Bayesian estimation of g-and-k distributions using MCMC

In this paper we investigate a Bayesian procedure for the estimation of a flexible generalised distribution, notably the MacGillivray adaptation of the g-and-κ distribution. This distribution, described through its inverse cdf or quantile function, generalises the standard normal through extra parameters which together describe skewness and kurtosis. The standard quantile-based methods for estimating the parameters of generalised distributions are often arbitrary and do not rely on computation of the likelihood. MCMC, however, provides a simulation-based alternative for obtaining the maximum likelihood estimates of parameters of these distributions or for deriving posterior estimates of the parameters through a Bayesian framework. In this paper we adopt the latter approach, The proposed methodology is illustrated through an application in which the parameter of interest is slightly skewed.

Estimation of water retention curve from mercury intrusion porosimetry and van Genuchten model

The water retention curve (WRC) is a hydraulic characteristic of concrete required for advanced modeling of water (and thus solute) transport in variably saturated, heterogeneous concrete. Unfortunately, determination by a direct experimental method (for example, measuring equilibrium moisture levels of large samples stored in constant humidity cells) is a lengthy process, taking over 2 years for large samples. A surrogate approach is presented in which the WRC is conveniently estimated from mercury intrusion porosimetry (MIP) and validated by water sorption isotherms: The well-known Barrett, Joyner and Halenda (BJH) method of estimating the pore size distribution (PSD) from the water sorption isotherm is shown to complement the PSD derived from conventional MIP. This provides a basis for predicting the complete WRC from MIP data alone. The van Genuchten equation is used to model the combined water sorption and MIP results. It is a convenient tool for describing water retention characteristics over the full moisture content range. The van Genuchten parameter estimation based solely on MIP is shown to give a satisfactory approximation to the WRC, with a simple restriction on one. of the parameters.

Enhanced detection-guided NLMS estimation of sparse FIR-modeled signal channels

In various signal-channel-estimation problems, the channel being estimated may be well approximated by a discrete finite impulse response (FIR) model with sparsely separated active or nonzero taps. A common approach to estimating such channels involves a discrete normalized least-mean-square (NLMS) adaptive FIR filter, every tap of which is adapted at each sample interval. Such an approach suffers from slow convergence rates and poor tracking when the required FIR filter is "long." Recently, NLMS-based algorithms have been proposed that employ least-squares-based structural detection techniques to exploit possible sparse channel structure and subsequently provide improved estimation performance. However, these algorithms perform poorly when there is a large dynamic range amongst the active taps. In this paper, we propose two modifications to the previous algorithms, which essentially remove this limitation. The modifications also significantly improve the applicability of the detection technique to structurally time varying channels. Importantly, for sparse channels, the computational cost of the newly proposed detection-guided NLMS estimator is only marginally greater than that of the standard NLMS estimator. Simulations demonstrate the favourable performance of the newly proposed algorithm. © 2006 IEEE.

Robust Parametric Estimation of Branching Processes with a Random Number of Ancestors

2000 Mathematics Subject Classification: 60J80.

Trimmed Likelihood Estimation of the Parameters of the Generalized Extreme Value Distributions: a Monte-Carlo Study

2000 Mathematics Subject Classification: Primary 62F35; Secondary 62P99

On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density

2000 Mathematics Subject Classification: 62G07, 62L20.

Estimation of computer waste quantities using forecasting techniques

Technology changes rapidly over years providing continuously more options for computer alternatives and making life easier for economic, intra-relation or any other transactions. However, the introduction of new technology “pushes” old Information and Communication Technology (ICT) products to non-use. E-waste is defined as the quantities of ICT products which are not in use and is bivariate function of the sold quantities, and the probability that specific computers quantity will be regarded as obsolete. In this paper, an e-waste generation model is presented, which is applied to the following regions: Western and Eastern Europe, Asia/Pacific, Japan/Australia/New Zealand, North and South America. Furthermore, cumulative computer sales were retrieved for selected countries of the regions so as to compute obsolete computer quantities. In order to provide robust results for the forecasted quantities, a selection of forecasting models, namely (i) Bass, (ii) Gompertz, (iii) Logistic, (iv) Trend model, (v) Level model, (vi) AutoRegressive Moving Average (ARMA), and (vii) Exponential Smoothing were applied, depicting for each country that model which would provide better results in terms of minimum error indices (Mean Absolute Error and Mean Square Error) for the in-sample estimation. As new technology does not diffuse in all the regions of the world with the same speed due to different socio-economic factors, the lifespan distribution, which provides the probability of a certain quantity of computers to be considered as obsolete, is not adequately modeled in the literature. The time horizon for the forecasted quantities is 2014-2030, while the results show a very sharp increase in the USA and United Kingdom, due to the fact of decreasing computer lifespan and increasing sales.

