Search

The church of San Luis de los Franceses in Seville (Spain), built in the 18th century, is one of the most impressive examples of the Spanish Baroque architecture by the architect Leonardo de Figueroa. Its most characteristic features are its great dome and Greek cross plan, while most of the other churches built by de Figueroa and other contemporaries in the city of Seville were based on a rectangular plan, possibly influenced by the guidelines set by the Company of Jesus. The role of the source position on the perception of sound has been investigated, showing that significant variations appeared in reverberation time and other acoustic parameters. After its desacralization the church is now used as a multipurpose site, hosting different types of performances mostly revolving around speech and music. The events where the sound source is located under the dome, with the audience located around it, are especially important. The behaviour of this source position was analysed in greater detail, due to the inherently complex acoustics of this type of surface, and the impulse responses were analysed using the Bayesian parameter estimation. Double slopes were found in the energy time decays for the receivers under the dome, confirming the complexity of the sound field in this space.

Statistical calibration of model parameters conditioned on observations is performed in a Bayesian framework by evaluating the joint posterior probability density function (pdf) of the parameters. The posterior pdf is very often inferred by sampling the parameters with Markov Chain Monte Carlo (MCMC) algorithms. Recently, an alternative technique to calculate the so-called Maximal Conditional Posterior Distribution (MCPD) appeared. This technique infers the individual probability distribution of a given parameter under the condition that the other parameters of the model are optimal. Whereas the MCMC approach samples probable draws of the parameters, the MCPD samples the most probable draws when one of the parameters is set at various prescribed values. In this study, the results of a user-friendly MCMC sampler called DREAM((zs)) and those of the MCPD sampler are compared. The differences between the two approaches are highlighted before running a comparison inferring two analytical distributions with collinearity and multimodality. Then, the performances of both samplers are compared on an artificial multistep outflow experiment from which the soil hydraulic parameters are inferred. The results show that parameter and predictive uncertainties can be accurately assessed with both the MCMC and MCPD approaches.

This article proposes a statistical framework for the development of design models for concrete sandwich panels with glass-fiber-reinforced polymer shear grids. The framework is developed by integrating the Bayesian parameter estimation method and the Eurocode-based capacity reduction factor calibration method. In the first part of the framework, probabilistic and deterministic shear flow prediction models are proposed based on 32 experimental data. It is seen that the contribution of glass-fiber-reinforced polymer grids is dominant, although parameters on the geometrical and material properties of insulation and concrete wythes also contribute. Different constant terms for bias correction of the proposed models are proposed according to the insulation type, and the prediction error of the developed model was reduced. In the second part of the framework, the capacity reduction factor for the proposed deterministic formulas is calculated for design purposes. Statistical calibrations for capacity factors are carried out to meet a target reliability level, and the value is estimated to be approximately 0.75 for all proposed models. Further data collection will improve the applicability of the proposed models and clarify quantification of the contribution of parameters.

In this paper, we propose a method for estimating the physical parameters from dispersion relation data. The conventional analysis method for dispersion relation data has a process of fitting param...

A fire that occurs in a reinforced concrete (RC) structure accompanies a heating temperature, and this negatively affects the concrete material properties, such as the compressive strength, the bond between cement paste and aggregate, and the cracking and spalling of concrete. To appropriately measure the reduced structural performance and durability of fire-damaged RC structures, it is important to accurately estimate the heating temperature of the structure. However, studies in the literature on RC structures damaged by fire have focused mostly on structural member tests at elevated temperatures to ensure the fire resistance or fire protection material development, studies on estimating the heating temperature are very limited except for the very few existing models. Therefore, in this study, a heating temperature estimation model for a reinforced concrete (RC) structure damaged by fire was developed using a statistical Bayesian parameter estimation approach. For the model development, a total of 77 concrete test specimens were utilized, based on them, a statistically highly accurate model has been developed. The usage of the proposed method in the framework of the 500 ℃ isotherm method in Eurocode 2 has been illustrated through an RC column resistance estimation application.

