Modified confidence intervals for the Mahalanobis distance

Reiser (2001) proposes a method of forming confidence interval for a Mahalanobis distance that yields intervals which have exactly the nominal coverage, but sometimes the interval is View the MathML source (0,0). We consider the case where Mahalanobis distance quantifies the difference between an individual and a population mean, and suggest a modification that avoids implausible intervals

Elicitation of Subjective Probability Distributions

To incorporate expert opinion into a Bayesian analysis, it must be quantified as a prior distribution through an elicitation process that asks the expert meaningful questions whose answers determine this distribution. The aim of this thesis is to fill some gaps in the available techniques for eliciting prior distributions for Generalized Linear Models (GLMs) and multinomial models. A general method for quantifying opinion about GLMs was developed in Garthwaite and Al-Awadhi (2006). They model the relationship between each continuous predictor and the dependant variable as a piecewise-linear function with a regression coefficient at each of its dividing points. However, coefficients were assumed a priori independent if associated with different predictors. We relax this simplifying assumption and propose three new methods for eliciting positive-definite variance-covariance matrices of a multivariate normal prior distribution. In addition, we extend the method of Garthwaite and Dickey (1988) for eliciting an inverse chi-squared conjugate prior for the error variance in normal linear models. We also propose a novel method for eliciting a lognormal prior distribution for the scale parameter of a gamma GLM. For multinomial models, novel methods are proposed that quantify expert opinion about a conjugate Dirichlet distribution and, additionally, about three more general and flexible prior distributions. First, an elicitation method is proposed for the generalized Dirichlet distribution that was introduced by Connor and Mosimann (1969). Second, a method is developed for eliciting the Gaussian copula as a multivariate distribution with marginal beta priors. Third, a further novel method is constructed that quantifies expert opinion about the most flexible alternate prior, the logistic normal distribution (Aitchison, 1986). This third method is extended to the case of multinomial models with explanatory covariates. All proposed methods in this thesis are designed to be used with interactive Prior Elicitation Graphical Software (PEGS) that is freely available at http://statistics.open.ac.uk/elicitation

SAR Sentinel 1 imaging and detection of palaeo-landscape features in the mediterranean area

The use of satellite radar in landscape archaeology offers great potential for manifold applications, such as the detection of ancient landscape features and anthropogenic transformations. Compared to optical data, the use and interpretation of radar imaging for archaeological investigations is more complex, due to many reasons including that: (i) ancient landscape features and anthropogenic transformations provide subtle signals, which are (ii) often covered by noise; and, (iii) only detectable in specific soil characteristics, moisture content, vegetation phenomenology, and meteorological parameters. In this paper, we assessed the capability of SAR Sentinel 1 in the imaging and detection of palaeo-landscape features in the Mediterranean area of Tavoliere delle Puglie. For the purpose of our investigations, a significant test site (larger than 200 km2) was selected in the Foggia Province (South of Italy) as this area has been characterized for millennia by human frequentation starting from (at least) the Neolithic. The results from the Sentinel 1 (S-1) data were successfully compared with independent data sets, and the comparison clearly showed an excellent match between the S-1 based outputs and ancient anthropogenic transformations and landscape features

Eliciting Dirichlet and Gaussian copula prior distributions for multinomial models

In this paper, we propose novel methods of quantifying expert opinion about prior distributions for multinomial models. Two different multivariate priors are elicited using median and quartile assessments of the multinomial probabilities. First, we start by eliciting a univariate beta distribution for the probability of each category. Then we elicit the hyperparameters of the Dirichlet distribution, as a tractable conjugate prior, from those of the univariate betas through various forms of reconciliation using least-squares techniques. However, a multivariate copula function will give a more flexible correlation structure between multinomial parameters if it is used as their multivariate prior distribution. So, second, we use beta marginal distributions to construct a Gaussian copula as a multivariate normal distribution function that binds these marginals and expresses the dependence structure between them. The proposed method elicits a positive-definite correlation matrix of this Gaussian copula. The two proposed methods are designed to be used through interactive graphical software written in Java

BIMAM—a tool for imputing variables missing across datasets using a Bayesian imputation and analysis model

Motivation Combination of multiple datasets is routine in modern epidemiology. However, studies may have measured different sets of variables; this is often inefficiently dealt with by excluding studies or dropping variables. Multilevel multiple imputation methods to impute these ‘systematically’ missing data (as opposed to ‘sporadically’ missing data within a study) are available, but problems may arise when many random effects are needed to allow for heterogeneity across studies. We show that the Bayesian IMputation and Analysis Model (BIMAM) implemented in our tool works well in this situation. General features BIMAM performs imputation and analysis simultaneously. It imputes both binary and continuous systematically and sporadically missing data, and analyses binary and continuous outcomes. BIMAM is a user-friendly, freely available tool that does not require knowledge of Bayesian methods. BIMAM is an R Shiny application. It is downloadable to a local machine and it automatically installs the required freely available packages (R packages, including R2MultiBUGS and MultiBUGS). Availability BIMAM is available at [www.alecstudy.org/bimam]

Impact of Tumor Burden Score on Conditional Survival after Curative-Intent Resection for Hepatocellular Carcinoma: A Multi-Institutional Analysis

