Sensor technology is rapidly developing and, consequently, the generation of point cloud data is constantly increasing. Since the recent release of PointNet, it is possible to process this unordered 3-dimensional data directly in a neural network. The company TLT Screen AB, which develops cutting-edge tracking technology, seeks to optimize the localization of the fingertips of a hand in a point cloud. To do so, the identification of relevant 3D neural network models for modeling hands and detection of fingertips in various hand orientations is essential. The Hand PointNet processes point clouds of hands directly and generate estimations of fixed points (joints), including fingertips, of the hands. Therefore, this model was selected to optimize the localization of fingertips for TLT Screen AB and forms the subject of this research. The model has advantages over conventional convolutional neural networks (CNN). First of all, in contrast to the 2D CNN, the Hand PointNet can use the full 3-dimensional spatial information. Compared to the 3D CNN, moreover, it avoids unnecessarily voluminous data and enables more efficient learning. The model was trained and evaluated on the public dataset MRSA Hand. In contrast to previously published work, the main object of this investigation is the estimation of only 5 joints, for the fingertips. The behavior of the model with a reduction from the usual 21 to 11 and only 5 joints are examined. It is found that the reduction of joints contributed to an increase in the mean error of the estimated joints. Furthermore, the examination of the distribution of the residuals of the estimate for fingertips is found to be less dense. MC dropout to study the prediction uncertainty for the fingertips has shown that the uncertainty increases when the joints are decreased. Finally, the results show that the uncertainty is greatest for the prediction of the thumb tip. Starting from the tip of the thumb, it is observed that the uncertainty of the estimates decreases with each additional fingertip.

The standard methodology when building statistical models has been to use one of several algorithms to systematically search the model space for a good model. If the number of variables is small then all possible models or best subset procedures may be used, but for data sets with a large number of variables, a stepwise procedure is usually implemented. The stepwise procedure of model selection was designed for its computational efficiency and is not guaranteed to find the best model with respect to any optimality criteria. While the model selected may not be the best possible of those in the model space, commonly it is almost as good as the best model. Many times there will be several models that exist that may be competitors of the best model in terms of the selection criterion, but classical model building dictates that a single model be chosen to the exclusion of all others. An alternative to this is Bayesian model averaging (BMA), which uses the information from all models based on how well each is supported by the data. Using BMA allows a variance component due to the uncertainty of the model selection process to be estimated. The variance of any statistic of interest is conditional on the model selected so if there is model uncertainty then variance estimates should reflect this. BMA methodology can also be used for variable assessment since the probability that a given variable is active is readily obtained from the individual model posterior probabilities. The multivariate methods considered in this research are principal components analysis (PCA), canonical variate analysis (CVA), and canonical correlation analysis (CCA). Each method is viewed as a particular multivariate extension of univariate multiple regression. The marginal likelihood of a univariate multiple regression model has been approximated using the Bayes information criteria (BIC), hence the marginal likelihood for these multivariate extensions also makes use of this approximation. One of the main criticisms of multivariate techniques in general is that they are difficult to interpret. To aid interpretation, BMA methodology is used to assess the contribution of each variable to the methods investigated. A second issue that is addressed is displaying of results of an analysis graphically. The goal here is to effectively convey the germane elements of an analysis when BMA is used in order to obtain a clearer picture of what conclusions should be drawn. Finally, the model uncertainty variance component can be estimated using BMA. The variance due to model uncertainty is ignored when the standard model building tenets are used giving overly optimistic variance estimates. Even though the model attained via standard techniques may be adequate, in general, it would be difficult to argue that the chosen model is in fact the correct model. It seems more appropriate to incorporate the information from all plausible models that are well supported by the data to make decisions and to use variance estimates that account for the uncertainty in the model estimation as well as model selection. / Ph. D.