Cocoa bean fermentation relies on the sequential activation of several microbial populations, triggering a temporal pattern of biochemical transformations. Understanding this complex process is of tremendous importance as it is known to form the precursors of the resulting chocolate’s flavour and taste. At the same time, cocoa bean fermentation is one of the least controlled processes in the food industry. Here, a quantitative model of cocoa bean fermentation is constructed based on available microbiological and biochemical knowledge. The model is formulated as a system of coupled ordinary differential equations with two distinct types of state variables: (i) metabolite concentrations of glucose, fructose, ethanol, lactic acid and acetic acid and (ii) population sizes of yeast, lactic acid bacteria and acetic acid bacteria. We demonstrate that the model can quantitatively describe existing fermentation time series and that the estimated parameters, obtained by a Bayesian framework, can be used to extract and interpret differences in environmental conditions. The proposed model is a valuable tool towards a mechanistic understanding of this complex biochemical process, and can serve as a starting point for hypothesis testing of new systemic adjustments. In addition to providing the first quantitative mathematical model of cocoa bean fermentation, the purpose of our investigation is to show how differences in estimated parameter values for two experiments allow us to deduce differences in experimental conditions.

Continuous glucose monitoring (CGM) sensors need to be calibrated twice/day by using self-monitoring of blood glucose (SMBG) samples. Recently, to reduce the calibration frequency, we developed an online calibration algorithm based on a multiple-day model of sensor time variability and Bayesian parameter estimation. When applied to Dexcom G4 Platinum (DG4P) sensor data, the algorithm allowed the frequency of calibrations to be reduced to one-every-four-days without significant worsening of sensor accuracy. The aim of this study is to assess the same methodology on raw CGM data acquired by a next-generation Dexcom CGM sensor prototype and compare the results with that obtained on DG4P.The database consists of 55 diabetic subjects monitored for 10 days by a next-generation Dexcom CGM sensor prototype. The new calibration algorithm is assessed, retrospectively, by simulating an online procedure using progressively fewer SMBG samples until zero. Accuracy is evaluated with mean absolute relative differences (MARD) between blood glucose versus CGM values.The one-per-day and one-every-two-days calibration scenarios in the next-generation CGM data have an accuracy of 8.5% MARD (vs. 11.59% of DG4P) and 8.4% MARD (vs. 11.63% of DG4P), respectively. Accuracy slightly worsens to 9.2% (vs. 11.62% of DG4P) when calibrations are reduced to one-every-four-days. The calibration-free scenario results in 9.3% MARD (vs. 12.97% of DG4P).In next-generation Dexcom CGM sensor data, the use of an online calibration algorithm based on a multiple-day model of sensor time variability and Bayesian parameter estimation aids in the shift toward a calibration-free scenario with even better results than those obtained in present-generation sensors.

The estimation of micromechanical parameters of discrete element method (DEM) models is a nonlinear history-dependent inverse problem. In order to reproduce the experimental measurements with high accuracy, this work aims to develop a machine learning-based calibration toolbox named “Grain learning”, which can extract grains from X-ray computed tomography (CT) images and perform Bayesian parameter estimation for DEM models of dry granular materials.

