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.

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.

Statistical Optimum Design of Heat Exchangers

The optimal design of a heat exchanger system is based on given model parameters together with given standard ranges for machine design variables. The goals set for minimizing the Life Cycle Cost (LCC) function which represents the price of the saved energy, for maximizing the momentary heat recovery output with given constraints satisfied and taking into account the uncertainty in the models were successfully done. Nondominated Sorting Genetic Algorithm II (NSGA-II) for the design optimization of a system is presented and implemented inMatlab environment. Markov ChainMonte Carlo (MCMC) methods are also used to take into account the uncertainty in themodels. Results show that the price of saved energy can be optimized. A wet heat exchanger is found to be more efficient and beneficial than a dry heat exchanger even though its construction is expensive (160 EUR/m2) compared to the construction of a dry heat exchanger (50 EUR/m2). It has been found that the longer lifetime weights higher CAPEX and lower OPEX and vice versa, and the effect of the uncertainty in the models has been identified in a simplified case of minimizing the area of a dry heat exchanger.

Validation and statistical analysis of two high performance liquid chromatography methods for the determination of indinavir sulfate raw material and capsules

Two high performance liquid chromatography (HPLC) methods for the quantitative determination of indinavir sulfate were tested, validated and statistically compared. Assays were carried out using as mobile phases mixtures of dibutylammonium phosphate buffer pH 6.5 and acetonitrile (55:45) at 1 mL/min or citrate buffer pH 5 and acetonitrile (60:40) at 1 mL/min, an octylsilane column (RP-8) and a UV spectrophotometric detector at 260 nm. Both methods showed good sensitivity, linearity, precision and accuracy. The statistical analysis using the t-student test for the determination of indinavir sulfate raw material and capsules indicated no statistically significant difference between the two methods.

The adequacy of different robust statistical tests in comparing two independent groups

In the current study, we evaluated various robust statistical methods for comparing two independent groups. Two scenarios for simulation were generated: one of equality and another of population mean differences. In each of the scenarios, 33 experimental conditions were used as a function of sample size, standard deviation and asymmetry. For each condition, 5000 replications per group were generated. The results obtained by this study show an adequate type error I rate but not a high power for the confidence intervals. In general, for the two scenarios studied (mean population differences and not mean population differences) in the different conditions analysed, the Mann-Whitney U-test demonstrated strong performance, and a little worse the t-test of Yuen-Welch.

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.

Gemifloxacin mesylate: UV spectrophotometric method for quantitative determination using experimental design for robustness

This study describes the validation of UV spectrophotometric method for quantitative determination of gemifloxacin mesylate (GFM) in tablets using methanol as solvent. The method was specific, linear, precise, exact and robust at 272 and 343 nm. The results confirmed that the method in both wavelengths is valid and useful to the routine quality control of GFM in coated tablets. The validate method was compared to liquid chromatography (HPLC), microbiological assay and visible (VIS) spectrophotometry, which were previously developed and validated to the same drug. There was not significative difference between the methods for GFM quantitation.

Optimization of solvent mixtures for extraction from bark of Schinus terebinthifolius by a statistical mixture-design technique and development of a UV-Vis spectrophotometric method for analysis of total polyphenols in the extract

A statistical mixture-design technique was used to study the effects of different solvents and their mixtures on the yield, total polyphenol content, and antioxidant capacity of the crude extracts from the bark of Schinus terebinthifolius Raddi (Anacardiaceae). The experimental results and their response-surface models showed that ternary mixtures with equal portions of all the three solvents (water, ethanol and acetone) were better than the binary mixtures in generating crude extracts with the highest yield (22.04 ± 0.48%), total polyphenol content (29.39 ± 0.39%), and antioxidant capacity (6.38 ± 0.21). An analytical method was developed and validated for the determination of total polyphenols in the extracts. Optimal conditions for the various parameters in this analytical method, namely, the time for the chromophoric reaction to stabilize, wavelength of the absorption maxima to be monitored, the reference standard and the concentration of sodium carbonate were determined to be 5 min, 780 nm, pyrogallol, and 14.06% w v-1, respectively. UV-Vis spectrophotometric monitoring of the reaction under these conditions proved the method to be linear, specific, precise, accurate, reproducible, robust, and easy to perform.

Statistical Model to DNA Melting

We explore a DNA statistical model to obtain information about the behavior of the thermodynamics quantities. Special attention is given to the thermal denaturation of this macromolecule.

