Papers by Priyantha Wijayatunga
Journal of the Royal Statistical Society, Feb 14, 2023
arXiv (Cornell University), Apr 21, 2018
Journal of the Royal Statistical Society Series B: Statistical Methodology
Statistical uncertainty in (an estimate of) a parameter of a probability distribution is due to m... more Statistical uncertainty in (an estimate of) a parameter of a probability distribution is due to missing (unseen) observations (when it is estimated), as authors have noted. We can think that an estimate of the parameter has the maximal uncertainty when no observation is used for it, and no uncertainty when all possible observations are used for it. For example, in Bayesian sense, for a Bernoulli parameter, Beta distribution with parameter values α = 1 and β = 1 represents the full uncertainty. If observation counts are infinite, i.e., α and β are infinite, then there is no uncertainty. The uncertainty of the parameter estimate may be vanished when imputed or really observed data counts used for it are infinite, but the two estimates may converge to different values where the latter is the true value. But unfortunately we often do not have the chance to get it. So, it is not possible to eliminate the uncertainty correctly, i.e., while obtaining the true limiting value for the estimate, by imputing some observations given that some other observations are unknown. This is because
Journal of the Royal Statistical Society Series A: Statistics in Society
HAL (Le Centre pour la Communication Scientifique Directe), May 1, 2018
Measuring dependence among random variables can be an important aspect of empirical data analysis... more Measuring dependence among random variables can be an important aspect of empirical data analysis and, statistical modeling and inference. Our recent proposal of a generalization of well-known Pearson's correlation coefficient for measuring non-linear dependencies is reviewed. We emphasize that if one wants to have a general measure of degree of dependence then, ideally, the conceptual definition of the Pearson's correlation coefficient should be followed. It is expressed as a ratio of dependence of interest to full linear dependence, in terms of Euclidean type distances among probability distributions/densities. A generalization of it should use a well-behaved distance among probability distributions/densities, such as a metric in the continuum of them, along with consideration of non-linear dependencies. We have proposed to use socalled Hellinger distance metric for the purpose. Along with some future research directions, we discuss some of the advantages of our proposed general measure. Here the discussion is without any mathematical details, thus reaching a wider readership. Our objective is to present some arguments of how to measure dependencies generally, and to make some remarks on our generalization, that may lead to new turns in the research directions of the dependence measures in the future.
HAL (Le Centre pour la Communication Scientifique Directe), Jan 14, 2022
Prevalence, sensitivity, specificity and OR of numbers of RF isotypes, alone and/or in combinatio... more Prevalence, sensitivity, specificity and OR of numbers of RF isotypes, alone and/or in combination with ten different ACPA specificities, anti-CCP2 antibodies and anti-carbamylated protein antibodies in pre-symptomatic individuals and population controls. (DOCX 17kb)
Journal of the Royal Statistical Society Series A: Statistics in Society, 2017
Summary Decisions in statistical data analysis are often justified, criticized or avoided by usin... more Summary Decisions in statistical data analysis are often justified, criticized or avoided by using concepts of objectivity and subjectivity. We argue that the words ‘objective’ and ‘subjective’ in statistics discourse are used in a mostly unhelpful way, and we propose to replace each of them with broader collections of attributes, with objectivity replaced by transparency, consensus, impartiality and correspondence to observable reality, and subjectivity replaced by awareness of multiple perspectives and context dependence. Together with stability, these make up a collection of virtues that we think is helpful in discussions of statistical foundations and practice. The advantage of these reformulations is that the replacement terms do not oppose each other and that they give more specific guidance about what statistical science strives to achieve. Instead of debating over whether a given statistical method is subjective or objective (or normatively debating the relative merits of su...
