation of the proposed procedures as an integral part in probabilistic inference schemes (notably in the form of Bayesian networks) that are intended to address uncertainties related to particular propositions of interest (e.g., whether or not a sample originates from a particular source). The conceptual tenets of the proposed methodologies are presented along with aspects of their practical implementation using currently available Bayesian network software.

Bayesian nash equilibrium in ''linear'' cournot models with private information about costs

Calculating explicit closed form solutions of Cournot models where firms have private information about their costs is, in general, very cumbersome. Most authors consider therefore linear demands and constant marginal costs. However, within this framework, the nonnegativity constraint on prices (and quantities) has been ignored or not properly dealt with and the correct calculation of all Bayesian Nash equilibria is more complicated than expected. Moreover, multiple symmetric and interior Bayesianf equilibria may exist for an open set of parameters. The reason for this is that linear demand is not really linear, since there is a kink at zero price: the general ''linear'' inverse demand function is P (Q) = max{a - bQ, 0} rather than P (Q) = a - bQ.

Bayesian Markov chain Monte Carlo inversion of geophysical data for the purpose of estimating the hydraulic properties of the unsaturated zone

Ground-penetrating radar (GPR) has the potential to provide valuable information on hydrological properties of the vadose zone because of their strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR data within a coupled geophysical-hydrological framework may allow for effective estimation of subsurface van-Genuchten-Mualem (VGM) parameters and their corresponding uncertainties. An important and still unresolved issue, however, is how to best integrate GPR data into a stochastic inversion in order to estimate the VGM parameters and their uncertainties, thus improving hydrological predictions. Recognizing the importance of this issue, the aim of the research presented in this thesis was to first introduce a fully Bayesian inversion called Markov-chain-Monte-carlo (MCMC) strategy to perform the stochastic inversion of steady-state GPR data to estimate the VGM parameters and their uncertainties. Within this study, the choice of the prior parameter probability distributions from which potential model configurations are drawn and tested against observed data was also investigated. Analysis of both synthetic and field data collected at the Eggborough (UK) site indicates that the geophysical data alone contain valuable information regarding the VGM parameters. However, significantly better results are obtained when these data are combined with a realistic, informative prior. A subsequent study explore in detail the dynamic infiltration case, specifically to what extent time-lapse ZOP GPR data, collected during a forced infiltration experiment at the Arrenaes field site (Denmark), can help to quantify VGM parameters and their uncertainties using the MCMC inversion strategy. The findings indicate that the stochastic inversion of time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions. In turn, this significantly improves knowledge of the hydraulic properties, which are required to predict hydraulic behaviour. Finally, another aspect that needed to be addressed involved the comparison of time-lapse GPR data collected under different infiltration conditions (i.e., natural loading and forced infiltration conditions) to estimate the VGM parameters using the MCMC inversion strategy. The results show that for the synthetic example, considering data collected during a forced infiltration test helps to better refine soil hydraulic properties compared to data collected under natural infiltration conditions. When investigating data collected at the Arrenaes field site, further complications arised due to model error and showed the importance of also including a rigorous analysis of the propagation of model error with time and depth when considering time-lapse data. Although the efforts in this thesis were focused on GPR data, the corresponding findings are likely to have general applicability to other types of geophysical data and field environments. Moreover, the obtained results allow to have confidence for future developments in integration of geophysical data with stochastic inversions to improve the characterization of the unsaturated zone but also reveal important issues linked with stochastic inversions, namely model errors, that should definitely be addressed in future research.

Using a Bayesian method to assign individuals to karyotypic taxa in shrew hybrid zones.

Individuals sampled in hybrid zones are usually analysed according to their sampling locality, morphology, behaviour or karyotype. But the increasing availability of genetic information more and more favours its use for individual sorting purposes and numerous assignment methods based on the genetic composition of individuals have been developed. The shrews of the Sorex araneus group offer good opportunities to test the genetic assignment on individuals identified by their karyotype. Here we explored the potential and efficiency of a Bayesian assignment method combined or not with a reference dataset to study admixture and individual assignment in the difficult context of two hybrid zones between karyotypic species of the Sorex araneus group. As a whole, we assigned more than 80% of the individuals to their respective karyotypic categories (i.e. 'pure' species or hybrids). This assignment level is comparable to what was obtained for the same species away from hybrid zones. Additionally, we showed that the assignment result for several individuals was strongly affected by the inclusion or not of a reference dataset. This highlights the importance of such comparisons when analysing hybrid zones. Finally, differences between the admixture levels detected in both hybrid zones support the hypothesis of an impact of chromosomal rearrangements on gene flow.

Probabilistic evidential assessment of gunshot residue particle evidence (Part II) : Bayesian parameter estimation for experimental count data.

Part I of this series of articles focused on the construction of graphical probabilistic inference procedures, at various levels of detail, for assessing the evidential value of gunshot residue (GSR) particle evidence. The proposed models - in the form of Bayesian networks - address the issues of background presence of GSR particles, analytical performance (i.e., the efficiency of evidence searching and analysis procedures) and contamination. The use and practical implementation of Bayesian networks for case pre-assessment is also discussed. This paper, Part II, concentrates on Bayesian parameter estimation. This topic complements Part I in that it offers means for producing estimates useable for the numerical specification of the proposed probabilistic graphical models. Bayesian estimation procedures are given a primary focus of attention because they allow the scientist to combine (his/her) prior knowledge about the problem of interest with newly acquired experimental data. The present paper also considers further topics such as the sensitivity of the likelihood ratio due to uncertainty in parameters and the study of likelihood ratio values obtained for members of particular populations (e.g., individuals with or without exposure to GSR).

