Statistical Inversion Theory in X-ray Tomography

In this thesis the X-ray tomography is discussed from the Bayesian statistical viewpoint. The unknown parameters are assumed random variables and as opposite to traditional methods the solution is obtained as a large sample of the distribution of all possible solutions. As an introduction to tomography an inversion formula for Radon transform is presented on a plane. The vastly used filtered backprojection algorithm is derived. The traditional regularization methods are presented sufficiently to ground the Bayesian approach. The measurements are foton counts at the detector pixels. Thus the assumption of a Poisson distributed measurement error is justified. Often the error is assumed Gaussian, altough the electronic noise caused by the measurement device can change the error structure. The assumption of Gaussian measurement error is discussed. In the thesis the use of different prior distributions in X-ray tomography is discussed. Especially in severely ill-posed problems the use of a suitable prior is the main part of the whole solution process. In the empirical part the presented prior distributions are tested using simulated measurements. The effect of different prior distributions produce are shown in the empirical part of the thesis. The use of prior is shown obligatory in case of severely ill-posed problem.

Multidata inverse problems and Bayesian solution methods in astronomy

Statistical analyses of measurements that can be described by statistical models are of essence in astronomy and in scientific inquiry in general. The sensitivity of such analyses, modelling approaches, and the consequent predictions, is sometimes highly dependent on the exact techniques applied, and improvements therein can result in significantly better understanding of the observed system of interest. Particularly, optimising the sensitivity of statistical techniques in detecting the faint signatures of low-mass planets orbiting the nearby stars is, together with improvements in instrumentation, essential in estimating the properties of the population of such planets, and in the race to detect Earth-analogs, i.e. planets that could support liquid water and, perhaps, life on their surfaces. We review the developments in Bayesian statistical techniques applicable to detections planets orbiting nearby stars and astronomical data analysis problems in general. We also discuss these techniques and demonstrate their usefulness by using various examples and detailed descriptions of the respective mathematics involved. We demonstrate the practical aspects of Bayesian statistical techniques by describing several algorithms and numerical techniques, as well as theoretical constructions, in the estimation of model parameters and in hypothesis testing. We also apply these algorithms to Doppler measurements of nearby stars to show how they can be used in practice to obtain as much information from the noisy data as possible. Bayesian statistical techniques are powerful tools in analysing and interpreting noisy data and should be preferred in practice whenever computational limitations are not too restrictive.

Aineominaisuuksien mallinnustarkkuuden vaikutukset lämmönsiirtimien lämpöteknisessä simuloinnissa

Työssä on käsitelty fluidien aineominaisuuksien vaikutuksia paperikoneiden kuivatusosissa käytettävien lämmönsiirtimien lämpöteknisessä simuloinnissa. Pääkohteena selvitettiin kostean ilman ja veden fysikaalisien aineominaisuuksien mallinnustarkkuuden vaikutuksia lämpövirtaan lauhduttamattomissa ja lauhduttavissa tapauksissa. Asiaa tutkittiin tekemällä herkkyysanalyysi työssä kehitetyille termodynaamisille malleille. Perinteisen herkkyysanalyysin lisäksi herkkyyksiä tutkittiin myös Bayesiläisellä tilastoanalyysillä. Työssä käsiteltiin myös aineominaisuuksien käyttäytymistä ja mallintamista lämmönsiirtimissä. Kirjallisuudesta etsittiin aineominaisuusmallit, joilla kostean ilman ja veden fysikaalisia aineominaisuuksia voidaan kuvata riittävän tarkasti. Työssä havaittiin, että yksittäisistä aineominaisuuksista selkeästi suurimmat vaikutukset on ominaisentalpioiden mallinnuksen epätarkkuuksilla. Myös kaikkien aineominaisuuksien epätarkkuuksilla havaittiin olevan huomattavan suuret yhteisvaikutukset lämpövirran laskentatarkkuuteen. Viiden prosentin epätarkkuus kaikkien aineominaisuuksien mallinnuksessa johtaa 3 - 7 %:n epätarkkuuteen lämpövirran laskennassa. Näin ollen kaikkien aineominaisuuksien mallintamiseen tulee kiinnittää huomiota.