International Journal of Business Intelligence and Data Mining, 2006
Amyloid, 2011
Recent studies of liver transplanted (LTx) familial amyloidotic polyneuropathy (FAP) patients hav... more Recent studies of liver transplanted (LTx) familial amyloidotic polyneuropathy (FAP) patients have shown a progression of cardiomyopathy in some patients after LTx, but knowledge of the underlying factors remains limited. Seventy-five patients, who had undergone LTx from 1996 to 2008, were included. They had all been examined by echocardiography 1-16 months before LTx. Fifty-four had been re-examined 7-34 months, and forty-two 36-137 months after LTx. A significant increase in interventricular septum (IVS) thickness occurred after LTx (p < 0.01), particularly in males (p = 0.002) and late onset patients (p = 0.003). The development of post-LTx cardiomyopathy was related to patient's age at onset of the disease, male gender and pre-LTx IVS thickness. On multivariate regression analysis, however, age at onset was the only significant predictor for the development of cardiomyopathy (odds ratio = 1.14, 95% confident interval 1.01-1.30, p = 0.04). An increase of IVS thickness can be observed in FAP patients after LTx. Age at onset of the disease is the main predictor for increased IVS thickness and for the development of cardiomyopathy after liver transplantation.
Journal of Mathematics Research, 2015
Propensity scores are often used for stratification of treatment and control groups of subjects i... more Propensity scores are often used for stratification of treatment and control groups of subjects in observational data to remove confounding bias when estimating of causal effect of the treatment on an outcome in so-called potential outcome causal modeling framework. In this article, we try to get some insights into basic behavior of the propensity scores in a probabilistic sense. We do a simple analysis of their usage confining to the case of discrete confounding covariates and outcomes. While making clear about behavior of the propensity score our analysis shows how the so-called prognostic score can be derived simultaneously. However the prognostic score is derived in a limited sense in the current literature whereas our derivation is more general and shows all possibilities of having the score. And we call it outcome score. We argue that application of both the propensity score and the outcome score is the most efficient way for reduction of dimension in the confounding covari...
Journal of the Royal Statistical Society Series A: Statistics in Society, 2019
I very much welcome this collection of insightful and complementary papers, Well-designed visuali... more I very much welcome this collection of insightful and complementary papers, Well-designed visualizations can add value both to exploratory analysis by revealing structure in a data set, and to confirmatory analysis as effective communication tools. On the first point, the papers by Castruccio, Genton and Sun, and by Bowman demonstrate imaginative use of animation and colour to capture variation over time, space and in distribution. A gentle warning about the use of sophisticated visualizations such as these is that their beauty can be beguiling. A consequent risk is that the inexperienced user may pay insufficient attention to the basics. At the meeting, I showed an example from Cleveland (1994) in which changing the aspect ratio of a simple line plot can hide or reveal the typically asymmetric shape of the quasi-cyclic variations in annual sunspot activity. The simple messages in Cleveland (1994), and in Cox (1978), are as relevant today as when they were written. On the second point, an important question is: communication to whom? The paper by Gabry and his colleagues focused primarily on self-communication, i.e. on providing feedback to the statistician during the various stages of a Bayesian analysis. As someone who is unconvinced that Bayesian inference should be used routinely, I found their discussion and example of prior predictive distributions striking in two ways. On the one hand, the demonstration that priors conventionally accepted as vague can induce implausible priors for the data is salutary. On the other, if you massage your prior until it generates realizations that are concentrated (to a greater or lesser extent) around the data and then 'turn the Bayesian handle', in what sense is your inference Bayesian? Other potential audiences for statistical visualizations include policy makers, public sector workers and the general public. In my own work with colleagues at Lancaster and elsewhere on prevalence mapping, we advocate the use of predictive probability mapping for communicating uncertainty to non-statisticians of whatever hue. This consists of plotting at each location of the map the predictive probability that local prevalence exceeds a user-specified threshold. Fig. 1 shows an example of predictive probability mapping, taken from an ongoing multinational programme for the control of onchocerciasis (river blindness) in sub-Saharan Africa (Zoure et al., 2014). The programme specifies that areas with prevalence greater than 20% should be prioritized for mass distribution of prophylactic medication. Accordingly, Fig. 1(b) maps the predictive probability that this criterion is met, based on a generalized linear geostatistical model (Diggle et al., 1998) fitted to empirical prevalence data obtained from the locations shown on the map. Figs 1(a) and 1(c) show the corresponding maps using a more stringent (10%) or a more relaxed (30%) prevalence threshold for prioritization. We draw two conclusions. Firstly, the different implications for how much of the country should be prioritized for treatment under different prevalence threshold criteria are inescapable. Secondly, the 20% exceedance map forces the reader to recognize that in some areas we simply do not know whether the prioritization criterion has been met. At the meeting, I also showed an animation, by Dr Emanuele Giorgi, of predictive probability exceedance mapping for malaria prevalence in Chikwawa, southern Malawi, over a 3-year period. This can be viewed at http://www.lancaster.ac.uk./staff/giorgi/malaria/. It shows very clearly both the seasonal variation in malaria and the dramatic reduction resulting from a range of government and community-led interventions over the 3-year period. In our experience, rural health workers have appreciated seeing this striking confirmation that their work can have such a positive influence on the health of their communities.
