BIAS-CORRECTED MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF THE WEIGHTED LINDLEY DISTRIBUTION

This report discusses the calculation of analytic second-order bias techniques for the maximum likelihood estimates (for short, MLEs) of the unknown parameters of the distribution in quality and reliability analysis. It is well-known that the MLEs are widely used to estimate the unknown parameters of the probability distributions due to their various desirable properties; for example, the MLEs are asymptotically unbiased, consistent, and asymptotically normal. However, many of these properties depend on an extremely large sample sizes. Those properties, such as unbiasedness, may not be valid for small or even moderate sample sizes, which are more practical in real data applications. Therefore, some bias-corrected techniques for the MLEs are desired in practice, especially when the sample size is small. Two commonly used popular techniques to reduce the bias of the MLEs, are ‘preventive’ and ‘corrective’ approaches. They both can reduce the bias of the MLEs to order O(n−2), whereas the ‘preventive’ approach does not have an explicit closed form expression. Consequently, we mainly focus on the ‘corrective’ approach in this report. To illustrate the importance of the bias-correction in practice, we apply the bias-corrected method to two popular lifetime distributions: the inverse Lindley distribution and the weighted Lindley distribution. Numerical studies based on the two distributions show that the considered bias-corrected technique is highly recommended over other commonly used estimators without bias-correction. Therefore, special attention should be paid when we estimate the unknown parameters of the probability distributions under the scenario in which the sample size is small or moderate.

Positron Emission Tomography (PET) Tumor Segmentation and Quantification: Development of New Algorithms

Tumor functional volume (FV) and its mean activity concentration (mAC) are the quantities derived from positron emission tomography (PET). These quantities are used for estimating radiation dose for a therapy, evaluating the progression of a disease and also use it as a prognostic indicator for predicting outcome. PET images have low resolution, high noise and affected by partial volume effect (PVE). Manually segmenting each tumor is very cumbersome and very hard to reproduce. To solve the above problem I developed an algorithm, called iterative deconvolution thresholding segmentation (IDTS) algorithm; the algorithm segment the tumor, measures the FV, correct for the PVE and calculates mAC. The algorithm corrects for the PVE without the need to estimate camera’s point spread function (PSF); also does not require optimizing for a specific camera. My algorithm was tested in physical phantom studies, where hollow spheres (0.5-16 ml) were used to represent tumors with a homogeneous activity distribution. It was also tested on irregular shaped tumors with a heterogeneous activity profile which were acquired using physical and simulated phantom. The physical phantom studies were performed with different signal to background ratios (SBR) and with different acquisition times (1-5 min). The algorithm was applied on ten clinical data where the results were compared with manual segmentation and fixed percentage thresholding method called T50 and T60 in which 50% and 60% of the maximum intensity respectively is used as threshold. The average error in FV and mAC calculation was 30% and -35% for 0.5 ml tumor. The average error FV and mAC calculation were ~5% for 16 ml tumor. The overall FV error was ~10% for heterogeneous tumors in physical and simulated phantom data. The FV and mAC error for clinical image compared to manual segmentation was around -17% and 15% respectively. In summary my algorithm has potential to be applied on data acquired from different cameras as its not dependent on knowing the camera’s PSF. The algorithm can also improve dose estimation and treatment planning.

Estimation of hexenuronic acids and kappa number in kraft pulps of Eucalyptus globulus by Fourier transform near infrared spectroscopy and multivariate analysis

