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Application of Copula functions in statistics
(2007-09) Nikoloulopoulos, Aristidis; Νικολουλόπουλος, Αριστείδης; Athens University of Economics and Business, Department of Statistics; Karlis, Dimitrios
Studying associations among multivariate outcomes is an interesting problem in statistical science. The dependence between random variables is completely described by their multivariate distribution. When the multivariate distribution has a simple form, standard methods can be used to make inference. On the other hand one may create multivariate distributions based on particular assumptions, limiting thus their use. Unfortunately, these limitations occur very often when working with multivariate discrete distributions. Some multivariate discrete distributions used in practice can have only certain properties, as for example they allow only for positive dependence or they can have marginal distributions of a given form. To solve this problem copulas seem to be a promising solution. Copulas are a currently fashionable way to model multivariate data as they account for the dependence structure and provide a flexible representation of the multivariate distribution. Furthermore, for copulas the dependence properties can be separated from their marginal properties and multivariate models with marginal densities of arbitrary form can be constructed, allowing a wide range of possible association structures. In fact they allow for flexible dependence modelling, different from assuming simple linear correlation structures. However, in the application of copulas to discrete data marginal parameters affect dependence structure, too, and, hence the dependence properties are not fully separated from the marginal properties. Introducing covariates to describe the dependence by modelling the copula parameters is of special interest in this thesis. Thus, covariate information can describe the dependence either indirectly through the marginal parameters or directly through the parameters of the copula . We examine the case when the covariates are used both in marginal and/or copula parameters aiming at creating a highly flexible model producing very elegant dependence structures. Furthermore, the literature contains many theoretical results and families of copulas with several properties but there are few papers that compare the copula families and discuss model selection issues among candidate copula models rendering the question of which copulas are appropriate and whether we are able, from real data, to select the true copula that generated the data, among a series of candidates with, perhaps, very similar dependence properties. We examined a large set of candidate copula families taking intoaccount properties like concordance and tail dependence. The comparison is made theoretically using Kullback-Leibler distances between them. We have selected this distance because it has a nice relationship with log-likelihood and thus it can provide interesting insight on the likelihood based procedures used in practice. Furthermore a goodness of fit test based on Mahalanobis distance, which is computed through parametric bootstrap, will be provided. Moreover we adopt a model averaging approach on copula modelling, based on the non-parametric bootstrap. Our intention is not to underestimate variability but add some additional variability induced by model selection making the precision of the estimate unconditional on the selected model. Moreover our estimates are synthesize from several different candidate copula models and thus they can have a flexible dependence structure. Taking under consideration the extended literature of copula for multivariate continuous data we concentrated our interest on fitting copulas on multivariate discrete data. The applications of multivariate copula models for discrete data are limited. Usually we have to trade off between models with limited dependence (e.g. only positive association) and models with flexible dependence but computational intractabilities. For example, the elliptical copulas provide a wide range of flexible dependence, but do not have closed form cumulative distribution functions. Thus one needs to evaluate the multivariate copula and, hence, a multivariate integral repeatedly for a large number of times. This can be time consuming but also, because of the numerical approach used to evaluate a multivariate integral, it may produce roundoff errors. On the other hand, multivariate Archimedean copulas, partially-symmetric m-variate copulas with m-1 dependence parameters and copulas that are mixtures of max-infinitely divisible bivariate copulas have closed form cumulative distribution functions and thus computations are easy, but allow only positive dependence among the random variables.The bridge of the two above-mentioned problems might be the definition of a copula family which has simple form for its distribution functionwhile allowing for negative dependence among the variables. We define sucha multivariate copula family exploiting the use of finite mixture of simple uncorrelated normal distributions. Since the correlation vanishes, the cumulative distribution is simply the product of univariate normal cumulative distribution functions. The mixing operation introduces dependence. Hence we obtain a kind of flexible dependence, and allow for negative dependence.