Methods for construction and analysis of computational models in systems biology : applications to the modelling of the heat shock response and the self-assembly of intermediate filaments

Systems biology is a new, emerging and rapidly developing, multidisciplinary research field that aims to study biochemical and biological systems from a holistic perspective, with the goal of providing a comprehensive, system- level understanding of cellular behaviour. In this way, it addresses one of the greatest challenges faced by contemporary biology, which is to compre- hend the function of complex biological systems. Systems biology combines various methods that originate from scientific disciplines such as molecu- lar biology, chemistry, engineering sciences, mathematics, computer science and systems theory. Systems biology, unlike “traditional” biology, focuses on high-level concepts such as: network, component, robustness, efficiency, control, regulation, hierarchical design, synchronization, concurrency, and many others. The very terminology of systems biology is “foreign” to “tra- ditional” biology, marks its drastic shift in the research paradigm and it indicates close linkage of systems biology to computer science. One of the basic tools utilized in systems biology is the mathematical modelling of life processes tightly linked to experimental practice. The stud- ies contained in this thesis revolve around a number of challenges commonly encountered in the computational modelling in systems biology. The re- search comprises of the development and application of a broad range of methods originating in the fields of computer science and mathematics for construction and analysis of computational models in systems biology. In particular, the performed research is setup in the context of two biolog- ical phenomena chosen as modelling case studies: 1) the eukaryotic heat shock response and 2) the in vitro self-assembly of intermediate filaments, one of the main constituents of the cytoskeleton. The range of presented approaches spans from heuristic, through numerical and statistical to ana- lytical methods applied in the effort to formally describe and analyse the two biological processes. We notice however, that although applied to cer- tain case studies, the presented methods are not limited to them and can be utilized in the analysis of other biological mechanisms as well as com- plex systems in general. The full range of developed and applied modelling techniques as well as model analysis methodologies constitutes a rich mod- elling framework. Moreover, the presentation of the developed methods, their application to the two case studies and the discussions concerning their potentials and limitations point to the difficulties and challenges one encounters in computational modelling of biological systems. The problems of model identifiability, model comparison, model refinement, model inte- gration and extension, choice of the proper modelling framework and level of abstraction, or the choice of the proper scope of the model run through this thesis.

Multivariate statistical analysis to support the minimum streamflow regionalization

ABSTRACT This study aimed to develop a methodology based on multivariate statistical analysis of principal components and cluster analysis, in order to identify the most representative variables in studies of minimum streamflow regionalization, and to optimize the identification of the hydrologically homogeneous regions for the Doce river basin. Ten variables were used, referring to the river basin climatic and morphometric characteristics. These variables were individualized for each of the 61 gauging stations. Three dependent variables that are indicative of minimum streamflow (Q7,10, Q90 and Q95). And seven independent variables that concern to climatic and morphometric characteristics of the basin (total annual rainfall – Pa; total semiannual rainfall of the dry and of the rainy season – Pss and Psc; watershed drainage area – Ad; length of the main river – Lp; total length of the rivers – Lt; and average watershed slope – SL). The results of the principal component analysis pointed out that the variable SL was the least representative for the study, and so it was discarded. The most representative independent variables were Ad and Psc. The best divisions of hydrologically homogeneous regions for the three studied flow characteristics were obtained using the Mahalanobis similarity matrix and the complete linkage clustering method. The cluster analysis enabled the identification of four hydrologically homogeneous regions in the Doce river basin.

Statistical analysis of survey-based event history data with application to modeling of unemployment duration

Longitudinal surveys are increasingly used to collect event history data on person-specific processes such as transitions between labour market states. Surveybased event history data pose a number of challenges for statistical analysis. These challenges include survey errors due to sampling, non-response, attrition and measurement. This study deals with non-response, attrition and measurement errors in event history data and the bias caused by them in event history analysis. The study also discusses some choices faced by a researcher using longitudinal survey data for event history analysis and demonstrates their effects. These choices include, whether a design-based or a model-based approach is taken, which subset of data to use and, if a design-based approach is taken, which weights to use. The study takes advantage of the possibility to use combined longitudinal survey register data. The Finnish subset of European Community Household Panel (FI ECHP) survey for waves 1–5 were linked at person-level with longitudinal register data. Unemployment spells were used as study variables of interest. Lastly, a simulation study was conducted in order to assess the statistical properties of the Inverse Probability of Censoring Weighting (IPCW) method in a survey data context. The study shows how combined longitudinal survey register data can be used to analyse and compare the non-response and attrition processes, test the missingness mechanism type and estimate the size of bias due to non-response and attrition. In our empirical analysis, initial non-response turned out to be a more important source of bias than attrition. Reported unemployment spells were subject to seam effects, omissions, and, to a lesser extent, overreporting. The use of proxy interviews tended to cause spell omissions. An often-ignored phenomenon classification error in reported spell outcomes, was also found in the data. Neither the Missing At Random (MAR) assumption about non-response and attrition mechanisms, nor the classical assumptions about measurement errors, turned out to be valid. Both measurement errors in spell durations and spell outcomes were found to cause bias in estimates from event history models. Low measurement accuracy affected the estimates of baseline hazard most. The design-based estimates based on data from respondents to all waves of interest and weighted by the last wave weights displayed the largest bias. Using all the available data, including the spells by attriters until the time of attrition, helped to reduce attrition bias. Lastly, the simulation study showed that the IPCW correction to design weights reduces bias due to dependent censoring in design-based Kaplan-Meier and Cox proportional hazard model estimators. The study discusses implications of the results for survey organisations collecting event history data, researchers using surveys for event history analysis, and researchers who develop methods to correct for non-sampling biases in event history data.