Fourier transform near infrared (FT-NIR) spectroscopy was evaluated as an analytical too[ for monitoring residual Lignin, kappa number and hexenuronic acids (HexA) content in kraft pulps of Eucalyptus globulus. Sets of pulp samples were prepared under different cooking conditions to obtain a wide range of compound concentrations that were characterised by conventional wet chemistry analytical methods. The sample group was also analysed using FT-NIR spectroscopy in order to establish prediction models for the pulp characteristics. Several models were applied to correlate chemical composition in samples with the NIR spectral data by means of PCR or PLS algorithms. Calibration curves were built by using all the spectral data or selected regions. Best calibration models for the quantification of lignin, kappa and HexA were proposed presenting R-2 values of 0.99. Calibration models were used to predict pulp titers of 20 external samples in a validation set. The lignin concentration and kappa number in the range of 1.4-18% and 8-62, respectively, were predicted fairly accurately (standard error of prediction, SEP 1.1% for lignin and 2.9 for kappa). The HexA concentration (range of 5-71 mmol kg(-1) pulp) was more difficult to predict and the SEP was 7.0 mmol kg(-1) pulp in a model of HexA quantified by an ultraviolet (UV) technique and 6.1 mmol kg(-1) pulp in a model of HexA quantified by anion-exchange chromatography (AEC). Even in wet chemical procedures used for HexA determination, there is no good agreement between methods as demonstrated by the UV and AEC methods described in the present work. NIR spectroscopy did provide a rapid estimate of HexA content in kraft pulps prepared in routine cooking experiments.

Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

Bedside estimation of recruitable alveolar collapse and hyperdistension by electrical impedance tomography

To present a novel algorithm for estimating recruitable alveolar collapse and hyperdistension based on electrical impedance tomography (EIT) during a decremental positive end-expiratory pressure (PEEP) titration. Technical note with illustrative case reports. Respiratory intensive care unit. Patients with acute respiratory distress syndrome. Lung recruitment and PEEP titration maneuver. Simultaneous acquisition of EIT and X-ray computerized tomography (CT) data. We found good agreement (in terms of amount and spatial location) between the collapse estimated by EIT and CT for all levels of PEEP. The optimal PEEP values detected by EIT for patients 1 and 2 (keeping lung collapse < 10%) were 19 and 17 cmH(2)O, respectively. Although pointing to the same non-dependent lung regions, EIT estimates of hyperdistension represent the functional deterioration of lung units, instead of their anatomical changes, and could not be compared directly with static CT estimates for hyperinflation. We described an EIT-based method for estimating recruitable alveolar collapse at the bedside, pointing out its regional distribution. Additionally, we proposed a measure of lung hyperdistension based on regional lung mechanics.

Concurreny based transition refinement for the verification of distributed algorithms

We suggest a new notion of behaviour preserving transition refinement based on partial order semantics. This notion is called transition refinement. We introduced transition refinement for elementary (low-level) Petri Nets earlier. For modelling and verifying complex distributed algorithms, high-level (Algebraic) Petri nets are usually used. In this paper, we define transition refinement for Algebraic Petri Nets. This notion is more powerful than transition refinement for elementary Petri nets because it corresponds to the simultaneous refinement of several transitions in an elementary Petri net. Transition refinement is particularly suitable for refinement steps that increase the degree of distribution of an algorithm, e.g. when synchronous communication is replaced by asynchronous message passing. We study how to prove that a replacement of a transition is a transition refinement.

Estimation of body water compartments in cirrhosis by multiple-frequency bioelectrical-impedance analysis

Estimation of total body water by measuring bioelectrical impedance at a fixed frequency of 50 kHz is useful in assessing body composition in healthy populations. However, in cirrhosis, the distribution of total body water between the extracellular and intracellular compartments is of greater clinical importance. We report an evaluation of a new multiple-frequency bioelectrical-impedance analysis technique (MFBIA) that may quantify the distribution of total body water in cirrhosis. In 21 cirrhotic patients and 21 healthy control subjects, impedance to the Row of current was measured at frequencies ranging from 4 to 1012 kHz. These measurements were used to estimate body water compartments and then compared with total body water and extracellular water determined by isotope methodology. In cirrhotic patients, extracellular water and total body water (as determined by isotope methods) were well predicted by MFBIA (r = 0.73 and 0.89, respectively).;However, the 95% confidence intervals of the limits of agreement between MFBIA and the isotope methods were +/- 14% and +/-9% for cirrhotics (extracellular water and total body water, respectively) and +/-9% and +/-9% for cirrhotics without ascites. The 95% confidence intervals estimated from the control group were +/-10% and +/-5% for extracellular water and total body water, respectively. Thus, despite strong correlations between MFBIA and isotope measurements, the relatively large limits of agreement with accepted techniques suggest that the MFBIA technique requires further refinement before it can be routinely used to determine the nutritional assessment of individual cirrhotic patients. Nutrition 2001,17.31-34. (C)Elsevier Science Inc. 2001.