Μοντελοποίηση των χρόνων προετοιμασίας παραγγελιών σε διαδικασία Detail Picking
(2007-11) Οικονόμου, Ιωάννης; Οικονομικό Πανεπιστήμιο Αθηνών, Τμήμα Στατιστικής; Ζαζάνης, Μιχαήλ
Διπλωματική εργασία - Οικονομικό Πανεπιστήμιο Αθηνών. ΜΠΣ, Τμήμα Στατιστικής με κατεύθυνση "Ποσοτικές Μέθοδοι στη Λήψη Αποφάσεων"
Hyperbolic SPDEs: analytical and numerical study using Wiener Chaos approach
(2011) Kalpinelli, Evangelia A.; Καλπινέλλη, Ευαγγελία Α.; Athens University of Economics and Business, Department of Statistics; Φράγκος, Νικόλαος; Γιαννακόπουλος, Αθανάσιος
In the first part of this dissertation we propose a constructive approach forgeneralized weighted Wiener Chaos solutions of linear hyperbolic SPDEsdriven by a cylindrical Brownian Motion. Explicit conditions for the existence,uniqueness and regularity of generalized (Wiener Chaos) solutions areestablished in Sobolev spaces. An equivalence relation between the WienerChaos solution and the traditional one is established.In the second part we propose a novel numerical scheme based on theWiener Chaos expansion for solving hyperbolic stochastic PDEs. Throughthe Wiener Chaos expansion the stochastic PDE is reduced to an infinite hierarchy of deterministic PDEs which is then truncated to a finite system ofPDEs, that can be addressed by standard techniques. A priori and a posterioriconvergence results for the method are provided. The proposed methodis applied to solve the stochastic forward rate Heath-Jarrow-Morton modelwith the Musiela parametrization and the results are compared to those derivedby the Monte Carlo method. The main advantage of the proposedscheme is that it is significantly faster than the Monte Carlo (MC) simulationmethod, for the same order of accuracy. It also provides a convenientway to compute not only the solution but also the statistical moments of thesolution numerically.
Modelling multivariate time series for count data
(2011-06) Pedeli, Xanthi; Athens University of Economics and Business, Department of Statistics; Karlis, D.
The study of time series models for count data has become a topic of special interest during the last years. However, while research on univariate time series for counts now flourishes, the literature on multivariate time series models for count data is notably more limited. The main reason for this is that the analysis of multivariate counting processes presents many more difficulties. Specifically, the need to account for both serial and cross–correlation complicates model specification, estimation and inference. This thesis deals with the class of INteger–valued AutoRegressive (INAR) processes, a recently popular class of models for time series of counts. The simple, univariate INAR(1) process is initially extended to the 2–dimensional space. In this way, a bivariate (BINAR(1)) process is introduced. Subsequently, the time invariant BINAR(1) model is generalized to a BINAR(1) regression model. Emphasis is given on models with bivariate Poisson and bivariate negative binomial innovations. The properties of the BINAR(1) model are studied in detail and the methods of moments, Yule-Walker and conditional maximum likelihood are proposed for the estimation of its unknown parameters. The small sample properties of the alternative estimators are examined and compared through a simulation experiment. Issues of diagnostics and forecasting are considered and predictions are produced by means of the conditional forecast distribution. Estimation uncertainty is accommodated by taking advantage of the asymptotic normality of maximum likelihood estimators and constructing appropriate confidence intervals for the h–step–ahead conditional probability mass function. A generalized specification of the BINAR(1) process, where cross–correlation between the two series receives contribution from two different sources, is also discussed. In this case, we mainly focus on a specific parametric case that arises under the assumption that the innovations follow jointly a bivariate Poisson distribution. The resulting joint distribution of the bivariate series is identified as an 8–parameters bivariate Hermite. At a second stage, the BINAR(1) process is extended to the multi–dimensional space. Thus, we define a multivariate integer–valued autoregressive process of order 1 (MINAR(1)) and examine its basic statistical properties. Such an extension is not simple and we emphasize on problems that occur, relating to selecting a reasonable innovation distribution as well as on problems related to inference. Apart from the general specification of the MINAR(1) process, we also study two specific parametric cases that arise under the assumptions of a multivariate Poisson and a multivariate negative binomial distribution for the innovations of the process. To overcome the computational difficulties of the maximum likelihood approach we suggest the method of composite likelihood. The performance of the two methods of estimation (i.e. maximum likelihood and composite likelihood) is compared through a small simulation experiment. Extensions to incorporate covariance information are also discussed. The proposed models are illustrated on multivariate count series from the fields of accident analysis, syndromic surveillance and finance.
