Bayesian image reconstruction with space-variant noise suppression

In this paper we present a Bayesian image reconstruction algorithm with entropy prior (FMAPE) that uses a space-variant hyperparameter. The spatial variation of the hyperparameter allows different degrees of resolution in areas of different statistical characteristics, thus avoiding the large residuals resulting from algorithms that use a constant hyperparameter. In the first implementation of the algorithm, we begin by segmenting a Maximum Likelihood Estimator (MLE) reconstruction. The segmentation method is based on using a wavelet decomposition and a self-organizing neural network. The result is a predetermined number of extended regions plus a small region for each star or bright object. To assign a different value of the hyperparameter to each extended region and star, we use either feasibility tests or cross-validation methods. Once the set of hyperparameters is obtained, we carried out the final Bayesian reconstruction, leading to a reconstruction with decreased bias and excellent visual characteristics. The method has been applied to data from the non-refurbished Hubble Space Telescope. The method can be also applied to ground-based images.

Analysis, modelling and classification of geospatial data using machine learning

The research considers the problem of spatial data classification using machine learning algorithms: probabilistic neural networks (PNN) and support vector machines (SVM). As a benchmark model simple k-nearest neighbor algorithm is considered. PNN is a neural network reformulation of well known nonparametric principles of probability density modeling using kernel density estimator and Bayesian optimal or maximum a posteriori decision rules. PNN is well suited to problems where not only predictions but also quantification of accuracy and integration of prior information are necessary. An important property of PNN is that they can be easily used in decision support systems dealing with problems of automatic classification. Support vector machine is an implementation of the principles of statistical learning theory for the classification tasks. Recently they were successfully applied for different environmental topics: classification of soil types and hydro-geological units, optimization of monitoring networks, susceptibility mapping of natural hazards. In the present paper both simulated and real data case studies (low and high dimensional) are considered. The main attention is paid to the detection and learning of spatial patterns by the algorithms applied.

The database search problem: a question of rational decision making

This paper applies probability and decision theory in the graphical interface of an influence diagram to study the formal requirements of rationality which justify the individualization of a person found through a database search. The decision-theoretic part of the analysis studies the parameters that a rational decision maker would use to individualize the selected person. The modeling part (in the form of an influence diagram) clarifies the relationships between this decision and the ingredients that make up the database search problem, i.e., the results of the database search and the different pairs of propositions describing whether an individual is at the source of the crime stain. These analyses evaluate the desirability associated with the decision of 'individualizing' (and 'not individualizing'). They point out that this decision is a function of (i) the probability that the individual in question is, in fact, at the source of the crime stain (i.e., the state of nature), and (ii) the decision maker's preferences among the possible consequences of the decision (i.e., the decision maker's loss function). We discuss the relevance and argumentative implications of these insights with respect to recent comments in specialized literature, which suggest points of view that are opposed to the results of our study.

The statistical accuracy of surveys on business and economic perspectives: a case study

In this paper, we develop a new decision making model and apply it in political Surveys of economic climate collect opinions of managers about the short-term future evolution of their business. Interviews are carried out on a regular basis and responses measure optimistic, neutral or pessimistic views about the economic perspectives. We propose a method to evaluate the sampling error of the average opinion derived from a particular type of survey data. Our variance estimate is useful to interpret historical trends and to decide whether changes in the index from one period to another are due to a structural change or whether ups and downs can be attributed to sampling randomness. An illustration using real data from a survey of business managers opinions is discussed.

Dosage optimization of treatments using population pharmacokinetic modeling and simulation.