Accurate estimation of isoelectric point of protein and peptide based on amino acid sequences

Motivation: In any macromolecular polyprotic system - for example protein, DNA or RNA - the isoelectric point - commonly referred to as the pI - can be defined as the point of singularity in a titration curve, corresponding to the solution pH value at which the net overall surface charge - and thus the electrophoretic mobility - of the ampholyte sums to zero. Different modern analytical biochemistry and proteomics methods depend on the isoelectric point as a principal feature for protein and peptide characterization. Protein separation by isoelectric point is a critical part of 2-D gel electrophoresis, a key precursor of proteomics, where discrete spots can be digested in-gel, and proteins subsequently identified by analytical mass spectrometry. Peptide fractionation according to their pI is also widely used in current proteomics sample preparation procedures previous to the LC-MS/MS analysis. Therefore accurate theoretical prediction of pI would expedite such analysis. While such pI calculation is widely used, it remains largely untested, motivating our efforts to benchmark pI prediction methods. Results: Using data from the database PIP-DB and one publically available dataset as our reference gold standard, we have undertaken the benchmarking of pI calculation methods. We find that methods vary in their accuracy and are highly sensitive to the choice of basis set. The machine-learning algorithms, especially the SVM-based algorithm, showed a superior performance when studying peptide mixtures. In general, learning-based pI prediction methods (such as Cofactor, SVM and Branca) require a large training dataset and their resulting performance will strongly depend of the quality of that data. In contrast with Iterative methods, machine-learning algorithms have the advantage of being able to add new features to improve the accuracy of prediction. Contact: yperez@ebi.ac.uk Availability and Implementation: The software and data are freely available at https://github.com/ypriverol/pIR. Supplementary information: Supplementary data are available at Bioinformatics online.

Development of safety performance functions for empirical Bayes estimation of crash reduction factors

Crash reduction factors (CRFs) are used to estimate the potential number of traffic crashes expected to be prevented from investment in safety improvement projects. The method used to develop CRFs in Florida has been based on the commonly used before-and-after approach. This approach suffers from a widely recognized problem known as regression-to-the-mean (RTM). The Empirical Bayes (EB) method has been introduced as a means to addressing the RTM problem. This method requires the information from both the treatment and reference sites in order to predict the expected number of crashes had the safety improvement projects at the treatment sites not been implemented. The information from the reference sites is estimated from a safety performance function (SPF), which is a mathematical relationship that links crashes to traffic exposure. The objective of this dissertation was to develop the SPFs for different functional classes of the Florida State Highway System. Crash data from years 2001 through 2003 along with traffic and geometric data were used in the SPF model development. SPFs for both rural and urban roadway categories were developed. The modeling data used were based on one-mile segments that contain homogeneous traffic and geometric conditions within each segment. Segments involving intersections were excluded. The scatter plots of data show that the relationships between crashes and traffic exposure are nonlinear, that crashes increase with traffic exposure in an increasing rate. Four regression models, namely, Poisson (PRM), Negative Binomial (NBRM), zero-inflated Poisson (ZIP), and zero-inflated Negative Binomial (ZINB), were fitted to the one-mile segment records for individual roadway categories. The best model was selected for each category based on a combination of the Likelihood Ratio test, the Vuong statistical test, and the Akaike's Information Criterion (AIC). The NBRM model was found to be appropriate for only one category and the ZINB model was found to be more appropriate for six other categories. The overall results show that the Negative Binomial distribution model generally provides a better fit for the data than the Poisson distribution model. In addition, the ZINB model was found to give the best fit when the count data exhibit excess zeros and over-dispersion for most of the roadway categories. While model validation shows that most data points fall within the 95% prediction intervals of the models developed, the Pearson goodness-of-fit measure does not show statistical significance. This is expected as traffic volume is only one of the many factors contributing to the overall crash experience, and that the SPFs are to be applied in conjunction with Accident Modification Factors (AMFs) to further account for the safety impacts of major geometric features before arriving at the final crash prediction. However, with improved traffic and crash data quality, the crash prediction power of SPF models may be further improved.