High dimensional time-varying covariance matrices with applications in finance
(2011-07-10) Plataniotis, Anastasios; Πλατανιώτης, Αναστάσιος; Athens University of Economics and Business, Department of Statistics; Dellaportas, Petros
The scope of this Thesis is to provide an original contribution in the area of Multivariate Volatility modeling. Multivariate Volatility modeling in the present context, involves developing models that can adequately describe the Covariance matrix process of Multivariate financial time series. Developmentof efficient algorithms for Bayesian model estimation using Markov Chain Monte Carlo (MCMC) and Nested Laplace approximations is our main objective in order to provide parsimonious and flexible volatility models. A detailed review of Univariate Volatility models for financial time series is first introduced in this Thesis. We illustrate the historical background of each model proposed and discuss its properties and advantages as well as comment on the several estimation methods that have emerged. We also provide a comparative analysis via a small simulation example for the dominant models in the literature. Continuing the review from the univariate models we move on to the multivariate case and extensively present competing models for Covariance matrices. The main argument presented is that currently no model is able to capture the dynamics of higher dimensional Covariance matrices fully, but their relative performance and applicability depends on the dataset and problem of interest. Problems are mainly due to the positive definiteness constraints required by most models as well as lack of interpretability of the model parameters in terms of the characteristics of the financial series. In addition, model development so far focus mostly in parameter estimation and in sample fit; it is our goal to examine the out-of-sample fit perspective of these models. We conclude the review section by proposing some small improvements for existing models that will lead towards more efficient parameter estimates, faster estimation methods and accurate forecasts. Subsequently, a new class of multivariate models for volatility is introduced. The new model is based on the Spectral decomposition of the time changing covariance matrix and the incorporation of autocorrelation modeling or the time changing elements. In these models we allow a priori for all the elements of the covariance matrix to be time changing as independent autoregressive processes and then for any given dataset we update our prior information and decide on the number of time changing elements. Theoretical properties of the new model are presented along with a series of estimation methods, bayesian and classical. We conclude that in order to estimate these models one may use an MCMC method for small dimension portfolios in terms of the size of the covariance matrix. For higher dimensions, due to the curse of dimensionality we propose to use a Nested Laplace approximation approach that provides results much faster with small loss in accuracy. Once the new model is proposed along with the estimation methods, we compare its performance against competing models in simulated and real datasets; we also examine its performance in small portfolios of less than 5 assets as well in the high dimensional case of up to 100 assets. Results indicate that the new model provides significantly better estimates and projections than current models in the majority of example datasets. We believe that small improvements in terms of forecasting is of significant importance in the finance industry. In addition, the new model allows for parameter interpretability and parsimony which is of huge importance due to the dimensionality curse. Simplifying inference and prediction of multivariate volatility models was our initial goal and inspiration. It is our hope that we have made a small step towards that direction, and a new path for studying multivariate financial data series has been revealed. We conclude by providing some proposals for future research that we hope may influence some people into furthering this class of models.
On variance reduction for Markov chain Monte Carlo
(2012-02) Tsourti, Zoi; Τσούρτη, Ζωή; Athens University of Economics and Business, Department of Statistics; Dellaportas, Petros; Kontoyannis, Ioannis
In the present thesis we are concerned with appropriate variance reduction methods for specific classes of Markov Chain Monte Carlo (MCMC) algorithms. The variance reduction method of main interest here is that of control variates. More particularly, we focus on control variates of the form U = G−PG, for arbitrary function G, where PG stands for the one-step ahead conditional expectation, that have been proposed by Henderson (1997). A key issue for the efficient implementation of control variates is the appropriate estimation of corresponding coefficients. In the case of Markov chains, this involves the solution of Poisson equation for the function of initial interest, which in most cases is intractable. Dellaportas & Kontoyiannis (2012) have further elaborated on this issue and they have proven optimal results for the case of reversible Markov chains, avoiding that function. In this context, we concentrate on the implementation of those results for Metropolis-Hastings (MH) algorithm, a popular MCMC technique. In the case of MH, the main issue of concern is the assessment of one-step ahead conditional expectations, since these are not usually available in closed form expressions. The main contribution of this thesis is the development and evaluation of appropriate techniques for dealing with the use of the above type of control variates in the MH setting. The basic approach suggested is the use of Monte Carlo method for estimating one-step ahead conditional expectations as empirical means. In the case of MH this is a straightforward task requiring minimum additional analytical effort. However, it is rather computationally demanding and, hence, alternative methods are also suggested. These include importance sampling of the available data resulting from the algorithm (that is, the initially proposed or finally accepted values), additional application of the notion of control variates for the estimation of PG’s, or parallel exploitation of the values that are produced in the frame of an MH algorithm but not included in the resulting Markov chain (hybrid strategy). The ultimate purpose is the establishment of a purely efficient strategy, that is, a strategy where the variance reduction attained overcomes the additional computational cost imposed. The applicability and efficiency of the methods is illustrated through a series of diverse applications.
Efficient Bayesian marginal likelihood estimation in generalised linear latent trait models
(2013) Vitoratou, Vasiliki; Βιτωράτου, Βασιλική; Athens University of Economics and Business, Department of Statistics; Ntzoufras, Ioannis
The term latent variable model (LVM) refers to a broad family of models which are used tocapture abstract concepts (unobserved / latent variables or factors) by means of multipleindicators (observed variables or items). The key idea is that all dependencies among pobserved variables are attributed to k unobserved ones, where k << p. That is, the LVMmethodology is a multivariate analysis technique which aims to reduce the dimensionality,with as little loss of information as possible. Most importantly, the LVMs accountfor constructs that are not directly measurable, as for instance individuals’ emotions,traits, attitudes and perceptions. In the current thesis, the LVMs are studied within theBayesian paradigm, where model evaluation is conducted on the basis of posterior modelprobabilities. A key role in this comparison is played by the models’ marginal likelihood,which is often a high dimensional integral, not available in closed form. The propertiesof the LVMs are implemented here in order to efficiently approximate the marginallikelihood.