Pharmacokinetic variability in drug levels represent for some drugs a major determinant of treatment success, since sub-therapeutic concentrations might lead to toxic reactions, treatment discontinuation or inefficacy. This is true for most antiretroviral drugs, which exhibit high inter-patient variability in their pharmacokinetics that has been partially explained by some genetic and non-genetic factors. The population pharmacokinetic approach represents a very useful tool for the description of the dose-concentration relationship, the quantification of variability in the target population of patients and the identification of influencing factors. It can thus be used to make predictions and dosage adjustment optimization based on Bayesian therapeutic drug monitoring (TDM). This approach has been used to characterize the pharmacokinetics of nevirapine (NVP) in 137 HIV-positive patients followed within the frame of a TDM program. Among tested covariates, body weight, co-administration of a cytochrome (CYP) 3A4 inducer or boosted atazanavir as well as elevated aspartate transaminases showed an effect on NVP elimination. In addition, genetic polymorphism in the CYP2B6 was associated with reduced NVP clearance. Altogether, these factors could explain 26% in NVP variability. Model-based simulations were used to compare the adequacy of different dosage regimens in relation to the therapeutic target associated with treatment efficacy. In conclusion, the population approach is very useful to characterize the pharmacokinetic profile of drugs in a population of interest. The quantification and the identification of the sources of variability is a rational approach to making optimal dosage decision for certain drugs administered chronically.

Decision-theoretic reflections on processing a fingermark

A recent publication in this journal [Neumann et al., Forensic Sci. Int. 212 (2011) 32-46] presented the results of a field study that revealed the data provided by the fingermarks not processed in a forensic science laboratory. In their study, the authors were interested in the usefulness of this additional data in order to determine whether such fingermarks would have been worth submitting to the fingermark processing workflow. Taking these ideas as a starting point, this communication here places the fingermark in its context of a case brought before a court, and examines the question of processing or not processing a fingermark from a decision-theoretic point of view. The decision-theoretic framework presented provides an answer to this question in the form of a quantified expression of the expected value of information (EVOI) associated with the processed fingermark, which can then be compared with the cost of processing the mark.

Bayesian classification of forest ecological type from satellite data

The main objective of this study was todo a statistical analysis of ecological type from optical satellite data, using Tipping's sparse Bayesian algorithm. This thesis uses "the Relevence Vector Machine" algorithm in ecological classification betweenforestland and wetland. Further this bi-classification technique was used to do classification of many other different species of trees and produces hierarchical classification of entire subclasses given as a target class. Also, we carried out an attempt to use airborne image of same forest area. Combining it with image analysis, using different image processing operation, we tried to extract good features and later used them to perform classification of forestland and wetland.

L'exploitation des peintures en spray en criminalistique: mise en place d'une procédure de gestion et de comparaison des spectres infrarouges à l'aide des statistiques multivariées