Background Insecticides used against Aedes aegypti and other disease vectors can elicit a multitude of dose-dependent effects on behavioral and bionomic traits. Estimating the potential epidemiological impact of a product requires thorough understanding of these effects and their interplay at different dosages. Volatile spatial repellent (SR) products come with an additional layer of complexity due to the potential for altered movement of affected mosquitoes and diffusion of volatile particles of the product beyond the treated house. Here, we propose a paired experimental design and statistical inference framework for estimating these nuanced effects of volatile SRs. Method We fitted a continuous-time Markov chain model in a Bayesian framework to data on marked mosquitoes released in interconnected experimental huts conducted in Iquitos, Peru. We estimated the effects of two dosages of transfluthrin on Ae. aegypti behaviors associated with human-vector contact: repellency, exiting and knockdown in the treated space and in connected, adjacent huts. We validated the framework using simulated data. Results The odds of a female Ae. aegypti being repelled, and thus prevented from entering a treated hut (HT), increased at both dosages (low dosage: odds = 1.64, 95% highest density interval (HDI) = 1.30–2.09; high dosage: odds = 1.35, HDI = 1.04–1.67). The relative risk of exiting from the treated hut was reduced (low: RR = 0.70, HDI = 0.62–1.09; high: RR = 0.70, HDI = 0.40–1.06), with this effect carrying over to untreated spaces two huts away from the treated hut (H2) (low: RR = 0.79, HDI = 0.59–1.01; high: RR = 0.66, HDI = 0.50–0.87). Knockdown rates were increased in both treated and downstream huts, particularly under high dosage (HT: RR = 8.37, HDI = 2.11–17.35; H1: RR = 1.39, HDI = 0.52–2.69; H2: RR = 2.22, HDI = 0.96–3.86). Conclusions Our framework is effective at elucidating multiple effects of volatile chemicals used in SR products, as well as their downstream effects. For the examined formulations of transfluthrin, we found notable dose-dependent effects on repellency, movement and knockdown that carry over to adjacent, untreated spaces. Electronic supplementary material The online version of this article (10.1186/s13071-018-2919-0) contains supplementary material, which is available to authorized users.

This paper proposes a Bayesian approach to parameter estimation in electrocardiogram state space models. The on-line nature of the proposed method allows it to be applied to real-world electrocardiogram recordings with varying beat morphology, heart rate, and noise; it thereby provides clear advantages over the conventional Gaussian kernel approach. The applicability of the proposed method is demonstrated on benchmark electrocardiogram data. The results indicate that the method provides a promising framework for noise reduction and wave delineation in electrocardiograms.

Variational Bayes (VB), variational maximum likelihood (VML), restricted maximum likelihood (ReML), and maximum likelihood (ML) are cornerstone parametric statistical estimation techniques in the analysis of functional neuroimaging data. However, the theoretical underpinnings of these model parameter estimation techniques are rarely covered in introductory statistical texts. Because of the widespread practical use of VB, VML, ReML, and ML in the neuroimaging community, we reasoned that. a theoretical treatment of their relationships and their application in a basic modelling scenario may be helpful for both neuroimaging novices and practitioners alike. In this technical study, we thus revisit the conceptual and formal underpinnings of VB, VML, ReML, and ML and provide a detailed account of their mathematical relationships and implementational details. We further apply VB, VML, ReML, and ML to the general linear model (GLM) with non-spherical error covariance as commonly encountered in the first-level analysis of fMRI data. To this end, we explicitly derive the corresponding free energy objective functions and ensuing iterative algorithms. Finally, in the applied part of our study, we evaluate the parameter and model recovery properties of VB, VML, ReML, and ML, first in an exemplary setting and then in the analysis of experimental fMRI data acquired from a single participant under visual stimulation.

The analysis of Bonner sphere measurements is typically done using unfolding codes. However, it is very difficult to implement reliable uncertainty propagation in standard unfolding procedures. An alternative approach, which does provide reliable estimates of the uncertainties of neutron spectra leading to rigorous estimates of uncertainties of the dose, is to analyze the data using Bayesian parameter estimation. In this work, we extend previous approaches and apply this method to secondary neutrons from radiation therapy proton beams. This requires introducing a parameterized model which can describe the main features of the neutron spectra. We choose the parameterization based on information that is available from measurements and detailed Monte Carlo simulations. To demonstrate the validity of this approach, we consider the results of an experiment carried out at the experimental hall at the OncoRay proton therapy facility in Dresden.

