Bayes linear spaces

Linear spaces consisting of σ-finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative. Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. For example, exponential families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in particular some well-known properties of conjugated priors and likelihood functions, are revisited and slightly extended

Linear Bayes policy for learning in contextual-bandits

Machine and Statistical Learning techniques are used in almost all online advertisement systems. The problem of discovering which content is more demanded (e.g. receive more clicks) can be modeled as a multi-armed bandit problem. Contextual bandits (i.e., bandits with covariates, side information or associative reinforcement learning) associate, to each specific content, several features that define the “context” in which it appears (e.g. user, web page, time, region). This problem can be studied in the stochastic/statistical setting by means of the conditional probability paradigm using the Bayes’ theorem. However, for very large contextual information and/or real-time constraints, the exact calculation of the Bayes’ rule is computationally infeasible. In this article, we present a method that is able to handle large contextual information for learning in contextual-bandits problems. This method was tested in the Challenge on Yahoo! dataset at ICML2012’s Workshop “new Challenges for Exploration & Exploitation 3”, obtaining the second place. Its basic exploration policy is deterministic in the sense that for the same input data (as a time-series) the same results are obtained. We address the deterministic exploration vs. exploitation issue, explaining the way in which the proposed method deterministically finds an effective dynamic trade-off based solely in the input-data, in contrast to other methods that use a random number generator.

Phylogenetics, Ancestral State Reconstruction, And A New Infrafamilial Classification Of The Pantropical Ochnaceae (medusagynaceae, Ochnaceae S.str., Quiinaceae) Based On Five Dna Regions.

Ochnaceae s.str. (Malpighiales) are a pantropical family of about 500 species and 27 genera of almost exclusively woody plants. Infrafamilial classification and relationships have been controversial partially due to the lack of a robust phylogenetic framework. Including all genera except Indosinia and Perissocarpa and DNA sequence data for five DNA regions (ITS, matK, ndhF, rbcL, trnL-F), we provide for the first time a nearly complete molecular phylogenetic analysis of Ochnaceae s.l. resolving most of the phylogenetic backbone of the family. Based on this, we present a new classification of Ochnaceae s.l., with Medusagynoideae and Quiinoideae included as subfamilies and the former subfamilies Ochnoideae and Sauvagesioideae recognized at the rank of tribe. Our data support a monophyletic Ochneae, but Sauvagesieae in the traditional circumscription is paraphyletic because Testulea emerges as sister to the rest of Ochnoideae, and the next clade shows Luxemburgia+Philacra as sister group to the remaining Ochnoideae. To avoid paraphyly, we classify Luxemburgieae and Testuleeae as new tribes. The African genus Lophira, which has switched between subfamilies (here tribes) in past classifications, emerges as sister to all other Ochneae. Thus, endosperm-free seeds and ovules with partly to completely united integuments (resulting in an apparently single integument) are characters that unite all members of that tribe. The relationships within its largest clade, Ochnineae (former Ochneae), are poorly resolved, but former Ochninae (Brackenridgea, Ochna) are polyphyletic. Within Sauvagesieae, the genus Sauvagesia in its broad circumscription is polyphyletic as Sauvagesia serrata is sister to a clade of Adenarake, Sauvagesia spp., and three other genera. Within Quiinoideae, in contrast to former phylogenetic hypotheses, Lacunaria and Touroulia form a clade that is sister to Quiina. Bayesian ancestral state reconstructions showed that zygomorphic flowers with adaptations to buzz-pollination (poricidal anthers), a syncarpous gynoecium (a near-apocarpous gynoecium evolved independently in Quiinoideae and Ochninae), numerous ovules, septicidal capsules, and winged seeds with endosperm are the ancestral condition in Ochnoideae. Although in some lineages poricidal anthers were lost secondarily, the evolution of poricidal superstructures secured the maintenance of buzz-pollination in some of these genera, indicating a strong selective pressure on keeping that specialized pollination system.

Oligocene CO2 decline promoted C4 photosynthesis in grasses.