La spectroscopie infrarouge (FTIR) est une technique de choix dans l'analyse des peintures en spray (traces ou bonbonnes de référence), grâce à son fort pouvoir discriminant, sa sensibilité, et ses nombreuses possibilités d'échantillonnage. La comparaison des spectres obtenus est aujourd'hui principalement faite visuellement, mais cette procédure présente des limitations telles que la subjectivité de la prise de décision car celle-ci dépend de l'expérience et de la formation suivie par l'expert. De ce fait, de faibles différences d'intensités relatives entre deux pics peuvent être perçues différemment par des experts, même au sein d'un même laboratoire. Lorsqu'il s'agit de justifier ces différences, certains les expliqueront par la méthode analytique utilisée, alors que d'autres estimeront plutôt qu'il s'agit d'une variabilité intrinsèque à la peinture et/ou à son vécu (par exemple homogénéité, sprayage, ou dégradation). Ce travail propose d'étudier statistiquement les différentes sources de variabilité observables dans les spectres infrarouges, de les identifier, de les comprendre et tenter de les minimiser. Le deuxième objectif principal est de proposer une procédure de comparaison des spectres qui soit davantage transparente et permette d'obtenir des réponses reproductibles indépendamment des experts interrogés. La première partie du travail traite de l'optimisation de la mesure infrarouge et des principaux paramètres analytiques. Les conditions nécessaires afin d'obtenir des spectres reproductibles et minimisant la variation au sein d'un même échantillon (intra-variabilité) sont présentées. Par la suite une procédure de correction des spectres est proposée au moyen de prétraitements et de sélections de variables, afin de minimiser les erreurs systématiques et aléatoires restantes, et de maximiser l'information chimique pertinente. La seconde partie présente une étude de marché effectuée sur 74 bonbonnes de peintures en spray représentatives du marché suisse. Les capacités de discrimination de la méthode FTIR au niveau de la marque et du modèle sont évaluées au moyen d'une procédure visuelle, et comparées à diverses procédures statistiques. Les limites inférieures de discrimination sont testées sur des peintures de marques et modèles identiques mais provenant de différents lots de production. Les résultats ont montré que la composition en pigments était particulièrement discriminante, à cause des étapes de corrections et d'ajustement de la couleur subies lors de la production. Les particularités associées aux peintures en spray présentes sous forme de traces (graffitis, gouttelettes) ont également été testées. Trois éléments sont mis en évidence et leur influence sur le spectre infrarouge résultant testée : 1) le temps minimum de secouage nécessaire afin d'obtenir une homogénéité suffisante de la peinture et, en conséquence, de la surface peinte, 2) la dégradation initiée par le rayonnement ultra- violet en extérieur, et 3) la contamination provenant du support lors du prélèvement. Finalement une étude de population a été réalisée sur 35 graffitis de la région lausannoise et les résultats comparés à l'étude de marché des bonbonnes en spray. La dernière partie de ce travail s'est concentrée sur l'étape de prise de décision lors de la comparaison de spectres deux-à-deux, en essayant premièrement de comprendre la pratique actuelle au sein des laboratoires au moyen d'un questionnaire, puis de proposer une méthode statistique de comparaison permettant d'améliorer l'objectivité et la transparence lors de la prise de décision. Une méthode de comparaison basée sur la corrélation entre les spectres est proposée, et ensuite combinée à une évaluation Bayesienne de l'élément de preuve au niveau de la source et au niveau de l'activité. Finalement des exemples pratiques sont présentés et la méthodologie est discutée afin de définir le rôle précis de l'expert et des statistiques dans la procédure globale d'analyse des peintures. -- Infrared spectroscopy (FTIR) is a technique of choice for analyzing spray paint speciments (i.e. traces) and reference samples (i.e. cans seized from suspects) due to its high discriminating power, sensitivity and sampling possibilities. The comparison of the spectra is currently carried out visually, but this procedure has limitations such as the subjectivity in the decision due to its dependency on the experience and training of the expert. This implies that small differences in the relative intensity of two peaks can be perceived differently by experts, even between analysts working in the same laboratory. When it comes to justifying these differences, some will explain them by the analytical technique, while others will estimate that the observed differences are mostly due to an intrinsic variability from the paint sample and/or its acquired characteristics (for example homogeneity, spraying, or degradation). This work proposes to statistically study the different sources of variability observed in infrared spectra, to identify them, understand them and try to minimize them. The second goal is to propose a procedure for spectra comparison that is more transparent, and allows obtaining reproducible answers being independent from the expert. The first part of the manuscript focuses on the optimization of infrared measurement and on the main analytical parameters. The necessary conditions to obtain reproducible spectra with a minimized variation within a sample (intra-variability) are presented. Following that a procedure of spectral correction is then proposed using pretreatments and variable selection methods, in order to minimize systematic and random errors, and increase simultaneously relevant chemical information. The second part presents a market study of 74 spray paints representative of the Swiss market. The discrimination capabilities of FTIR at the brand and model level are evaluated by means of visual and statistical procedures. The inferior limits of discrimination are tested on paints coming from the same brand and model, but from different production batches. The results showed that the pigment composition was particularly discriminatory, because of the corrections and adjustments made to the paint color during its manufacturing process. The features associated with spray paint traces (graffitis, droplets) were also tested. Three elements were identified and their influence on the resulting infrared spectra were tested: 1) the minimum shaking time necessary to obtain a sufficient homogeneity of the paint and subsequently of the painted surface, 2) the degradation initiated by ultraviolet radiation in an exterior environment, and 3) the contamination from the support when paint is recovered. Finally a population study was performed on 35 graffitis coming from the city of Lausanne and surroundings areas, and the results were compared to the previous market study of spray cans. The last part concentrated on the decision process during the pairwise comparison of spectra. First, an understanding of the actual practice among laboratories was initiated by submitting a questionnaire. Then, a proposition for a statistical method of comparison was advanced to improve the objectivity and transparency during the decision process. A method of comparison based on the correlation between spectra is proposed, followed by the integration into a Bayesian framework at both source and activity levels. Finally, some case examples are presented and the recommended methodology is discussed in order to define the role of the expert as well as the contribution of the tested statistical approach within a global analytical sequence for paint examinations.