Adaptive MCMC methods with applications in environmental and geophysical models

This work presents new, efficient Markov chain Monte Carlo (MCMC) simulation methods for statistical analysis in various modelling applications. When using MCMC methods, the model is simulated repeatedly to explore the probability distribution describing the uncertainties in model parameters and predictions. In adaptive MCMC methods based on the Metropolis-Hastings algorithm, the proposal distribution needed by the algorithm learns from the target distribution as the simulation proceeds. Adaptive MCMC methods have been subject of intensive research lately, as they open a way for essentially easier use of the methodology. The lack of user-friendly computer programs has been a main obstacle for wider acceptance of the methods. This work provides two new adaptive MCMC methods: DRAM and AARJ. The DRAM method has been built especially to work in high dimensional and non-linear problems. The AARJ method is an extension to DRAM for model selection problems, where the mathematical formulation of the model is uncertain and we want simultaneously to fit several different models to the same observations. The methods were developed while keeping in mind the needs of modelling applications typical in environmental sciences. The development work has been pursued while working with several application projects. The applications presented in this work are: a winter time oxygen concentration model for Lake Tuusulanjärvi and adaptive control of the aerator; a nutrition model for Lake Pyhäjärvi and lake management planning; validation of the algorithms of the GOMOS ozone remote sensing instrument on board the Envisat satellite of European Space Agency and the study of the effects of aerosol model selection on the GOMOS algorithm.

Applications of Industrial Statistics

This dissertation examines knowledge and industrial knowledge creation processes. It looks at the way knowledge is created in industrial processes based on data, which is transformed into information and finally into knowledge. In the context of this dissertation the main tool for industrial knowledge creation are different statistical methods. This dissertation strives to define industrial statistics. This is done using an expert opinion survey, which was sent to a number of industrial statisticians. The survey was conducted to create a definition for this field of applied statistics and to demonstrate the wide applicability of statistical methods to industrial problems. In this part of the dissertation, traditional methods of industrial statistics are introduced. As industrial statistics are the main tool for knowledge creation, the basics of statistical decision making and statistical modeling are also included. The widely known Data Information Knowledge Wisdom (DIKW) hierarchy serves as a theoretical background for this dissertation. The way that data is transformed into information, information into knowledge and knowledge finally into wisdom is used as a theoretical frame of reference. Some scholars have, however, criticized the DIKW model. Based on these different perceptions of the knowledge creation process, a new knowledge creation process, based on statistical methods is proposed. In the context of this dissertation, the data is a source of knowledge in industrial processes. Because of this, the mathematical categorization of data into continuous and discrete types is explained. Different methods for gathering data from processes are clarified as well. There are two methods for data gathering in this dissertation: survey methods and measurements. The enclosed publications provide an example of the wide applicability of statistical methods in industry. In these publications data is gathered using surveys and measurements. Enclosed publications have been chosen so that in each publication, different statistical methods are employed in analyzing of data. There are some similarities between the analysis methods used in the publications, but mainly different methods are used. Based on this dissertation the use of statistical methods for industrial knowledge creation is strongly recommended. With statistical methods it is possible to handle large datasets and different types of statistical analysis results can easily be transformed into knowledge.

Communicative and Anticipatory Decision-Making Supported by Bayesian Networks

The purpose of this research is to draw up a clear construction of an anticipatory communicative decision-making process and a successful implementation of a Bayesian application that can be used as an anticipatory communicative decision-making support system. This study is a decision-oriented and constructive research project, and it includes examples of simulated situations. As a basis for further methodological discussion about different approaches to management research, in this research, a decision-oriented approach is used, which is based on mathematics and logic, and it is intended to develop problem solving methods. The approach is theoretical and characteristic of normative management science research. Also, the approach of this study is constructive. An essential part of the constructive approach is to tie the problem to its solution with theoretical knowledge. Firstly, the basic definitions and behaviours of an anticipatory management and managerial communication are provided. These descriptions include discussions of the research environment and formed management processes. These issues define and explain the background to further research. Secondly, it is processed to managerial communication and anticipatory decision-making based on preparation, problem solution, and solution search, which are also related to risk management analysis. After that, a solution to the decision-making support application is formed, using four different Bayesian methods, as follows: the Bayesian network, the influence diagram, the qualitative probabilistic network, and the time critical dynamic network. The purpose of the discussion is not to discuss different theories but to explain the theories which are being implemented. Finally, an application of Bayesian networks to the research problem is presented. The usefulness of the prepared model in examining a problem and the represented results of research is shown. The theoretical contribution includes definitions and a model of anticipatory decision-making. The main theoretical contribution of this study has been to develop a process for anticipatory decision-making that includes management with communication, problem-solving, and the improvement of knowledge. The practical contribution includes a Bayesian Decision Support Model, which is based on Bayesian influenced diagrams. The main contributions of this research are two developed processes, one for anticipatory decision-making, and the other to produce a model of a Bayesian network for anticipatory decision-making. In summary, this research contributes to decision-making support by being one of the few publicly available academic descriptions of the anticipatory decision support system, by representing a Bayesian model that is grounded on firm theoretical discussion, by publishing algorithms suitable for decision-making support, and by defining the idea of anticipatory decision-making for a parallel version. Finally, according to the results of research, an analysis of anticipatory management for planned decision-making is presented, which is based on observation of environment, analysis of weak signals, and alternatives to creative problem solving and communication.

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.

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.