Stand dynamics modelling approaches for multicohort management of eastern Canadian boreal forests

Abstract

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

Analysis of sensitivity with respect to a compositional parameter : A comment on 'Local sensitivity analysis for compositional data with application to soil texture in hydrologic modelling' by L. Loosvelt and co-authors

A comment about the article “Local sensitivity analysis for compositional data with application to soil texture in hydrologic modelling” writen by L. Loosvelt and co-authors. The present comment is centered in three specific points. The first one is related to the fact that the authors avoid the use of ilr-coordinates. The second one refers to some generalization of sensitivity analysis when input parameters are compositional. The third tries to show that the role of the Dirichlet distribution in the sensitivity analysis is irrelevant

Bayesian Networks and the Value of the Evidence for the Forensic Two-Trace Transfer Problem

Forensic scientists face increasingly complex inference problems for evaluating likelihood ratios (LRs) for an appropriate pair of propositions. Up to now, scientists and statisticians have derived LR formulae using an algebraic approach. However, this approach reaches its limits when addressing cases with an increasing number of variables and dependence relationships between these variables. In this study, we suggest using a graphical approach, based on the construction of Bayesian networks (BNs). We first construct a BN that captures the problem, and then deduce the expression for calculating the LR from this model to compare it with existing LR formulae. We illustrate this idea by applying it to the evaluation of an activity level LR in the context of the two-trace transfer problem. Our approach allows us to relax assumptions made in previous LR developments, produce a new LR formula for the two-trace transfer problem and generalize this scenario to n traces.

Bayesian genetic parameters for body weight and survival of Nile tilapia farmed in Brazil

The objective of this study was to estimate genetic parameters for survival and weight of Nile tilapia (Oreochromis niloticus), farmed in cages and ponds in Brazil, and to predict genetic gain under different scenarios. Survival was recorded as a binary response (dead or alive), during harvest time in the 2008 grow-out period. Genetic parameters were estimated using a Bayesian mixed linear-threshold animal model via Gibbs sampling. The breeding population consisted of 2,912 individual fish, which were analyzed together with the pedigree of 5,394 fish. The heritabilities estimates, with 95% posterior credible intervals, for tagging weight, harvest weight and survival were 0.17 (0.09-0.27), 0.21 (0.12-0.32) and 0.32 (0.22-0.44), respectively. Credible intervals show a 95% probability that the true genetic correlations were in a favourable direction. The selection for weight has a positive impact on survival. Estimated genetic gain was high when selecting for harvest weight (5.07%), and indirect gain for tagging weight (2.17%) and survival (2.03%) were also considerable.

Modelling variation of needle density of Scots pine at high latitudes

[Abstract]

Bayesian Markov-chain-Monte-Carlo inversion of time-lapse cross hole ground-penetrating radar data to characterize the vadose zone at the Arrenaes field site, Denmark

The ground-penetrating radar (GPR) geophysical method has the potential to provide valuable information on the hydraulic properties of the vadose zone because of its strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR traveltime data can allow for a significant reduction in uncertainty regarding subsurface van Genuchten-Mualem (VGM) parameters. Much of the previous work on the stochastic estimation of VGM parameters from crosshole GPR data has considered the case of steady-state infiltration conditions, which represent only a small fraction of practically relevant scenarios. We explored in detail the dynamic infiltration case, specifically examining to what extent time-lapse crosshole GPR traveltimes, measured during a forced infiltration experiment at the Arreneas field site in Denmark, could help to quantify VGM parameters and their uncertainties in a layered medium, as well as the corresponding soil hydraulic properties. We used a Bayesian Markov-chain-Monte-Carlo inversion approach. We first explored the advantages and limitations of this approach with regard to a realistic synthetic example before applying it to field measurements. In our analysis, we also considered different degrees of prior information. Our findings indicate that the stochastic inversion of the time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions compared with the corresponding priors, which in turn significantly improves knowledge of soil hydraulic properties. Overall, the results obtained clearly demonstrate the value of the information contained in time-lapse GPR data for characterizing vadose zone dynamics.

A Playful Glance at Hierarchical Questions for Two-Way Alternating Automata

Two-way alternating automata were introduced by Vardi in order to study the satisfiability problem for the modal μ-calculus extended with backwards modalities. In this paper, we present a very simple proof by way of Wadge games of the strictness of the hierarchy of Motowski indices of two-way alternating automata over trees.