The development of decision limits for the GH-2000 detection methodology using additional insulin-like growth factor-I and amino-terminal pro-peptide of type III collagen assays.

The GH-2000 and GH-2004 projects have developed a method for detecting GH misuse based on measuring insulin-like growth factor-I (IGF-I) and the amino-terminal pro-peptide of type III collagen (P-III-NP). The objectives were to analyze more samples from elite athletes to improve the reliability of the decision limit estimates, to evaluate whether the existing decision limits needed revision, and to validate further non-radioisotopic assays for these markers. The study included 998 male and 931 female elite athletes. Blood samples were collected according to World Anti-Doping Agency (WADA) guidelines at various sporting events including the 2011 International Association of Athletics Federations (IAAF) World Athletics Championships in Daegu, South Korea. IGF-I was measured by the Immunotech A15729 IGF-I IRMA, the Immunodiagnostic Systems iSYS IGF-I assay and a recently developed mass spectrometry (LC-MS/MS) method. P-III-NP was measured by the Cisbio RIA-gnost P-III-P, Orion UniQ? PIIINP RIA and Siemens ADVIA Centaur P-III-NP assays. The GH-2000 score decision limits were developed using existing statistical techniques. Decision limits were determined using a specificity of 99.99% and an allowance for uncertainty because of the finite sample size. The revised Immunotech IGF-I - Orion P-III-NP assay combination decision limit did not change significantly following the addition of the new samples. The new decision limits are applied to currently available non-radioisotopic assays to measure IGF-I and P-III-NP in elite athletes, which should allow wider flexibility to implement the GH-2000 marker test for GH misuse while providing some resilience against manufacturer withdrawal or change of assays. Copyright © 2015 John Wiley & Sons, Ltd.

Bayesian Networks for the Age Classification of Living Individuals: a Study on Transition Analysis

Over the past few decades, age estimation of living persons has represented a challenging task for many forensic services worldwide. In general, the process for age estimation includes the observation of the degree of maturity reached by some physical attributes, such as dentition or several ossification centers. The estimated chronological age or the probability that an individual belongs to a meaningful class of ages is then obtained from the observed degree of maturity by means of various statistical methods. Among these methods, those developed in a Bayesian framework offer to users the possibility of coherently dealing with the uncertainty associated with age estimation and of assessing in a transparent and logical way the probability that an examined individual is younger or older than a given age threshold. Recently, a Bayesian network for age estimation has been presented in scientific literature; this kind of probabilistic graphical tool may facilitate the use of the probabilistic approach. Probabilities of interest in the network are assigned by means of transition analysis, a statistical parametric model, which links the chronological age and the degree of maturity by means of specific regression models, such as logit or probit models. Since different regression models can be employed in transition analysis, the aim of this paper is to study the influence of the model in the classification of individuals. The analysis was performed using a dataset related to the ossifications status of the medial clavicular epiphysis and results support that the classification of individuals is not dependent on the choice of the regression model.

Probabilistic age classification with Bayesian networks: a study on the ossification status of the medial clavicular epiphysis

In the past few decades, the rise of criminal, civil and asylum cases involving young people lacking valid identification documents has generated an increase in the demand of age estimation. The chronological age or the probability that an individual is older or younger than a given age threshold are generally estimated by means of some statistical methods based on observations performed on specific physical attributes. Among these statistical methods, those developed in the Bayesian framework allow users to provide coherent and transparent assignments which fulfill forensic and medico-legal purposes. The application of the Bayesian approach is facilitated by using probabilistic graphical tools, such as Bayesian networks. The aim of this work is to test the performances of the Bayesian network for age estimation recently presented in scientific literature in classifying individuals as older or younger than 18 years of age. For these exploratory analyses, a sample related to the ossification status of the medial clavicular epiphysis available in scientific literature was used. Results obtained in the classification are promising: in the criminal context, the Bayesian network achieved, on the average, a rate of correct classifications of approximatively 97%, whilst in the civil context, the rate is, on the average, close to the 88%. These results encourage the continuation of the development and the testing of the method in order to support its practical application in casework.