C4 photosynthesis is an adaptation derived from the more common C3 photosynthetic pathway that confers a higher productivity under warm temperature and low atmospheric CO2 concentration [1, 2]. C4 evolution has been seen as a consequence of past atmospheric CO2 decline, such as the abrupt CO2 fall 32-25 million years ago (Mya) [3-6]. This relationship has never been tested rigorously, mainly because of a lack of accurate estimates of divergence times for the different C4 lineages [3]. In this study, we inferred a large phylogenetic tree for the grass family and estimated, through Bayesian molecular dating, the ages of the 17 to 18 independent grass C4 lineages. The first transition from C3 to C4 photosynthesis occurred in the Chloridoideae subfamily, 32.0-25.0 Mya. The link between CO2 decrease and transition to C4 photosynthesis was tested by a novel maximum likelihood approach. We showed that the model incorporating the atmospheric CO2 levels was significantly better than the null model, supporting the importance of CO2 decline on C4 photosynthesis evolvability. This finding is relevant for understanding the origin of C4 photosynthesis in grasses, which is one of the most successful ecological and evolutionary innovations in plant history.

New perspectives in the use of ink evidence in forensic science: Part I. Development of a quality assurance process for forensic ink analysis by HPTLC

The level of information provided by ink evidence to the criminal and civil justice system is limited. The limitations arise from the weakness of the interpretative framework currently used, as proposed in the ASTM 1422-05 and 1789-04 on ink analysis. It is proposed to use the likelihood ratio from the Bayes theorem to interpret ink evidence. Unfortunately, when considering the analytical practices, as defined in the ASTM standards on ink analysis, it appears that current ink analytical practices do not allow for the level of reproducibility and accuracy required by a probabilistic framework. Such framework relies on the evaluation of the statistics of the ink characteristics using an ink reference database and the objective measurement of similarities between ink samples. A complete research programme was designed to (a) develop a standard methodology for analysing ink samples in a more reproducible way, (b) comparing automatically and objectively ink samples and (c) evaluate the proposed methodology in a forensic context. This report focuses on the first of the three stages. A calibration process, based on a standard dye ladder, is proposed to improve the reproducibility of ink analysis by HPTLC, when these inks are analysed at different times and/or by different examiners. The impact of this process on the variability between the repetitive analyses of ink samples in various conditions is studied. The results show significant improvements in the reproducibility of ink analysis compared to traditional calibration methods.

Is there a common factor for vision?

In cognition, common factors play a crucial role. For example, different types of intelligence are highly correlated, pointing to a common factor, which is often called g. One might expect that a similar common factor would also exist for vision. Surprisingly, no one in the field has addressed this issue. Here, we provide the first evidence that there is no common factor for vision. We tested 40 healthy students' performance in six basic visual paradigms: visual acuity, vernier discrimination, two visual backward masking paradigms, Gabor detection, and bisection discrimination. One might expect that performance levels on these tasks would be highly correlated because some individuals generally have better vision than others due to superior optics, better retinal or cortical processing, or enriched visual experience. However, only four out of 15 correlations were significant, two of which were nontrivial. These results cannot be explained by high intraobserver variability or ceiling effects because test-retest reliability was high and the variance in our student population is commensurate with that from other studies with well-sighted populations. Using a variety of tests (e.g., principal components analysis, Bayes theorem, test-retest reliability), we show the robustness of our null results. We suggest that neuroplasticity operates during everyday experience to generate marked individual differences. Our results apply only to the normally sighted population (i.e., restricted range sampling). For the entire population, including those with degenerate vision, we expect different results.

Endogenous steroid profiling in the athlete biological passport.