Production and Abatement Distortions under Noisy Green Taxes, October 2005

Pigouvian taxes are typically imposed in situations where there is imperfect knowledge on the extent of damage caused by a producing firm. A regulator imposing imperfectly informed Pigouvian taxes may cause the firms that should (should not) produce to shut down (produce). In this paper we use a Bayesian information framework to identify optimal signal-conditioned taxes in the presence of such losses. The tax system involves reducing (increasing) taxes on firms identified as causing high (low) damage. Unfortunately, when an abatement decision has to be made, the tax system that minimizes production distortions also dampens the incentive to abate. In the absence of wrong-firm concerns, a regulator can solve the problem by not adjusting taxes for signal noise. When wrong-firm losses are a concern, the regulator has to trade off losses from distorted production incentives with losses from distorted abatement incentives. The most appropriate policy may involve a combination of instruments.

Bayesian networks for evaluating forensic DNA profiling evidence: a review and guide to literature

Almost 30 years ago, Bayesian networks (BNs) were developed in the field of artificial intelligence as a framework that should assist researchers and practitioners in applying the theory of probability to inference problems of more substantive size and, thus, to more realistic and practical problems. Since the late 1980s, Bayesian networks have also attracted researchers in forensic science and this tendency has considerably intensified throughout the last decade. This review article provides an overview of the scientific literature that describes research on Bayesian networks as a tool that can be used to study, develop and implement probabilistic procedures for evaluating the probative value of particular items of scientific evidence in forensic science. Primary attention is drawn here to evaluative issues that pertain to forensic DNA profiling evidence because this is one of the main categories of evidence whose assessment has been studied through Bayesian networks. The scope of topics is large and includes almost any aspect that relates to forensic DNA profiling. Typical examples are inference of source (or, 'criminal identification'), relatedness testing, database searching and special trace evidence evaluation (such as mixed DNA stains or stains with low quantities of DNA). The perspective of the review presented here is not exclusively restricted to DNA evidence, but also includes relevant references and discussion on both, the concept of Bayesian networks as well as its general usage in legal sciences as one among several different graphical approaches to evidence evaluation.

Substantial advantage of a combined Bayesian and genotyping approach in testosterone doping tests.

Testosterone abuse is conventionally assessed by the urinary testosterone/epitestosterone (T/E) ratio, levels above 4.0 being considered suspicious. A deletion polymorphism in the gene coding for UGT2B17 is strongly associated with reduced testosterone glucuronide (TG) levels in urine. Many of the individuals devoid of the gene would not reach a T/E ratio of 4.0 after testosterone intake. Future test programs will most likely shift from population based- to individual-based T/E cut-off ratios using Bayesian inference. A longitudinal analysis is dependent on an individual's true negative baseline T/E ratio. The aim was to investigate whether it is possible to increase the sensitivity and specificity of the T/E test by addition of UGT2B17 genotype information in a Bayesian framework. A single intramuscular dose of 500mg testosterone enanthate was given to 55 healthy male volunteers with either two, one or no allele (ins/ins, ins/del or del/del) of the UGT2B17 gene. Urinary excretion of TG and the T/E ratio was measured during 15 days. The Bayesian analysis was conducted to calculate the individual T/E cut-off ratio. When adding the genotype information, the program returned lower individual cut-off ratios in all del/del subjects increasing the sensitivity of the test considerably. It will be difficult, if not impossible, to discriminate between a true negative baseline T/E value and a false negative one without knowledge of the UGT2B17 genotype. UGT2B17 genotype information is crucial, both to decide which initial cut-off ratio to use for an individual, and for increasing the sensitivity of the Bayesian analysis.

Panel index VAR models: Specification, Estimation, Testing and Leading Indicators

This paper proposes a method to conduct inference in panel VAR models with cross unit interdependencies and time variations in the coefficients. The approach can be used to obtain multi-unit forecasts and leading indicators and to conduct policy analysis in a multiunit setups. The framework of analysis is Bayesian and MCMC methods are used to estimate the posterior distribution of the features of interest. The model is reparametrized to resemble an observable index model and specification searches are discussed. As an example, we construct leading indicators for inflation and GDP growth in the Euro area using G-7 information.

Policy and the Evolution of the US Economy: 1948-2002

This paper investigates the relationship between monetary policy and the changes experienced by the US economy using a small scale New-Keynesian model. The model is estimated with Bayesian techniques and the stability of policy parameter estimates and of the transmission of policy shocks examined. The model fits well the data and produces forecasts comparable or superior to those of alternative specifications. The parameters of the policy rule, the variance and the transmission of policy shocks have been remarkably stable. The parameters of the Phillips curve and of the Euler equations are varying.

Modeling the forensic two-trace problem with Bayesian networks

The forensic two-trace problem is a perplexing inference problem introduced by Evett (J Forensic Sci Soc 27:375-381, 1987). Different possible ways of wording the competing pair of propositions (i.e., one proposition advanced by the prosecution and one proposition advanced by the defence) led to different quantifications of the value of the evidence (Meester and Sjerps in Biometrics 59:727-732, 2003). Here, we re-examine this scenario with the aim of clarifying the interrelationships that exist between the different solutions, and in this way, produce a global vision of the problem. We propose to investigate the different expressions for evaluating the value of the evidence by using a graphical approach, i.e. Bayesian networks, to model the rationale behind each of the proposed solutions and the assumptions made on the unknown parameters in this problem.

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.