This tutorial on Bayesian inference targets psychological researchers who are trained in the null hypothesis testing approach and use of SPSS software. There a number ofexcellent quality tutorials on Bayesian inference, but their problem is that, they assume mathematical knowledge that most psychological researchers do not possess. Thistutorial starts from the idea that Bayesian inference is not more difficult than the traditional approach, but before being introduced to probability theory notation is necessary for the newcomer to understand simple probability principles, which could be explained without mathematical formulas or probability notation. For this purpose in this tutorial I use a simple tool-the parameter-data table-to explain how probability theory can easily be used to make inferences in research. Then I compare the Bayesian and the null hypothesis testing approach using the same tool. Only after having introduced these principles I show the formulas and notations and explain how they relate to the parameter-data table. It is to be expected that this tutorial will increase the use of Bayesian inference by psychological researchers. Moreover, Bayesian researchers may use this tutorial to teach Bayesian inference to undergraduate or postgraduate students.

We consider the regression approach based on Gaussian processes and outline our theoretical results about the properties of the posterior distribution of the corresponding covariance function’s parameter vector. We perform statistical experiments confirming that the obtained theoretical propositions are valid for a wide class of covariance functions commonly used in applied problems.

This paper presents the limit state shear design formulas for both normal and high-strength reinforced concrete deep beams using strut-and-tie model (STM). The proposed equations are based on the STMs with six state-of-the-art efficiency factors. These STMs were improved by correcting the bias and quantifying the scatter using a Bayesian parameter estimation method. The statistical parameters of material properties, dimensions, and the accuracy of design equations are considered to develop the resistance models obtained by Monte Carlo simulations. The reliability analysis is performed to determine the strength reduction factors. The calculated values of strength reduction factors are proposed for each of the considered efficiency factors.

A strut-and-tie model (STM) has been used as a rational and simple method for analysis and design of reinforced concrete deep beams. The STM idealizes the discontinuity regions in such members as a truss-like structure consisting of compression struts and tension ties. The strength of a deep beam is usually controlled by the capacity of the diagonal concrete struts which is generally proposed in terms of the concrete strength and the efficiency factor. The efficiency factor accounts for the variation of the concrete material and the compression softening effect. One has been used in many STMs and often exhibit biases and uncertain errors in prediction of the shear strengths of deep beams. This uncertainty is due to the imperfection of formulation, missing parameters, and insufficient experimental data. Based on a database of 406 test results and six state-of-the-art formulations of the efficiency factors found in the international building codes and literature, this paper proposes improved STMs for accurate prediction of shear strength of simply supported reinforced concrete deep beams by correcting the bias and quantifying the scatter using a Bayesian parameter estimation method.

We present a Bayesian model for estimating the parameters of the VS-Lite forward model of tree-ring width for a particular chronology and its local climatology. The scheme also provides information about the uncertainty of the parameter estimates, as well as the model error in representing the observed proxy time series. By inferring VS-Lite's parameters independently for synthetically generated ring-width series at several hundred sites across the United States, we show that the algorithm is skillful. We also infer optimal parameter values for modeling observed ring-width data at the same network of sites. The estimated parameter values covary in physical space, and their locations in multidimensional parameter space provide insight into the dominant climatic controls on modeled tree-ring growth at each site as well as the stability of those controls. The estimation procedure is useful for forward and inverse modeling studies using VS-Lite to quantify the full range of model uncertainty stemming from its parameterization.

Parameters of physiological models of glucose-insulin regulation in type 1 diabetes have previously been estimated using data collected over short periods of time and lack the quantification of day-to-day variability. We developed a new hierarchical model to relate subcutaneous insulin delivery and carbohydrate intake to continuous glucose monitoring over 12 weeks while describing day-to-day variability. Sensor glucose data sampled every 10 min, insulin aspart delivery and meal intake were analyzed from 8 adults with type 1 diabetes (male/female 5/3, age 39.9±9.5 years, BMI 25.4±4.4 kg/m2, HbA1c 8.4±0.6%) who underwent a 12-week home study of closed-loop insulin delivery. A compartment model comprised five linear differential equations; model parameters were estimated using the Markov chain Monte Carlo approach within a hierarchical Bayesian model framework. Physiologically plausible a posteriori distributions of model parameters including insulin sensitivity, time-to-peak insulin action, time-to-peak gut absorption, and carbohydrate bioavailability, and good model fit were observed. Day-to-day variability of model parameters was estimated in the range of 38 to 79% for insulin sensitivity and 27 to 48% for time-to-peak of insulin action. In conclusion, a linear Bayesian hierarchical approach is feasible to describe a 12-week glucose-insulin relationship using conventional clinical data. The model may facilitate in silico testing to aid the development of closed-loop insulin delivery systems.