Tool cutting force modeling and wear estimation of micro -end-milling operations

The applications of micro-end-milling operations have increased recently. A Micro-End-Milling Operation Guide and Research Tool (MOGART) package has been developed for the study and monitoring of micro-end-milling operations. It includes an analytical cutting force model, neural network based data mapping and forecasting processes, and genetic algorithms based optimization routines. MOGART uses neural networks to estimate tool machinability and forecast tool wear from the experimental cutting force data, and genetic algorithms with the analytical model to monitor tool wear, breakage, run-out, cutting conditions from the cutting force profiles. ^ The performance of MOGART has been tested on the experimental data of over 800 experimental cases and very good agreement has been observed between the theoretical and experimental results. The MOGART package has been applied to the micro-end-milling operation study of Engineering Prototype Center of Radio Technology Division of Motorola Inc. ^

Tool cutting force modeling and wear estimation of micro-end-milling operations

The applications of micro-end-milling operations have increased recently. A Micro-End-Milling Operation Guide and Research Tool (MOGART) package has been developed for the study and monitoring of micro-end-milling operations. It includes an analytical cutting force model, neural network based data mapping and forecasting processes, and genetic algorithms based optimization routines. MOGART uses neural networks to estimate tool machinability and forecast tool wear from the experimental cutting force data, and genetic algorithms with the analytical model to monitor tool wear, breakage, run-out, cutting conditions from the cutting force profiles. The performance of MOGART has been tested on the experimental data of over 800 experimental cases and very good agreement has been observed between the theoretical and experimental results. The MOGART package has been applied to the micro-end-milling operation study of Engineering Prototype Center of Radio Technology Division of Motorola Inc.

Energy estimation of cosmic rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30-80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy-corrected for geometrical effects-is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.

Prospective Estimation of Radiation Dose and Image Quality for Optimized CT Performance

X-ray computed tomography (CT) is a non-invasive medical imaging technique that generates cross-sectional images by acquiring attenuation-based projection measurements at multiple angles. Since its first introduction in the 1970s, substantial technical improvements have led to the expanding use of CT in clinical examinations. CT has become an indispensable imaging modality for the diagnosis of a wide array of diseases in both pediatric and adult populations [1, 2]. Currently, approximately 272 million CT examinations are performed annually worldwide, with nearly 85 million of these in the United States alone [3]. Although this trend has decelerated in recent years, CT usage is still expected to increase mainly due to advanced technologies such as multi-energy [4], photon counting [5], and cone-beam CT [6].

Despite the significant clinical benefits, concerns have been raised regarding the population-based radiation dose associated with CT examinations [7]. From 1980 to 2006, the effective dose from medical diagnostic procedures rose six-fold, with CT contributing to almost half of the total dose from medical exposure [8]. For each patient, the risk associated with a single CT examination is likely to be minimal. However, the relatively large population-based radiation level has led to enormous efforts among the community to manage and optimize the CT dose.

As promoted by the international campaigns Image Gently and Image Wisely, exposure to CT radiation should be appropriate and safe [9, 10]. It is thus a responsibility to optimize the amount of radiation dose for CT examinations. The key for dose optimization is to determine the minimum amount of radiation dose that achieves the targeted image quality [11]. Based on such principle, dose optimization would significantly benefit from effective metrics to characterize radiation dose and image quality for a CT exam. Moreover, if accurate predictions of the radiation dose and image quality were possible before the initiation of the exam, it would be feasible to personalize it by adjusting the scanning parameters to achieve a desired level of image quality. The purpose of this thesis is to design and validate models to quantify patient-specific radiation dose prospectively and task-based image quality. The dual aim of the study is to implement the theoretical models into clinical practice by developing an organ-based dose monitoring system and an image-based noise addition software for protocol optimization.

More specifically, Chapter 3 aims to develop an organ dose-prediction method for CT examinations of the body under constant tube current condition. The study effectively modeled the anatomical diversity and complexity using a large number of patient models with representative age, size, and gender distribution. The dependence of organ dose coefficients on patient size and scanner models was further evaluated. Distinct from prior work, these studies use the largest number of patient models to date with representative age, weight percentile, and body mass index (BMI) range.

With effective quantification of organ dose under constant tube current condition, Chapter 4 aims to extend the organ dose prediction system to tube current modulated (TCM) CT examinations. The prediction, applied to chest and abdominopelvic exams, was achieved by combining a convolution-based estimation technique that quantifies the radiation field, a TCM scheme that emulates modulation profiles from major CT vendors, and a library of computational phantoms with representative sizes, ages, and genders. The prospective quantification model is validated by comparing the predicted organ dose with the dose estimated based on Monte Carlo simulations with TCM function explicitly modeled.