In a world of imbalance, food consumption exhibits great diversity among regions and countries. Although farmers in developed economies benefit from up-to-date agricultural technology and produce much more than they consume, households in the developing world are still combating food insecurity. This dissertation is composed of two manuscripts. One is about consumption in developing countries, while the other is related to promoting agricultural production in a developed economy. Chapter 1 applies a three-stage demand system to nationally representative household survey data to identify food demand behavior with an emphasis on food staples in two West Africa countries ‒ Niger and Nigeria. The third stage of the demand system offers demand elasticities of specific staple items. Instead of treating the population as a whole, the study distinguishes rural and urban households and households of different welfare status. Results confirm the complexity of the food and staples demand between rural/urban areas and among welfare quintiles. Therefore, researchers and policymakers should consider not only the average demand response but also its distribution among households. In addition to demand elasticities, the effects of household demographic characteristics on the structure of food consumption are also obtained. Chapter 2 estimates the rates of return to Virginia's public expenditure on agricultural research and extension (RandE) during 1949-2016 and attempts to address the ad hoc model selection problem common in previous studies. Among the econometric modeling strategies in previous literature, Bayesian Model Averaging (BMA) and Bayesian Hierarchical Model (BHM) are two promising methods to solve the issue of model uncertainty. The rate-of-return estimates by BHM are preferable because BHM imposes fewer restrictions on lag structures and offers more reasonable lag shapes. By BHM, the internal rates of return (IRR) of Virginia's public expenditures on agricultural RandE are 26% and 42%, respectively. Nineteen percent of Virginia's agricultural productivity growth during 1949-2016 results from its RandE investments, and the contribution of research to that growth is about twice of that of extension. One extra million dollar expenditure on research in 1992 would have brought a benefit of $4.5 million, and the same expenditure in 1983 would have brought $5.4 million in additional benefits. If the extra expenditure is spent on extension, it would have brought a benefit of $6.1 million and $6.3 million if the expenditure occurs in 1992 and 1983, respectively. Besides the modeling strategy, this study is distinguished from previous studies in that distributions of rates of return instead of only point estimates are obtained, which is missing in most studies. / Doctor of Philosophy / In a world of imbalance, food production and consumption exhibit great diversity among regions and countries. While farmers of developed economies benefit from up-todate agricultural technology and produce more than they consume, households in the developing world are still facing food insecurity. This dissertation is composed of two manuscripts. Chapter 1 is about food consumption in developing countries. It analyzes household food demand behavior in the two West Africa countries Niger and Nigeria with a focus on staple foods. Food demand behavior differs for rural and urban households and households of different income. Therefore, when evaluating the effects of policies and other impacts, policymakers and researchers should treat households with different attributes separately. Chapter 2 is on how to improve agricultural production within the context of a developed economy: it evaluates the returns to public expenditures on agricultural research and extension (R&E) in Virginia. Previous studies choose statistical models arbitrarily, and this study attempts to address this issue. It finds that Virginia’s investments in agricultural R&E contribute to nineteen percent of the productivity growth in 1949-2016, and the contribution of research is about twice of that of extension.

This paper uses Bayesian model comparison methods to simultaneously specify both the spatial weight structure and explanatory variables for a spatial growth regression involving 255 NUTS 2 regions across 25 European countries. In addition, a correct interpretation of the spatial regression parameter estimates that takes into account the simultaneous feed- back nature of the spatial autoregressive model is provided. Our findings indicate that incorporating model uncertainty in conjunction with appropriate parameter interpretation decreased the importance of explanatory variables traditionally thought to exert an important influence on regional income growth rates. (authors' abstract)