Estimation of pollutant partition in sandy soils with different water contents

The objectives of this work were: (1) to identify an isotherm model to relate the contaminant contents in the gas phase with those in the solid and non-aqueous liquid phases; (2) to develop a methodology for the estimation of the contaminant distribution in the different phases of the soil; and (3) to evaluate the influence of soil water content on the contaminant distribution in soil. For sandy soils with negligible contents of clay and natural organic matter, contaminated with benzene, toluene, ethylbenzene, xylene, trichloroethylene (TCE), and perchloroethylene (PCE), it was concluded that: (1) Freundlich’s model showed to be adequate to relate the contaminant contents in the gas phase with those in the solid and non-aqueous liquid phases; (2) the distribution of the contaminants in the different phases present in the soil could be estimated with differences lower than 10% for 83% of the cases; and (3) an increase of the soil water content led to a decrease of the amount of contaminant in the solid and non-aqueous liquid phases, increasing the amount in the other phases.

Estimation of vegetation carbon stock in Portugal using land use/ land cover data

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies

Estimation of signal subspace on hyperspectral data

Dimensionality reduction plays a crucial role in many hyperspectral data processing and analysis algorithms. This paper proposes a new mean squared error based approach to determine the signal subspace in hyperspectral imagery. The method first estimates the signal and noise correlations matrices, then it selects the subset of eigenvalues that best represents the signal subspace in the least square sense. The effectiveness of the proposed method is illustrated using simulated and real hyperspectral images.

Nonparametric estimation of the survival function for ordered multivariate failure time data: a comparative study

In longitudinal studies of disease, patients may experience several events through a follow-up period. In these studies, the sequentially ordered events are often of interest and lead to problems that have received much attention recently. Issues of interest include the estimation of bivariate survival, marginal distributions and the conditional distribution of gap times. In this work we consider the estimation of the survival function conditional to a previous event. Different nonparametric approaches will be considered for estimating these quantities, all based on the Kaplan-Meier estimator of the survival function. We explore the finite sample behavior of the estimators through simulations. The different methods proposed in this article are applied to a data set from a German Breast Cancer Study. The methods are used to obtain predictors for the conditional survival probabilities as well as to study the influence of recurrence in overall survival.

Estimation of glomerular filtration rate in hospitalised patients: are we overestimating renal function?

QUESTIONS UNDER STUDY AND PRINCIPLES: Estimating glomerular filtration rate (GFR) in hospitalised patients with chronic kidney disease (CKD) is important for drug prescription but it remains a difficult task. The purpose of this study was to investigate the reliability of selected algorithms based on serum creatinine, cystatin C and beta-trace protein to estimate GFR and the potential added advantage of measuring muscle mass by bioimpedance. In a prospective unselected group of patients hospitalised in a general internal medicine ward with CKD, GFR was evaluated using inulin clearance as the gold standard and the algorithms of Cockcroft, MDRD, Larsson (cystatin C), White (beta-trace) and MacDonald (creatinine and muscle mass by bioimpedance). 69 patients were included in the study. Median age (interquartile range) was 80 years (73-83); weight 74.7 kg (67.0-85.6), appendicular lean mass 19.1 kg (14.9-22.3), serum creatinine 126 μmol/l (100-149), cystatin C 1.45 mg/l (1.19-1.90), beta-trace protein 1.17 mg/l (0.99-1.53) and GFR measured by inulin 30.9 ml/min (22.0-43.3). The errors in the estimation of GFR and the area under the ROC curves (95% confidence interval) relative to inulin were respectively: Cockcroft 14.3 ml/min (5.55-23.2) and 0.68 (0.55-0.81), MDRD 16.3 ml/min (6.4-27.5) and 0.76 (0.64-0.87), Larsson 12.8 ml/min (4.50-25.3) and 0.82 (0.72-0.92), White 17.6 ml/min (11.5-31.5) and 0.75 (0.63-0.87), MacDonald 32.2 ml/min (13.9-45.4) and 0.65 (0.52-0.78). Currently used algorithms overestimate GFR in hospitalised patients with CKD. As a consequence eGFR targeted prescriptions of renal-cleared drugs, might expose patients to overdosing. The best results were obtained with the Larsson algorithm. The determination of muscle mass by bioimpedance did not provide significant contributions.