Mechanistic understanding of multi-scale biological processes, such as cell proliferation in a changing biological tissue, is readily facilitated by computational models. While tools exist to construct and simulate multi-scale models, the statistical inference of the unknown model parameters remains an open problem. Here, we present and benchmark a parallel approximate Bayesian computation sequential Monte Carlo (pABC SMC) algorithm, tailored for high-performance computing clusters. pABC SMC is fully automated and returns reliable parameter estimates and confidence intervals. By running the pABC SMC algorithm for ∼106 hr, we parameterize multi-scale models that accurately describe quantitative growth curves and histological data obtained in vivo from individual tumor spheroid growth in media droplets. The models capture the hybrid deterministic-stochastic behaviors of 105-106 of cells growing in a 3D dynamically changing nutrient environment. The pABC SMC algorithm reliably converges to a consistent set of parameters. Our study demonstrates a proof of principle for robust, data-driven modeling of multi-scale biological systems and the feasibility of multi-scale model parameterization through statistical inference. A new parallel approximate Bayesian computation sequential Monte Carlo (pABC SMC) algorithm allows for robust, data-driven modeling of multi-scale biological systems and demonstrates the feasibility of multi-scale model parameterization through statistical inference.

In this paper, we address the optimal quantizer design problem for distributed Bayesian parameter estimation with one-bit quantization at local sensors. A performance limit obtained for any distributed parameter estimator with a known prior is adopted as a guidance for quantizer design. Aided by the performance limit, the optimal quantizer and a set of noisy observation models that achieve the performance limit are derived. Further, when the performance limit may not be achievable for some applications, we develop a near-optimal estimator which consists of a dithered noise and a single threshold quantizer. In the scenario where the parameter is Gaussian and signal-to-noise ratio is greater than −1.138 dB, we show that one can construct such an estimator that achieves approximately 99.65% of the performance limit.

Biological invasions are one of the most significant threats to marine biodiversity, and can be facilitated and amplified by climate change. Among all aspects of invasion biology, biotic interactions between invaders and native species are of particular importance. They strongly influence the invasion velocity as well as species responses to climate-induced stressors. Yet the effects of biotic interactions and other important demographic processes remain overlooked among most studies of climate-mediated invasions. We critically assessed current modelling techniques for forecasting marine invasions under climate change, with a particular focus on their ability to account for important biotic interactions and demographic processes. We show that coupled range dynamics models currently represent the most comprehensive and promising approach for modelling and managing marine invasions under climate change. We show, using the crown-of-thorns seastar (Acanthaster planci), why model architectures that account for biotic interactions and demographic and spatial processes (and their interaction) are required to provide ecologically realistic predictions of the distribution and abundance of invader species, both under present-day conditions and into the future. We suggest potential solutions to inform data-poor situations, such as Bayesian parameter estimation and meta-analysis, and identify strategic and targeted gaps in marine invasion research.