Background: The impact of tumor burden score (TBS) on conditional survival (CS) among patients undergoing curative-intent resection of hepatocellular carcinoma (HCC) has not been examined to date. Methods: Patients who underwent liver resection of HCC between 2000 and 2017 were identified from a multi-institutional database. The impact of TBS and other clinicopathologic factors on 3-year conditional survival (CS3) was examined. Results: Among 1,040 patients, 263 (25.3%) patients had low TBS, 668 (64.2%) had medium TBS and 109 (10.5%) had high TBS. TBS was strongly associated with OS; 5-year OS was 39.0% among patients with high TBS compared with 61.1% and 79.4% among patients with medium and low TBS, respectively (p < 0.001). While actuarial survival decreased as time elapsed from resection, CS increased over time irrespective of TBS. The largest differences between 3-year actuarial survival and CS3 were noted among patients with high TBS (5-years postoperatively; CS3: 78.7% vs. 3-year actuarial survival: 30.7%). The effect of adverse clinicopathologic factors including high TBS, poor/undifferentiated tumor grade, microvascular invasion, liver capsule involvement, and positive margins on prognosis decreased over time. Conclusions: CS rates among patients who underwent resection for HCC increased as patients survived additional years, irrespective of TBS. CS estimates can be used to provide important dynamic information relative to the changing survival probability after resection of HCC.info:eu-repo/semantics/publishedVersio

Big Earth Data for Cultural Heritage in the Copernicus Era

Digital data is stepping in its golden age characterized by an increasing growth of both classical and emerging big earth data along with trans- and multidisciplinary methodological approaches and services addressed to the study, preservation and sustainable exploitation of cultural heritage (CH). The availability of new digital technologies has opened new possibilities, unthinkable only a few years ago for cultural heritage. The currently available digital data, tools and services with particular reference to Copernicus initiatives make possible to characterize and understand the state of conservation of CH for preventive restoration and opened up a frontier of possibilities for the discovery of archaeological sites from above and also for supporting their excavation, monitoring and preservation. The different areas of intervention require the availability and integration of rigorous information from different sources for improving knowledge and interpretation, risk assessment and management in order to make more successful all the actions oriented to the preservation of cultural properties. One of the biggest challenges is to fully involve the citizen also from an emotional point of view connecting “pixels with people” and “bridging” remote sensing and social sensing

Prevalence and Population Attributable Risk for Chronic Airflow Obstruction in a Large Multinational Study

Rationale: The Global Burden of Disease programme identified smoking, and ambient and household air pollution as the main drivers of death and disability from Chronic Obstructive Pulmonary Disease (COPD).Objective: To estimate the attributable risk of chronic airflow obstruction (CAO), a quantifiable characteristic of COPD, due to several risk factors.Methods: The Burden of Obstructive Lung Disease study is a cross-sectional study of adults, aged≥40, in a globally distributed sample of 41 urban and rural sites. Based on data from 28,459 participants, we estimated the prevalence of CAO, defined as a post-bronchodilator one-second forced expiratory volume to forced vital capacity ratio Measurements and Main Results: Mean prevalence of CAO was 11.2% in men and 8.6% in women. Mean PAR for smoking was 5.1% in men and 2.2% in women. The next most influential risk factors were poor education levels, working in a dusty job for ≥10 years, low body mass index (BMI), and a history of tuberculosis. The risk of CAO attributable to the different risk factors varied across sites.Conclusions: While smoking remains the most important risk factor for CAO, in some areas poor education, low BMI and passive smoking are of greater importance. Dusty occupations and tuberculosis are important risk factors at some sites

On eliciting expert opinion in generalized linear models

Suitable elicitation methods play a key role in Bayesian analysis of generalized linear models (GLMs) by obtaining and including expert knowledge as a prior distribution for the model parameters. Some elicitation methods for GLMs available in the literature focus mainly on logistic regression. A more general elicitation method of quantifying opinion about any GLM was developed in Garthwaite and Al-Awadhi (2006). The relationship between each continuous predictor and the dependant variable was modeled as a piecewise-linear function and each of its dividing points is accompanied with a regression coefficient. However, a simplifying assumption was made regarding independence between these coefficients, in the sense that regression coefficients were a priori independent if associated with different predictors. In this current research we relax the independence assumption between coefficients of different variables. In this case the variance-covariance matrix of the prior distribution is no longer block-diagonal. A method of elicitation for this more complex case is given and it is shown that the resulting covariance matrix is positive-definite. The method was designed to be used with the aid of interactive graphical software. It has been used in practical case studies to quantify the opinions of ecologists and medical doctors (Al-Awadhi and Garthwaite (2006); Garthwaite, Chilcott, Jenkinson, and Tappenden (2008)). The software is being revised and extended further in this research to handle the case of GLM with correlated pairs of covariates

Two-Term Edgeworth Expansions for the Classes of U- and V-statistics

Much effort has been devoted to deriving Edgeworth expansions for various classes of statistics that are asymptotically normally distributed, with derivations tailored to the individual structure of each class. Expansions with smaller error rates are needed for more accurate statistical inference. Two such Edgeworth expansions are derived analytically in this paper. One is a two-term expansion for the standardized U-statistic of order m, m ⩾ 3, with an error rate o(n− 1). The other is an expansion with the same error rate for the distribution of the standardized V-statistic of the same order. In deriving the Edgeworth expansion, we made use of the close connection between the V- and U-statistics, which permits to first derive the needed expansion for the related U-statistic, then extend it to the V-statistic, taking into consideration the estimation of all difference terms between the two statistics