Today, in structural design, a structure is verified against failure by using the partial coefficient method provided by the Eurocodes. The verification method is, in its nature, a deterministic method where the input variables for load and resistance are assigned partial coefficients to ensure that the resistance is exceeded by the load effect. Since these coefficients are calibrated by using probabilistic methods, the partial coefficient method is also called a semi-probabilistic method. As an alternative, the verification is possible by using probabilistic methods. Instead of assigning partial coefficients to load- and resistance variables, they are treated as stochastic variables considering any physical- and statistical uncertainties associated with the same. For a complete probabilistic analysis, however, the model uncertainty must be considered. This uncertainty is associated with the mathematical models that are used to transform load- and material values into load effects and resistance and also uncertainties due to variations and simplifications of e.g. geometrical quantities and failure modes. There is another uncertainty not explicitly dealt with in the Eurocodes and the background material to the codes, that is the uncertainties related to the designers’ choice. That is, how the designer interprets given design conditions and existing codes and also due to the assumptions- and simplifications that takes place when the designer, based on a realistically given design task, must presume e.g. geometrical dimensions, loads and other necessary parameters when designing a structural element. As a basis for this study is a large statistical material, were a number of structural engineers have solved the exact same task which includes the calculation of loads- and load effects and to design a number of elements in an industrial single-storey building in steel. Statistical parameters, associated with the load effect variations due to the designers’ choice, has been estimated using mathematical statistics. Based on this results, a probabilistic level 2 method has been carried out in order to assess how the failure probability is affected when this model uncertainty is varied. It was found in the study that, using a 95% confidence interval, the coefficient of variance of the calculated load effects, defined herein as the model uncertainty due to the designers’ choice and denoted VθS, varies somewhat between 0 – 0,3 depending on the load combination- and type. By using simple examples, including only one variable load, it was shown that the variations in the model uncertainty VθS increases the failure probability thus decrease the reliability index β. The magnitude of these effects depends on the ratio φ between the permanent- and variable load. As an example, when φ = 0,75 (75% of the total load is variable thus 25% is permanent) and VθS = 0,3 then β ≈ 3,24 as compared to the target reliability index βt = 4,75 of safety class 3, which is a 32% reduction. Moreover, it was shown in the examples that the negative effects of increasing VθS, in terms of a decreased reliability index β, is more eminent in the case when the permanent load dominates the variable load, i.e. as φ = 0,25. Thus, increasing VθS from 0,1 to 0,2 decreases the reliability index by 30% (as compared to a 16% reduction when φ = 0,75). / Det vanligaste sättet att, i dagsläget, verifiera en byggnads säkerhet mot brott är med hjälp av partialkoefficientmetoden enligt Eurokoderna. Verifikationsmetoden är till sin form en deterministisk metod där de ingående variablerna som last och bärförmåga tillskrivs partialkoefficienter som verifierar att bärförmågan inte understiger lasteffekten. Då dessa koefficienter är kalibrerade med sannolikhetsteoretiska metoder brukar man kalla partialkoefficientmetoden för semi-probabilistisk.   Alternativt, kan verifieringen ske med hjälp av sannolikhetsteoretiska metoder. Istället för att tillskriva last- och bärförmågeparametrar partialkoefficienter så behandlas dessa som stokastiska variabler och inkluderar fysiska- såväl som statistiska osäkerheter. En korrekt sannolikhetsteoretisk analys måste även inkludera modellosäkerheter. Denna osäkerhet är förknippad med de matematiska modeller som används för att översätta last- och materialvärden till lasteffekt och bärförmåga samt osäkerheter på grund av variationer och förenklingar i exempelvis val av geometriska storheter och brottyp. Det finns en annan typ av osäkerhet som inte explicit behandlas av Eurokoderna samt bakgrundsdokumenten till dessa, och det är de osäkerheter som svarar mot ingenjörens val. Det vill säga, hur denne tolkar givna dimensioneringsunderlag och aktuella regelverk samt de antaganden och förenklingar som uppkommer då ingenjören, utifrån ett realistiskt konstruktionsuppdrag, förutsätter exempelvis geometriska mått, laster och andra nödvändiga parametrar som krävs för att dimensionera en byggnadsdel. Som underlag till detta arbete finns ett omfattande statistiskt material, där ett stort antal byggnadskonstruktörer har tillhandahållits exakt samma uppgift som handlar om att ta fram laster, beräkna lasteffekter och dimensionera ett antal komponenter i en mindre hallbyggnad i stål. Statistiska parametrar, kopplade till variationerna i beräknade lasteffekter på grund av ingenjörens val, har skattats med hjälp av matematisk statistik. Utifrån detta resultat, har en sannolikhetsteoretisk nivå 2 metod använts för att analysera hur brottsannolikheten påverkas då denna modellosäkerhet varieras. I studien konstaterades, utifrån ett 95% konfidensintervall, att variationskoefficienten för de beräknade lasteffekterna, härvid definierad som modellosäkerheten på grund av ingenjörens val med beteckningen VθS, varierar någonstans mellan 0 – 0,3 beroende på aktuell lastkombination och lasttyp. Med hjälp av enkla exempel, innehållandes endast en variabel last, påvisades att variationerna hos modellosäkerheten VθS medför en ökning av brottsannolikheten och därmed en minskning av säkerhetsindexet β. Storleken på dessa effekter beror av fördelningen φ mellan den permanenta- och variabla lasten. Som ett exempel konstaterades att då φ = 0,75 (75% av den totala lasten är variabel och 25% är permanent) samt VθS = 0,3 så reducerades målvärdet för säkerhetsindexet βt = 4,75 i säkerhetsklass 3, med 32% till β ≈ 3,24. Vidare så konstaterades att de negativa effekterna av att öka VθS, beträffande en minskning av säkerhetsindexet β, är mer påtagliga då den permanenta lasten är den dominerande lasten, det vill säga då φ = 0,25. Genom att exempelvis öka VθS från 0,1 till 0,2 så minskas säkerhetsindexet med 30% (jämfört med en minskning på 16% då φ = 0,75).