Monitoring the decreasing trend of testicular cancer mortality in Spain during 2005-2019 through a Bayesian approach

Purpose : To assess time trends of testicular cancer (TC) mortality in Spain for period 1985-2019 for age groups 15-74 years old through a Bayesian age-period-cohort (APC) analysis. Methods: A Bayesian age-drift model has been fitted to describe trends. Projections for 2005-2019 have been calculated by means of an autoregressive APC model. Prior precision for these parameters has been selected through evaluation of an adaptive precision parameter and 95% credible intervals (95% CRI) have been obtained for each model parameter. Results: A decrease of -2.41% (95% CRI: -3.65%; -1.13%) per year has been found for TC mortality rates in age groups 15-74 during 1985-2004, whereas mortality showed a lower annual decrease when data was restricted to age groups 15-54 (-1.18%; 95% CRI: -2.60%; -0.31%). During 2005-2019 is expected a decrease of TC mortality of 2.30% per year for men younger than 35, whereas a leveling off for TC mortality rates is expected for men older than 35. Conclusions: A Bayesian approach should be recommended to describe and project time trends for those diseases with low number of cases. Through this model it has been assessed that management of TC and advances in therapy led to decreasing trend of TC mortality during the period 1985-2004, whereas a leveling off for these trends can be considered during 2005-2019 among men older than 35.

Monitoring the decreasing trend of testicular cancer mortality in Spain during 2005-2019 through a Bayesian approach

Purpose : To assess time trends of testicular cancer (TC) mortality in Spain for period 1985-2019 for age groups 15-74 years old through a Bayesian age-period-cohort (APC) analysis. Methods: A Bayesian age-drift model has been fitted to describe trends. Projections for 2005-2019 have been calculated by means of an autoregressive APC model. Prior precision for these parameters has been selected through evaluation of an adaptive precision parameter and 95% credible intervals (95% CRI) have been obtained for each model parameter. Results: A decrease of -2.41% (95% CRI: -3.65%; -1.13%) per year has been found for TC mortality rates in age groups 15-74 during 1985-2004, whereas mortality showed a lower annual decrease when data was restricted to age groups 15-54 (-1.18%; 95% CRI: -2.60%; -0.31%). During 2005-2019 is expected a decrease of TC mortality of 2.30% per year for men younger than 35, whereas a leveling off for TC mortality rates is expected for men older than 35. Conclusions: A Bayesian approach should be recommended to describe and project time trends for those diseases with low number of cases. Through this model it has been assessed that management of TC and advances in therapy led to decreasing trend of TC mortality during the period 1985-2004, whereas a leveling off for these trends can be considered during 2005-2019 among men older than 35.

Monitoring the decreasing trend of testicular cancer mortality in Spain during 2005-2019 through a Bayesian approach

Purpose : To assess time trends of testicular cancer (TC) mortality in Spain for period 1985-2019 for age groups 15-74 years old through a Bayesian age-period-cohort (APC) analysis. Methods: A Bayesian age-drift model has been fitted to describe trends. Projections for 2005-2019 have been calculated by means of an autoregressive APC model. Prior precision for these parameters has been selected through evaluation of an adaptive precision parameter and 95% credible intervals (95% CRI) have been obtained for each model parameter. Results: A decrease of -2.41% (95% CRI: -3.65%; -1.13%) per year has been found for TC mortality rates in age groups 15-74 during 1985-2004, whereas mortality showed a lower annual decrease when data was restricted to age groups 15-54 (-1.18%; 95% CRI: -2.60%; -0.31%). During 2005-2019 is expected a decrease of TC mortality of 2.30% per year for men younger than 35, whereas a leveling off for TC mortality rates is expected for men older than 35. Conclusions: A Bayesian approach should be recommended to describe and project time trends for those diseases with low number of cases. Through this model it has been assessed that management of TC and advances in therapy led to decreasing trend of TC mortality during the period 1985-2004, whereas a leveling off for these trends can be considered during 2005-2019 among men older than 35.

Monitoring the decreasing trend of testicular cancer mortality in Spain during 2005-2019 through a Bayesian approach

Purpose : To assess time trends of testicular cancer (TC) mortality in Spain for period 1985-2019 for age groups 15-74 years old through a Bayesian age-period-cohort (APC) analysis. Methods: A Bayesian age-drift model has been fitted to describe trends. Projections for 2005-2019 have been calculated by means of an autoregressive APC model. Prior precision for these parameters has been selected through evaluation of an adaptive precision parameter and 95% credible intervals (95% CRI) have been obtained for each model parameter. Results: A decrease of -2.41% (95% CRI: -3.65%; -1.13%) per year has been found for TC mortality rates in age groups 15-74 during 1985-2004, whereas mortality showed a lower annual decrease when data was restricted to age groups 15-54 (-1.18%; 95% CRI: -2.60%; -0.31%). During 2005-2019 is expected a decrease of TC mortality of 2.30% per year for men younger than 35, whereas a leveling off for TC mortality rates is expected for men older than 35. Conclusions: A Bayesian approach should be recommended to describe and project time trends for those diseases with low number of cases. Through this model it has been assessed that management of TC and advances in therapy led to decreasing trend of TC mortality during the period 1985-2004, whereas a leveling off for these trends can be considered during 2005-2019 among men older than 35.