The toxicity and efficacy of more than 30 anticancer agents present very high variations, depending on the dosing time. Therefore, the biologists studying the circadian rhythm require a very precise method for estimating the periodic component (PC) vector of chronobiological signals. Moreover, in recent developments, not only the dominant period or the PC vector present a crucial interest but also their stability or variability. In cancer treatment experiments, the recorded signals corresponding to different phases of treatment are short, from 7 days for the synchronization segment to 2 or 3 days for the after-treatment segment. When studying the stability of the dominant period, we have to consider very short length signals relative to the prior knowledge of the dominant period, placed in the circadian domain. The classical approaches, based on Fourier transform (FT) methods are inefficient (i.e., lack of precision) considering the particularities of the data (i.e., the short length). Another particularity of the signals considered in such experiments is the level of noise: such signals are very noisy and establishing the periodic components that are associated with the biological phenomena and distinguishing them from the ones associated with the noise are difficult tasks. In this paper, we propose a new method for the estimation of the PC vector of biomedical signals, using the biological prior informations and considering a model that accounts for the noise. The experiments developed in cancer treatment context are recording signals expressing a limited number of periods. This is a prior information that can be translated as the sparsity of the PC vector. The proposed method considers the PC vector estimation as an Inverse Problem (IP) using the general Bayesian inference in order to infer the unknown of our model, i.e. the PC vector but also the hyperparameters (i.e the variances). The sparsity prior information is modeled using a sparsity enforcing prior law. In this paper, we propose a Student’s t distribution, viewed as the marginal distribution of a bivariate normal-inverse gamma distribution. We build a general infinite Gaussian scale mixture (IGSM) hierarchical model where we assign prior distributions also for the hyperparameters. The expression of the joint posterior law of the unknown PC vector and hyperparameters is obtained via Bayes rule, and then, the unknowns are estimated via joint maximum a posteriori (JMAP) or posterior mean (PM). For the PM estimator, the expression of the posterior distribution is approximated by a separable one, via variational Bayesian approximation (VBA), using the Kullback-Leibler (KL) divergence. For the PM estimation, two possibilities are considered: an approximation with a partially separable distribution and an approximation with a fully separable one. Both resulting algorithms corresponding to the PM estimation and the one corresponding to the JMAP estimation are iterative algorithms. The algorithms are presented in detail and are compared with the ones corresponding to the Gaussian model. We examine the convergency of the algorithms and give simulation results to compare their performances. Finally, we show simulation results on synthetic and real data in cancer treatment applications. The real data considered in this paper examines the rest-activity patterns of KI/KI Per2::luc mouse, aged 10 weeks, singly housed in RealTime Biolumicorder (RT-BIO). Electronic supplementary material The online version of this article (doi:10.1186/s13637-015-0033-6) contains supplementary material, which is available to authorized users.

Current haul road management techniques, such as routine, periodic and urgent maintenance have shortcomings in many complex haul road environments. Real-time road condition monitoring may significantly reduce maintenance costs, both to the road and to the vehicles. A recent idea is that vehicle on-board data collection systems could be used to monitor haul roads on a real-time basis by means of vibration signature analysis. This paper proposes a methodology based on Bayesian regression to isolate the effect of varying vehicle speed on the measured vehicle response metric. A key feature of the proposed methodology is that it avoids the costly need to generate analytical or empirical vehicle models.

An extensive database has been constructed of reinforced concrete (RC) beam-column connection tests subjected to cyclic lateral loading. All cases within the database experienced joint shear failure, either in conjunction with or without yielding of longitudinal beam reinforcement. Using the experimental database, envelope curves of joint shear stress vs. joint shear strain behavior have been created by connecting key points such as cracking, yielding, and peak loading. Various prediction approaches for RC joint shear behavior are discussed using the constructed experimental database. RC joint shear strength and deformation models are first presented using the database in conjunction with a Bayesian parameter estimation method, and then a complete model applicable to the full range of RC joint shear behavior is suggested. An RC joint shear prediction model following a U.S. standard is next summarized and evaluated. Finally, a particular joint shear prediction model using basic joint shear resistance mechanisms is described and for the first time critically assessed.