The Athlete Biological Passport (ABP) is an individual electronic document that collects data regarding a specific athlete that is useful in differentiating between natural physiologic variations of selected biomarkers and deviations caused by artificial manipulations. A subsidiary of the endocrine module of the ABP, that which here is called Athlete Steroidal Passport (ASP), collects data on markers of an altered metabolism of endogenous steroidal hormones measured in urine samples. The ASP aims to identify not only doping with anabolic-androgenic steroids, but also most indirect steroid doping strategies such as doping with estrogen receptor antagonists and aromatase inhibitors. Development of specific markers of steroid doping, use of the athlete's previous measurements to define individual limits, with the athlete becoming his or her own reference, the inclusion of heterogeneous factors such as the UDPglucuronosyltransferase B17 genotype of the athlete, the knowledge of potentially confounding effects such as heavy alcohol consumption, the development of an external quality control system to control analytical uncertainty, and finally the use of Bayesian inferential methods to evaluate the value of indirect evidence have made the ASP a valuable alternative to deter steroid doping in elite sports. The ASP can be used to target athletes for gas chromatography/combustion/ isotope ratio mass spectrometry (GC/C/IRMS) testing, to withdraw temporarily the athlete from competing when an abnormality has been detected, and ultimately to lead to an antidoping infraction if that abnormality cannot be explained by a medical condition. Although the ASP has been developed primarily to ensure fairness in elite sports, its application in endocrinology for clinical purposes is straightforward in an evidence-based medicine paradigm.

DNA evidence, probabilistic evaluation and collaborative tests.

Forensic scientists working in 12 state or private laboratories participated in collaborative tests to improve the reliability of the presentation of DNA data at trial. These tests were motivated in response to the growing criticism of the power of DNA evidence. The experts' conclusions in the tests are presented and discussed in the context of the Bayesian approach to interpretation. The use of a Bayesian approach and subjective probabilities in trace evaluation permits, in an easy and intuitive manner, the integration into the decision procedure of any revision of the measure of uncertainty in the light of new information. Such an integration is especially useful with forensic evidence. Furthermore, we believe that this probabilistic model is a useful tool (a) to assist scientists in the assessment of the value of scientific evidence, (b) to help jurists in the interpretation of judicial facts and (c) to clarify the respective roles of scientists and of members of the court. Respondents to the survey were reluctant to apply this methodology in the assessment of DNA evidence.

Large multi-gene phylogenetic trees of the grasses (Poaceae): progress towards complete tribal and generic level sampling.

In this paper we included a very broad representation of grass family diversity (84% of tribes and 42% of genera). Phylogenetic inference was based on three plastid DNA regions rbcL, matK and trnL-F, using maximum parsimony and Bayesian methods. Our results resolved most of the subfamily relationships within the major clades (BEP and PACCMAD), which had previously been unclear, such as, among others the: (i) BEP and PACCMAD sister relationship, (ii) composition of clades and the sister-relationship of Ehrhartoideae and Bambusoideae + Pooideae, (iii) paraphyly of tribe Bambuseae, (iv) position of Gynerium as sister to Panicoideae, (v) phylogenetic position of Micrairoideae. With the presence of a relatively large amount of missing data, we were able to increase taxon sampling substantially in our analyses from 107 to 295 taxa. However, bootstrap support and to a lesser extent Bayesian inference posterior probabilities were generally lower in analyses involving missing data than those not including them. We produced a fully resolved phylogenetic summary tree for the grass family at subfamily level and indicated the most likely relationships of all included tribes in our analysis.

Detection of nandrolone metabolites in urine after a football game in professional and amateur players: a Bayesian comparison.

Nandrolone (19-nortestosterone) is a widely used anabolic steroid in sports where strength plays an essential role. Once nandrolone has been metabolised, two major metabolites are excreted in urine, 19-norandrosterone (NA) and 19-noretiocholanolone (NE). In 1997, in France, quite a few sportsmen had concentrations of 19-norandrosterone very close to the IOC cut off limit (2ng/ml). At that time, a debate took place about the capability of the human male body to produce by itself these metabolites without any intake of nandrolone or related compounds. The International Football Federation (FIFA) was very concerned with this problematic, especially because the World Cup was about to start in France. In this respect, a statistical study was held with all football players from the first and second divisions of the Swiss Football National League. All players gave a urine sample after effort and around 6% of them showed traces of 19-norandrosterone. These results were compared with amateur football players (control group) and around 6% of them had very small amounts of 19-norandrosterone and/or 19-noretiocholanolone in urine after effort, whereas none of them had detectable traces of one or the other metabolite before effort. The origin of these compounds in urine after a strenuous physical activity is still unknown, but three hypotheses can be put forward. First, an endogenous production of nandrolone metabolites takes place. Second, nandrolone metabolites are released from the fatty tissues after an intake of nandrolone, some related compounds or some contaminated nutritive supplements. Finally, the sportsmen may have taken something during or just before the football game.