Statistical segmentation methods and color variance analysis of retinal images

In this research, the effectiveness of Naive Bayes and Gaussian Mixture Models classifiers on segmenting exudates in retinal images is studied and the results are evaluated with metrics commonly used in medical imaging. Also, a color variation analysis of retinal images is carried out to find how effectively can retinal images be segmented using only the color information of the pixels.

Novel virtual environment and real-time simulation based methods for improving life-cycle efficiency of non-road mobile machinery

Virtual environments and real-time simulators (VERS) are becoming more and more important tools in research and development (R&D) process of non-road mobile machinery (NRMM). The virtual prototyping techniques enable faster and more cost-efficient development of machines compared to use of real life prototypes. High energy efficiency has become an important topic in the world of NRMM because of environmental and economic demands. The objective of this thesis is to develop VERS based methods for research and development of NRMM. A process using VERS for assessing effects of human operators on the life-cycle efficiency of NRMM was developed. Human in the loop simulations are ran using an underground mining loader to study the developed process. The simulations were ran in the virtual environment of the Laboratory of Intelligent Machines of Lappeenranta University of Technology. A physically adequate real-time simulation model of NRMM was shown to be reliable and cost effective in testing of hardware components by the means of hardware-in-the-loop (HIL) simulations. A control interface connecting integrated electro-hydraulic energy converter (IEHEC) with virtual simulation model of log crane was developed. IEHEC consists of a hydraulic pump-motor and an integrated electrical permanent magnet synchronous motorgenerator. The results show that state of the art real-time NRMM simulators are capable to solve factors related to energy consumption and productivity of the NRMM. A significant variation between the test drivers is found. The results show that VERS can be used for assessing human effects on the life-cycle efficiency of NRMM. HIL simulation responses compared to that achieved with conventional simulation method demonstrate the advances and drawbacks of various possible interfaces between the simulator and hardware part of the system under study. Novel ideas for arranging the interface are successfully tested and compared with the more traditional one. The proposed process for assessing the effects of operators on the life-cycle efficiency will be applied for wider group of operators in the future. Driving styles of the operators can be analysed statistically from sufficient large result data. The statistical analysis can find the most life-cycle efficient driving style for the specific environment and machinery. The proposed control interface for HIL simulation need to be further studied. The robustness and the adaptation of the interface in different situations must be verified. The future work will also include studying the suitability of the IEHEC for different working machines using the proposed HIL simulation method.

Statistical analysis of event-related potential elicited by verb-complement merge in Brazilian Portuguese

An interesting fact about language cognition is that stimulation involving incongruence in the merge operation between verb and complement has often been related to a negative event-related potential (ERP) of augmented amplitude and latency of ca. 400 ms - the N400. Using an automatic ERP latency and amplitude estimator to facilitate the recognition of waves with a low signal-to-noise ratio, the objective of the present study was to study the N400 statistically in 24 volunteers. Stimulation consisted of 80 experimental sentences (40 congruous and 40 incongruous), generated in Brazilian Portuguese, involving two distinct local verb-argument combinations (nominal object and pronominal object series). For each volunteer, the EEG was simultaneously acquired at 20 derivations, topographically localized according to the 10-20 International System. A computerized routine for automatic N400-peak marking (based on the ascendant zero-cross of the first waveform derivative) was applied to the estimated individual ERP waveform for congruous and incongruous sentences in both series for all ERP topographic derivations. Peak-to-peak N400 amplitude was significantly augmented (P < 0.05; one-sided Wilcoxon signed-rank test) due to incongruence in derivations F3, T3, C3, Cz, T5, P3, Pz, and P4 for nominal object series and in P3, Pz and P4 for pronominal object series. The results also indicated high inter-individual variability in ERP waveforms, suggesting that the usual procedure of grand averaging might not be considered a generally adequate approach. Hence, signal processing statistical techniques should be applied in neurolinguistic ERP studies allowing waveform analysis with low signal-to-noise ratio.