Cumulative prospect theory (CPT Tversky & Kahneman, 1992) has provided one of the most influential accounts of how people make decisions under risk. CPT is a formal model with parameters that quantify psychological processes such as loss aversion, subjective values of gains and losses, and subjective probabilities. In practical applications of CPT, the model’s parameters are usually estimated using a single-participant maximum likelihood approach. The present study shows the advantages of an alternative, hierarchical Bayesian parameter estimation procedure. Performance of the procedure is illustrated with a parameter recovery study and application to a real data set. The work reveals that without particular constraints on the parameter space, CPT can produce loss aversion without the parameter that has traditionally been associated with loss aversion. In general, the results illustrate that inferences about people’s decision processes can crucially depend on the method used to estimate model parameters.

The first part of this article provides a concise survey of some of the mathematical methods that have been proposed for neutron spectrum unfolding. The aim is to give a pedagogical introduction to the subject without going into a detailed discussion of technical issues. The second part of this article concerns the evaluation of uncertainties. Spectra derived using unfolding techniques (and any quantities computed from these spectra; e.g., fluences and doses) will be subject to uncertainties and it is important to provide estimates of these uncertainties. This is not straightforward, due in part to the special role played by the prior information. It is shown that an approach using Bayesian parameter estimation can overcome these difficulties.

As a thorough aggregation of probability and graph theory, Bayesian networks currently enjoy widespread interest as a means for studying factors that affect the coherent evaluation of scientific evidence in forensic science. Paper I of this series of papers intends to contribute to the discussion of Bayesian networks as a framework that is helpful for both illustrating and implementing statistical procedures that are commonly employed for the study of uncertainties (e.g. the estimation of unknown quantities). While the respective statistical procedures are widely described in literature, the primary aim of this paper is to offer an essentially non-technical introduction on how interested readers may use these analytical approaches – with the help of Bayesian networks – for processing their own forensic science data. Attention is mainly drawn to the structure and underlying rationale of a series of basic and context-independent network fragments that users may incorporate as building blocs while constructing larger inference models. As an example of how this may be done, the proposed concepts will be used in a second paper (Part II) for specifying graphical probability networks whose purpose is to assist forensic scientists in the evaluation of scientific evidence encountered in the context of forensic document examination (i.e. results of the analysis of black toners present on printed or copied documents).

Bayesian parameter estimation is a popular method to address inverse problems. However, since prior distributions are chosen based on expert judgement, the method can inherently introduce bias into the understanding of the parameters. This can be especially relevant in the case of distributed parameters where it is difficult to check for error. To minimize this bias, we develop the idea of a minimally corrective, approximately recovering prior (MCAR prior) that generates a guide for the prior and corrects the expert supplied prior according to that guide. We demonstrate this approach for the 1D elliptic equation or the elliptic partial differential equation and observe how this method works in cases with significant and without any expert bias. In the case of significant expert bias, the method substantially reduces the bias and, in the case with no expert bias, the method only introduces minor errors. The cost of introducing these small errors for good judgement is worth the benefit of correcting major errors in bad judgement. This is particularly true when the prior is only determined using a heuristic or an assumed distribution. Master of Science

This paper introduces PJM Interconnection's new method to model and predict transformers' service lives. A simplified Perks' equation is used to model the hazard rates, which will be used synonymously with retirement rates in this paper, of transmission transformers. A Bayesian Method is used to model the uncertainty in the three parameters of Perks' equation. This method is different from the traditional Iowa Curve method in that: 1) it gives a continuous family of transformer life distributions as well as the extinction likelihoods, rather than a limited number of distribution patterns and 2) a closed-form distribution can also be deduced with only three parameters, which can assume all the three distribution patterns of Iowa Curves: right, left, and symmetrically modal. The method has been successfully applied to the statistics on hundreds of large electric transformers in PJM. Example problems are provided and solved with this new method

New applications in materials, medicine, and computers are being discovered where the control of events at the molecular and nanoscopic scales is critical to product quality, although the primary manipulation of these events during processing occurs at macroscopic length scales. This motivates the creation of tools for the engineering of multiscale reacting systems that have length scales ranging from the atomistic to the macroscopic. This paper describes a systematic approach that consists of stochastic parameter sensitivity analysis, Bayesian parameter estimation applied to ab initio calculations and experimental data, model-based experimental design, hypothesis mechanism selection, and multistep optimization.