The complex history of the olive tree: from Late Quaternary diversification of Mediterranean lineages to primary domestication in the northern Levant.

The location and timing of domestication of the olive tree, a key crop in Early Mediterranean societies, remain hotly debated. Here, we unravel the history of wild olives (oleasters), and then infer the primary origins of the domesticated olive. Phylogeography and Bayesian molecular dating analyses based on plastid genome profiling of 1263 oleasters and 534 cultivated genotypes reveal three main lineages of pre-Quaternary origin. Regional hotspots of plastid diversity, species distribution modelling and macrofossils support the existence of three long-term refugia; namely the Near East (including Cyprus), the Aegean area and the Strait of Gibraltar. These ancestral wild gene pools have provided the essential foundations for cultivated olive breeding. Comparison of the geographical pattern of plastid diversity between wild and cultivated olives indicates the cradle of first domestication in the northern Levant followed by dispersals across the Mediterranean basin in parallel with the expansion of civilizations and human exchanges in this part of the world.

The likelihood approach to compare populations : a study on DNA evidence and pitfalls of intuitions

The paper follows on from earlier work [Taroni F and Aitken CGG. Probabilistic reasoning in the law, Part 1: assessment of probabilities and explanation of the value of DNA evidence. Science & Justice 1998; 38: 165-177]. Different explanations of the value of DNA evidence were presented to students from two schools of forensic science and to members of fifteen laboratories all around the world. The responses were divided into two groups; those which came from a school or laboratory identified as Bayesian and those which came from a school or laboratory identified as non-Bayesian. The paper analyses these responses using a likelihood approach. This approach is more consistent with a Bayesian analysis than one based on a frequentist approach, as was reported by Taroni F and Aitken CGG. [Probabilistic reasoning in the law, Part 1: assessment of probabilities and explanation of the value of DNA evidence] in Science & Justice 1998.

Detecting the number of clusters of individuals using the software STRUCTURE: a simulation study.

The identification of genetically homogeneous groups of individuals is a long standing issue in population genetics. A recent Bayesian algorithm implemented in the software STRUCTURE allows the identification of such groups. However, the ability of this algorithm to detect the true number of clusters (K) in a sample of individuals when patterns of dispersal among populations are not homogeneous has not been tested. The goal of this study is to carry out such tests, using various dispersal scenarios from data generated with an individual-based model. We found that in most cases the estimated 'log probability of data' does not provide a correct estimation of the number of clusters, K. However, using an ad hoc statistic DeltaK based on the rate of change in the log probability of data between successive K values, we found that STRUCTURE accurately detects the uppermost hierarchical level of structure for the scenarios we tested. As might be expected, the results are sensitive to the type of genetic marker used (AFLP vs. microsatellite), the number of loci scored, the number of populations sampled, and the number of individuals typed in each sample.

An empirical hierarchical Bayesian unification of occupational exposure assessment methods.

In occupational exposure assessment of airborne contaminants, exposure levels can either be estimated through repeated measurements of the pollutant concentration in air, expert judgment or through exposure models that use information on the conditions of exposure as input. In this report, we propose an empirical hierarchical Bayesian model to unify these approaches. Prior to any measurement, the hygienist conducts an assessment to generate prior distributions of exposure determinants. Monte-Carlo samples from these distributions feed two level-2 models: a physical, two-compartment model, and a non-parametric, neural network model trained with existing exposure data. The outputs of these two models are weighted according to the expert's assessment of their relevance to yield predictive distributions of the long-term geometric mean and geometric standard deviation of the worker's exposure profile (level-1 model). Bayesian inferences are then drawn iteratively from subsequent measurements of worker exposure. Any traditional decision strategy based on a comparison with occupational exposure limits (e.g. mean exposure, exceedance strategies) can then be applied. Data on 82 workers exposed to 18 contaminants in 14 companies were used to validate the model with cross-validation techniques. A user-friendly program running the model is available upon request.