Understanding the determinants of aggregated default probabilities (PDs) has attracted substantial research over the past decades. This study addresses two major difficulties in understanding the determinants of aggregate PDs: Model uncertainty and multicollinearity among the regressors. We present Bayesian Model Averaging (BMA) as a powerful tool that overcomes model uncertainty. Furthermore, we supplement BMA with ridge regression to mitigate multicollinearity. We apply our approach to an Austrian dataset. Our findings suggest that factor prices like short term interest rates and energy prices constitute major drivers of default rates, while firms' profits reduce the expected number of failures. Finally, we show that the results of our baseline model are fairly robust to the choice of the prior model size. / Series: Research Report Series / Department of Statistics and Mathematics

The spread between interest rate and sovereign bond rate is commonly used in- dicator for country's probability to default. Existing literature proposes many different potential spread determinants but fails to agree on which of them are important. As a result, there is a considerable uncertainty about the cor- rect model explaining the spread. We address this uncertainty by employing Bayesian Model Averaging method (BMA). The BMA technique attempts to consider all the possible combinations of variables and averages them using a model fit measure as weights. For this empirical exercise, we consider 20 different explanatory variables for a panel of 47 countries for the 1980-2010 period. Most of the previously suggested determinants were attributed high inclusion probabilities. Only the "foreign exchange reserves growth" and the "exports growth" scored low by their inclusion probabilities. We also find a role of variables previously not included in the literature's spread determinants - "openness" and "unemployment" which rank high by the inclusion probability. These results are robust to a wide range of both parameter and model priors. JEL Classification C6, C8, C11, C51, E43 Keywords Sovereign Spread Determinants, Model Uncer- tainty, Bayesian Model Averaging Author's e-mail semanv()gmail()com...

Inflation is one of the often used monetary indicators in conducting monetary policy. Even though money supply is an essential determinant of inflation, it is not used in inflation modeling. Currently, output gap is considered as most predicative variable. This thesis brings the empirical evidence on the hypothesis of money supply carrying more information on estimating inflation than the output gap. It is provided on the case of 16 developed European economies using Bayesian Model Averaging (BMA). BMA is a comprehensive approach that deals with the model uncertainty and thus solves the variable selection problem. The results of analysis confirmed that money supply includes more information of inflation than the output gap and thus should be used in inflation modeling. These outcomes are robust towards prior selection and high correlation of some variables.