Досліджено застосування байєсівського підходу до оцінювання параметрів математичних моделей та методу аналізу статистичних даних у страхуванні на основі узагальнених лінійних моделей, які являють собою розширення лінійної регресії на випадки, коли розподіл випадкових величин може відрізнятись від нормального. Це дає можливість докладніше описати структуру та зміст досліджуваної моделі. Процедура оцінювання параметрів моделі виконується із використанням класичного методу та байєсівського підходу. На основі статистичних даних стосовно величини збитків у сфері автомобільного страхування побудовано модель для прогнозування цього актуарного процесу. Прийнят­ною для подальшого використання виявилась модель із законом розподілу Пуассона та експоненціальною функцією зв’язку. Це підтверджується мінімальною величиною похибки, а також достовірною оцінкою параметрів узагальнених лінійних моделей, отриманих із використанням байєсівського підходу. Встановлено, що нормальна модель з тотожною функцією зв’язку дає можливість отримати результат за одну ітерацію з незначною відносною похибкою, але недостатньо точними прогнозними значеннями збитків., The article deals with Bayesian methodology for estimating unknown parameters of mathematical models and the method of analysis statistic data in insurance based on generalized linear models. These models are extension of linear regression when distribution of random variable can differ from normal. For estimating the parameters of proposed models classical and Bayesian approach were used. The main advantage of Bayesian approach is its ability to generate not only accurate estimates but probability distributions too. It gives the opportunity to describe in details the structure and the nature of investigated models. The value of damages in autoinsurance were hired for creating the forecasting model of actuarial process. The model with Poisson distribution and an exponential link function turned out to be acceptable for further use because it has minimum value of observation error and reliable estimate for risk value which was received using Bayesian approach. A normal model with identity link function allows to generate a result after one iteration with small value of observation error but “weak” predicted value of losses and poor risk assessment., Исследовано применение байесовского подхода к задаче оценивания неизвестных параметров моделей и метода анализа статистических данных в сфере страхования на основе обобщенных линейных моделей, которые представляют собой расширение линейной регрессии на случаи, когда распределение случайных величин может отличаться от нормального. Для данной задачи оценивание неизвестных параметров моделей осуществлено c помощью байесовского подхода и метода максимального правдоподобия. На основании статистических данных об убытках в сфере автострахования построена прогнозирующая модель для актуарного процесса. Допустимой для дальнейшего применения оказалась модель с законом распределения Пуассона и экспоненциальной функцией связи. Это обосновывается минимальной величиной погрешности, а также достоверной величиной риска и достоверной оценкой параметров обобщенных линейных моделей с применением байесовского похода. Установлено, что нормальная модель с тождественной функцией связи позволяет получить результат за одну итерацию с допустимым значением относительной погрешности, но “слабым” прогнозным значением убытков и недопустимой оценкой риска.

The delineation of flood-prone areas is one of the most important steps for flood risk assessment and mitigation. This study uses a probabilistic and DEM-based framework for the delineation of flood-prone areas based on information about the extent of historical flooding in the area of interest. This is particularly useful for the delineation of flood-prone areas in cases where more accurate hydraulic profile calculations are not available. The delineation of flood-prone areas is carried out by using the Topographic Wetness Index (TWI) which allows for the delineation of a portion of a hydrographic basin potentially exposed to flooding by identifying all the areas characterized by a topographic index that exceeds a given threshold. A Bayesian updating framework is used for estimating the TWI threshold for identifying the flood-prone areas based on available information on the spatial extent of historical flooding. An application of the proposed method is demonstrated for the delineation of potentially flood-prone areas in the city of Ouagadougou, based on the observed spatial extent of the 2009 flooding event in the city.