Statistical Analysis of an SEIR Epidemic Model

This thesis was focussed on statistical analysis methods and proposes the use of Bayesian inference to extract information contained in experimental data by estimating Ebola model parameters. The model is a system of differential equations expressing the behavior and dynamics of Ebola. Two sets of data (onset and death data) were both used to estimate parameters, which has not been done by previous researchers in (Chowell, 2004). To be able to use both data, a new version of the model has been built. Model parameters have been estimated and then used to calculate the basic reproduction number and to study the disease-free equilibrium. Estimates of the parameters were useful to determine how well the model fits the data and how good estimates were, in terms of the information they provided about the possible relationship between variables. The solution showed that Ebola model fits the observed onset data at 98.95% and the observed death data at 93.6%. Since Bayesian inference can not be performed analytically, the Markov chain Monte Carlo approach has been used to generate samples from the posterior distribution over parameters. Samples have been used to check the accuracy of the model and other characteristics of the target posteriors.

Expertise and decision making among clinicians in investigations of alleged child sexual abuse

The purpose of the present thesis was to explore different aspects of decision making and expertise in investigations of child sexual abuse (CSA) and subsequently shed some light on the reasons for shortcomings in the investigation processes. Clinicians’ subjective attitudes as well as scientifically based knowledge concerning CSA, CSA investigation and interviewing were explored. Furthermore the clinicians’ own view on their expertise and what enhances this expertise was investigated. Also, the effects of scientific knowledge, experience and attitudes on the decision making in a case of CSA were explored. Finally, the effects of different kinds of feedback as well as experience on the ability to evaluate CSA in the light of children’s behavior and base rates were investigated. Both explorative and experimental methods were used. The purpose of Study I was to investigate whether clinicians investigating child sexual abuse (CSA) rely more on scientific knowledge or on clinical experience when evaluating their own expertise. Another goal was to check what kind of beliefs the clinicians held. The connections between these different factors were investigated. A questionnaire covering items concerning demographic data, experience, knowledge about CSA, selfevaluated expertise and beliefs about CSA was given to social workers, child psychiatrists and psychologists working with children. The results showed that the clinicians relied more on their clinical experience than on scientific knowledge when evaluating their expertise as investigators of CSA. Furthermore, social workers possessed stronger attitudes in favor of children than the other groups, while child psychiatrists had more negative attitudes towards the criminal justice system. Male participants held less strong beliefs than female participants. The findings indicate that the education of CSA investigators should focus more on theoretical knowledge and decision making processes as well as the role of beliefs In Study II school and family counseling psychologists completed a Child Sexual Abuse Attitude and Belief Scale. Four CSA related attitude and belief subscales were identified: 1. The Disclosure subscale reflecting favoring a disclosure at any cost, 2. The Pro-Child subscale reflecting unconditional belief in children's reports, 3. The Intuition subscale reflecting favoring an intuitive approach to CSA investigations, and 4. The Anti Criminal Justice System subscale reflecting negative attitudes towards the legal system. Beliefs that were erroneous according to empirical research were analyzed separately. The results suggest that some psychologists hold extreme attitudes and many erroneous beliefs related to CSA. Some misconceptions are common. Female participants tended to hold stronger attitudes than male participants. The more training in interviewing children the participants have, the more erroneous beliefs and stronger attitudes they hold. Experience did not affect attitudes and beliefs. In Study III mental health professionals’ sensitivity to suggestive interviewing in CSA cases was explored. Furthermore, the effects of attitudes and beliefs related to CSA and experience with CSA investigations on the sensitivity to suggestive influences in the interview were investigated. Also, the effect of base rate estimates of CSA on decisions was examined. A questionnaire covering items concerning demographic data, different aspects of clinical experience, self-evaluated expertise, beliefs and knowledge about CSA and a set of ambiguous material based on real trial documents concerning an alleged CSA case was given to child mental health professionals. The experiment was based on a 2 x 2 x 2 x 2 (leading questions: yes vs no) x (stereotype induction: yes vs no) x (emotional tone: pressure to respond vs no pressure to respond) x (threats and rewards: yes vs no) between-subjects factorial design, in which the suggestiveness of the methods with which the responses of the child were obtained were varied. There was an additional condition in which the material did not contain any interview transcripts. The results showed that clinicians are sensitive only to the presence of leading questions but not to the presence of other suggestive techniques. Furthermore, the clinicians were not sensitive to the possibility that suggestive techniques could have been used when no interview transcripts had been included in the trial material. Experience had an effect on the sensitivity of the clinicians only regarding leading questions. Strong beliefs related to CSA lessened the sensitivity to leading questions. Those showing strong beliefs on the belief scales used in this study were even more prone to prosecute than other participants when other suggestive influences than leading questions were present. Controversy exists regarding effects of experience and feedback on clinical decision making. In Study IV the impact of the number of handled cases and of feedback on the decisions in cases of alleged CSA was investigated. One-hundred vignettes describing cases of suspected CSA were given to students with no experience with investigating CSA. The vignettes were based on statistical data about symptoms and prevalence of CSA. According to the theoretical likelihood of CSA the children described were categorized as abused or not abused. The participants were asked to decide whether abuse had occurred. They were divided into 4 groups: one received feedback on whether their decision was right or wrong, one received information about cognitive processes involved in decision making, one received both, and one did not receive feedback at all. The results showed that participants who received feedback on their performance made more correct positive decisions and participants who got information about decision making processes made more correct negative decisions. Feedback and information combined decreased the number of correct positive decisions but increased the number of correct negative decisions. The number of read cases had in itself a positive effect on correct positive decision.