Probability is a better tool for handling uncertainty and reasoning. But it is often easy to go w... more Probability is a better tool for handling uncertainty and reasoning. But it is often easy to go wrong with the task. Here we talk about some instances where the probability is misused and, then show how to use it correctly. Firstly, we talk about how to adjust p-values in statistical significance testing so that uncertainty in replication studies can be lowered, thus minimizing so-called replication crisis. Also, Monty Hall problem is discussed to show how puzzling the probability can be. The solution lies on differentiating the conditional probability from the marginal probability. And finally, a simple logical way of quantifying uncertainty of a probabilistic prediction is discussed. We use Bayesian network inference for the task. The method is extended to deep neural networks.
Liver Transplantation, 2000
So-called two-envelope, wallet-game, Sleeping Beauty and Newcomb’s paradoxes are resolved through... more So-called two-envelope, wallet-game, Sleeping Beauty and Newcomb’s paradoxes are resolved through simple logical and analytical arguments. We stress the need of such simple solutions to them, due t ...
Journal of Statistical and Econometric Methods, 2014
Relationship between two popular modelling frameworks of causal inference from observational data... more Relationship between two popular modelling frameworks of causal inference from observational data, namely, causal graphical model and potential outcome causal model is discussed. How some popular causal effect estimators found in applications of the potential outcome causal model, such as inverse probability of treatment weighted estimator and doubly robust estimator can be obtained by using the causal graphical model is shown. We confine to the simple case of binary outcome and treatment variables with discrete confounders and it is shown how to generalize results to cases of continuous variables.
Administrative data are becoming increasingly important. They are typically the side effect of so... more Administrative data are becoming increasingly important. They are typically the side effect of some operational exercise, and are often seen as having significant advantages over alternative sources of data. While it is true that such data do have merits, statisticians should approach the analysis of such data with the same cautious and critical eye they approach the analysis of data from any other source. This paper identifies a number of statistical challenges, with the aim of stimulating debate about and improving the analysis of administrative data, and encouraging methodology researchers to explore some of the important statistical problems which arise with such data.
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Generation, Transmission and …, 2003
... An optimal pricing methodology based on maximising consumer net benefit (CNB) has been publis... more ... An optimal pricing methodology based on maximising consumer net benefit (CNB) has been published by Farmer, Cory and Perera [I, 5, 61 in which the ... where a(x) is half the losses in all the circuits connected to node k and A is the branch-node incidencc matrix consisting of 0 ...
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Papers by Priyantha Wijayatunga
• The paradox in another popular case
• Probability problems –the two-envelope paradox
complex, subtle and tricky; therefore, their solutions require many aspects of critical thinking. In the following, the Introduction outlines some of the current research on the topic without going into more details. We provide background descriptions of the paradoxes and probability paradoxes in Section 2. Section 3 provides a short description of critical
thinking. We present several definitions since there is no clear consensus on one single definition, both in the literature and in the general literature. And in Section 4 current research on using puzzles for enhancing critical thinking is given. We then discuss several probability paradoxes, namely, the Monte Hall paradox, the two-envelope (exchange) paradox and the St. Petersberg paradox, in Sections 5, 6 and 7, respectively. In Section 8, a brief discussion of the statistical hypothesis testing is given emphasizing its controversial nature. We analyze these problems and concepts in such a way
that critical thinking is evoked while keeping the technical details to a minimum.