Chapter 5 aims to implement the organ dose-estimation framework in clinical practice to develop an organ dose-monitoring program based on a commercial software (Dose Watch, GE Healthcare, Waukesha, WI). In the first phase of the study we focused on body CT examinations, and so the patient’s major body landmark information was extracted from the patient scout image in order to match clinical patients against a computational phantom in the library. The organ dose coefficients were estimated based on CT protocol and patient size as reported in Chapter 3. The exam CTDIvol, DLP, and TCM profiles were extracted and used to quantify the radiation field using the convolution technique proposed in Chapter 4.

With effective methods to predict and monitor organ dose, Chapters 6 aims to develop and validate improved measurement techniques for image quality assessment. Chapter 6 outlines the method that was developed to assess and predict quantum noise in clinical body CT images. Compared with previous phantom-based studies, this study accurately assessed the quantum noise in clinical images and further validated the correspondence between phantom-based measurements and the expected clinical image quality as a function of patient size and scanner attributes.

Chapter 7 aims to develop a practical strategy to generate hybrid CT images and assess the impact of dose reduction on diagnostic confidence for the diagnosis of acute pancreatitis. The general strategy is (1) to simulate synthetic CT images at multiple reduced-dose levels from clinical datasets using an image-based noise addition technique; (2) to develop quantitative and observer-based methods to validate the realism of simulated low-dose images; (3) to perform multi-reader observer studies on the low-dose image series to assess the impact of dose reduction on the diagnostic confidence for multiple diagnostic tasks; and (4) to determine the dose operating point for clinical CT examinations based on the minimum diagnostic performance to achieve protocol optimization.

Chapter 8 concludes the thesis with a summary of accomplished work and a discussion about future research.

Estimation of Sample Size and Power For Quantile Regression

Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of the response, QR provides an alternative way to model the relationship between quantiles of the response and covariates. Therefore, QR can be widely used to solve problems in econometrics, environmental sciences and health sciences. Sample size is an important factor in the planning stage of experimental design and observational studies. In ordinary linear regression, sample size may be determined based on either precision analysis or power analysis with closed form formulas. There are also methods that calculate sample size based on precision analysis for QR like C.Jennen-Steinmetz and S.Wellek (2005). A method to estimate sample size for QR based on power analysis was proposed by Shao and Wang (2009). In this paper, a new method is proposed to calculate sample size based on power analysis under hypothesis test of covariate effects. Even though error distribution assumption is not necessary for QR analysis itself, researchers have to make assumptions of error distribution and covariate structure in the planning stage of a study to obtain a reasonable estimate of sample size. In this project, both parametric and nonparametric methods are provided to estimate error distribution. Since the method proposed can be implemented in R, user is able to choose either parametric distribution or nonparametric kernel density estimation for error distribution. User also needs to specify the covariate structure and effect size to carry out sample size and power calculation. The performance of the method proposed is further evaluated using numerical simulation. The results suggest that the sample sizes obtained from our method provide empirical powers that are closed to the nominal power level, for example, 80%.

A probabilistic approach to the estimation of regional photovoltaic power generation using meteorological data

In Germany the upscaling algorithm is currently the standard approach for evaluating the PV power produced in a region. This method involves spatially interpolating the normalized power of a set of reference PV plants to estimate the power production by another set of unknown plants. As little information on the performances of this method could be found in the literature, the first goal of this thesis is to conduct an analysis of the uncertainty associated to this method. It was found that this method can lead to large errors when the set of reference plants has different characteristics or weather conditions than the set of unknown plants and when the set of reference plants is small. Based on these preliminary findings, an alternative method is proposed for calculating the aggregate power production of a set of PV plants. A probabilistic approach has been chosen by which a power production is calculated at each PV plant from corresponding weather data. The probabilistic approach consists of evaluating the power for each frequently occurring value of the parameters and estimating the most probable value by averaging these power values weighted by their frequency of occurrence. Most frequent parameter sets (e.g. module azimuth and tilt angle) and their frequency of occurrence have been assessed on the basis of a statistical analysis of parameters of approx. 35 000 PV plants. It has been found that the plant parameters are statistically dependent on the size and location of the PV plants. Accordingly, separate statistical values have been assessed for 14 classes of nominal capacity and 95 regions in Germany (two-digit zip-code areas). The performances of the upscaling and probabilistic approaches have been compared on the basis of 15 min power measurements from 715 PV plants provided by the German distribution system operator LEW Verteilnetz. It was found that the error of the probabilistic method is smaller than that of the upscaling method when the number of reference plants is sufficiently large (>100 reference plants in the case study considered in this chapter). When the number of reference plants is limited (<50 reference plants for the considered case study), it was found that the proposed approach provides a noticeable gain in accuracy with respect to the upscaling method.