Statistical Analysis and Numerics of Heat Exchanger Models

The identifiability of the parameters of a heat exchanger model without phase change was studied in this Master’s thesis using synthetically made data. A fast, two-step Markov chain Monte Carlo method (MCMC) was tested with a couple of case studies and a heat exchanger model. The two-step MCMC-method worked well and decreased the computation time compared to the traditional MCMC-method. The effect of measurement accuracy of certain control variables to the identifiability of parameters was also studied. The accuracy used did not seem to have a remarkable effect to the identifiability of parameters. The use of the posterior distribution of parameters in different heat exchanger geometries was studied. It would be computationally most efficient to use the same posterior distribution among different geometries in the optimisation of heat exchanger networks. According to the results, this was possible in the case when the frontal surface areas were the same among different geometries. In the other cases the same posterior distribution can be used for optimisation too, but that will give a wider predictive distribution as a result. For condensing surface heat exchangers the numerical stability of the simulation model was studied. As a result, a stable algorithm was developed.

Bayesian methods for estimation, optimization and experimental design

Mathematical models often contain parameters that need to be calibrated from measured data. The emergence of efficient Markov Chain Monte Carlo (MCMC) methods has made the Bayesian approach a standard tool in quantifying the uncertainty in the parameters. With MCMC, the parameter estimation problem can be solved in a fully statistical manner, and the whole distribution of the parameters can be explored, instead of obtaining point estimates and using, e.g., Gaussian approximations. In this thesis, MCMC methods are applied to parameter estimation problems in chemical reaction engineering, population ecology, and climate modeling. Motivated by the climate model experiments, the methods are developed further to make them more suitable for problems where the model is computationally intensive. After the parameters are estimated, one can start to use the model for various tasks. Two such tasks are studied in this thesis: optimal design of experiments, where the task is to design the next measurements so that the parameter uncertainty is minimized, and model-based optimization, where a model-based quantity, such as the product yield in a chemical reaction model, is optimized. In this thesis, novel ways to perform these tasks are developed, based on the output of MCMC parameter estimation. A separate topic is dynamical state estimation, where the task is to estimate the dynamically changing model state, instead of static parameters. For example, in numerical weather prediction, an estimate of the state of the atmosphere must constantly be updated based on the recently obtained measurements. In this thesis, a novel hybrid state estimation method is developed, which combines elements from deterministic and random sampling methods.