Estimation of the lateral correlation structure of subsurface water content from surface-based ground-penetrating radar reflection images

Over the past decade, significant interest has been expressed in relating the spatial statistics of surface-based reflection ground-penetrating radar (GPR) data to those of the imaged subsurface volume. A primary motivation for this work is that changes in the radar wave velocity, which largely control the character of the observed data, are expected to be related to corresponding changes in subsurface water content. Although previous work has indeed indicated that the spatial statistics of GPR images are linked to those of the water content distribution of the probed region, a viable method for quantitatively analyzing the GPR data and solving the corresponding inverse problem has not yet been presented. Here we address this issue by first deriving a relationship between the 2-D autocorrelation of a water content distribution and that of the corresponding GPR reflection image. We then show how a Bayesian inversion strategy based on Markov chain Monte Carlo sampling can be used to estimate the posterior distribution of subsurface correlation model parameters that are consistent with the GPR data. Our results indicate that if the underlying assumptions are valid and we possess adequate prior knowledge regarding the water content distribution, in particular its vertical variability, this methodology allows not only for the reliable recovery of lateral correlation model parameters but also for estimates of parameter uncertainties. In the case where prior knowledge regarding the vertical variability of water content is not available, the results show that the methodology still reliably recovers the aspect ratio of the heterogeneity.

Nonparametric estimation of Value-at-Risk

A method to estimate an extreme quantile that requires no distributional assumptions is presented. The approach is based on transformed kernel estimation of the cumulative distribution function (cdf). The proposed method consists of a double transformation kernel estimation. We derive optimal bandwidth selection methods that have a direct expression for the smoothing parameter. The bandwidth can accommodate to the given quantile level. The procedure is useful for large data sets and improves quantile estimation compared to other methods in heavy tailed distributions. Implementation is straightforward and R programs are available.

Estimation of the real population and its impact on the utilisation of healthcare services in Mediterranean resort regions: an ecological study.

BACKGROUND The demographic structure has a significant influence on the use of healthcare services, as does the size of the population denominators. Very few studies have been published on methods for estimating the real population such as tourist resorts. The lack of information about these problems means there is a corresponding lack of information about the behaviour of populational denominators (the floating population or tourist load) and the effect of this on the use of healthcare services. The objectives of the study were: a) To determine the Municipal Solid Waste (MSW) ratio, per person per day, among populations of known size; b) to estimate, by means of this ratio, the real population in an area where tourist numbers are very significant; and c) to determine the impact on the utilisation of hospital emergency healthcare services of the registered population, in comparison to the non-resident population, in two areas where tourist numbers are very significant. METHODS An ecological study design was employed. We analysed the Healthcare Districts of the Costa del Sol and the island of Menorca. Both are Spanish territories in the Mediterranean region. RESULTS In the two areas analysed, the correlation coefficient between the MSW ratio and admissions to hospital emergency departments exceeded 0.9, with p < 0.001. On the basis of MSW generation ratios, obtained for a control zone and also measured in neighbouring countries, we estimated the real population. For the summer months, when tourist activity is greatest and demand for emergency healthcare at hospitals is highest, this value was found to be double that of the registered population. CONCLUSION The MSW indicator, which is both ecological and indirect, can be used to estimate the real population in areas where population levels vary significantly during the year. This parameter is of interest in planning and dimensioning the provision of healthcare services.