A norma brasileira de cálculo de alvenaria é baseada no método de tensões admissíveis e passa por revisão para ser escrita no método dos estados limites. A confiabilidade estrutural é um ramo da engenharia que mede segurança das estruturas, sendo muitas vezes empregada para calibrar fatores de segurança. Para medir a confiabilidade de uma estrutura deve-se conhecer as incertezas que envolvem o problema. A incerteza de modelo estima a tendência do modelo (que pode ser eventualmente ser eliminada) e a variância do modelo (uma medida da sua variabilidade). O presente trabalho propõe um método de cálculo da incerteza de um modelo numérico de um prisma formado por três unidades concreto sujeito à compressão. O estudo numérico é feito em elementos finitos com análise não-linear baseada em dano. A incerteza é avaliada através de variáveis de projeto: tensão máxima, deformação na tensão máxima e módulo de elasticidade. São aplicados métodos probabilísticos para comparar resultados numéricos e ensaios experimentais disponíveis na literatura. Confronta-se a probabilidade de falha resultante de resistências corrigidas, sem correção e obtidas experimentalmente. Conclui-se que a incerteza de modelo é importante para quantificar a medida de segurança e deve ser levada em conta na análise da confiabilidade de uma estrutura. O procedimento também é útil para qualificar e comparar modelos de cálculo, com aplicações em alvenaria ou quaisquer outros tipos de estruturas. / The brazilian masonry code is based on the allowable stress method and is currently in revision to be written in the partial safety factor format. Structural reliability is a branch of engineering which allows quantitative evaluation of the safety of structures, being useful in the calibration of safety factors. To measure structural safety, it is necessary to know the uncertainties present in the problem. Model error variables estimate the bias of the model (wich can eventually be eliminated) and the variance of the model (a measure of the model variability). The present work suggests a method for evaluation of modeling uncertainty of the resistence of a prism made of three concrete units subject to compression. The numerical study is based on the finite element method and nonlinear analysis with damage mechanics. The uncertainty is evaluated by design variables: maximum stress, deformation in maximum stress and elasticity modulus of the prism. A probabilistic method is used to compare numerical results with experimental results taken from the literature. The probability of failure based on experimental resistances are compared with the probability of failure based on the model and corrected resistances. It is concluded that the model uncertainty is important to quantify safety and must be taken into account in structural reliability analysis. The procedure is also useful to qualify and compare different models, with application to masonry or other kinds of structural materials.

<p>Water is essential for all life on earth. Global population increase and climate change are projected to increase the water stress, which already today is very high in many areas of the world. The differences between the largest and smallest global runoff estimates exceed the highest continental runoff estimates. These differences, which are caused by different modelling and measurement techniques together with large natural variabilities need to be further addressed. This thesis focuses on global water balance models that calculate global runoff, evaporation and water storage from precipitation and other climate data.</p><p>A new global water balance model, WASMOD-M was developed. Already when tuned against the volume error it reasonable produced within-year runoff patterns, but the volume error was not enough to confine the model parameter space. The parameter space and the simulated hydrograph could be better confined with, e.g., the Nash criterion. Calibration against snow-cover data confined the snow parameters better, although some equifinality still persisted. Thus, even the simple WASMOD-M showed signs of being overparameterised. </p><p>A simple regionalisation procedure that only utilised proximity contributed to calculate a global runoff estimate in line with earlier estimations. The need for better specifications of global runoff estimates was highlighted. </p><p>Global modellers depend on global data-sets that can have low quality in many areas. Major sources of uncertainty are precipitation and river regulation. A new routing method that utilises high-resolution flow network information in low-resolution calculations was developed and shown to perform well over all spatial scales, while the standard linear reservoir routing decreased in performance with decreasing resolution. This algorithm, called aggregated time-delay-histogram routing, is intended for inclusion in WASMOD-M.</p>