Actuarial modelling of claim counts and losses in motor third party liability insurance
(2013-07) Tzougas, George J.; Τζουγάς, Γεώργιος Ι.; Athens University of Economics and Business, Department of Statistics; Frangos, Nikolaos
Actuarial science is the discipline that deals with uncertain events where clearly theconcepts of probability and statistics provide for an indispensable instrument in themeasurement and management of risks in insurance and finance. An important aspectof the business of insurance is the determination of the price, typically calledpremium, to pay in exchange for the transfer of risks. It is the duty of the actuary toevaluate a fair price given the nature of the risk. Actuarial literature research covers awide range of actuarial subjects among which is risk classification and experiencerating in motor third-party liability insurance, which are the driving forces of theresearch presented in this thesis. This is an area of applied statistics that has beenborrowing tools from various kits of theoretical statistics, notably empirical Bayes,regression, and generalized linear models, GLM, (Nelder and Wedderburn, 1972).However, the complexity of the typical application, featuring unobservable riskheterogeneity, imbalanced design, and nonparametric distributions, inspiredindependent fundamental research under the label `credibility theory', now acornerstone in contemporary insurance mathematics. Our purpose in this thesis is tomake a contribution to the connection between risk classification and experiencerating with generalized additive models for location scale and shape, GAMLSS,(Rigby and Stasinopoulos, 2005) and finite mixture models (Mclachlan and Peel,2000). In Chapter 1, we present a literature review of statistical techniques that can bepractically implemented for pricing risks through ratemaking based on a priori riskclassification and experience rated or Bonus-Malus Systems. The idea behind a prioririsk classification is to divide an insurance portfolio into different classes that consistof risks with a similar profile and to design a fair tariff for each of them. Recentactuarial literature research assumes that the risks can be rated a priori usinggeneralized linear models GLM, (see, for example, Denuit et al., 2007 & Boucher etal., 2007, 2008). Typical response variables involved in this process are the number ofclaims (or the claim frequency) and its corresponding severity (i.e. the amount theinsurer paid out, given that a claim occurred). In Chapter 2, we extend this setupfollowing the GAMLSS approach of Rigby and Stasinopoulos (2005). The GAMLSSmodels extend GLM framework allowing joint modeling of location and shapeparameters. Therefore both mean and variance may be assessed by choosing a marginal distribution and building a predictive model using ratemaking factors asindependent variables. In the setup we consider, risk heterogeneity is modeled as thedistribution of frequency and cost of claims changes between clusters by a function ofthe level of ratemaking factors underlying the analyzed clusters. GAMLSS modelingis performed on all frequency and severity models. Specifically, we model the claimfrequency using the Poisson, Negative Binomial Type II, Delaporte, Sichel and Zero-Inflated Poisson GAMLSS and the claim severity using the Gamma, Weibull, WeibullType III, Generalized Gamma and Generalized Pareto GAMLSS as these models havenot been studied in risk classification literature. The difference between these modelsis analyzed through the mean and the variance of the annual number of claims and thecosts of claims of the insureds, who belong to different risk classes. The resulting apriori premiums rates are calculated via the expected value and standard deviationprinciples with independence between the claim frequency and severity componentsassumed. However, in risk classification many important factors cannot be taken intoaccount a priori. Thus, despite the a priori rating system, tariff cells will not becompletely homogeneous and may generate a ratemaking structure that is unfair to thepolicyholders. In order to reduce the gap between the individual's premium and riskand to increase incentives for road safety, the individual's past record must taken intoconsideration under an a posteriori model. Bonus-Malus Systems (BMSs) are aposteriori rating systems that penalize insureds responsible for one or more accidentsby premium surcharges or maluses and reward claim-free policyholders by awardingthem discounts or bonuses. A basic interest of the actuarial literature is theconstruction of an optimal or `ideal' BMS defined as a system obtained throughBayesian analysis. A BMS is called optimal if it is financially balanced for theinsurer: the total amount of bonuses must be equal to the total amount of maluses andif it is fair for the policyholder: the premium paid by each policyholder is proportionalto the risk that they impose on the pool. The study of such systems based on differentstatistical models will be the main objective of this thesis. In Chapter 3, we extend thecurrent BMS literature using the Sichel distribution to model the claim frequencydistribution. This system is proposed as an alternative to the optimal BMS obtained bythe Negative Binomial model (see, Lemaire, 1995). We also consider the optimalBMS provided by the Poisson-Inverse Gaussian distribution, which is a special caseof the Sichel distribution. Furthermore, we introduce a generalized BMS that takesinto account both the a priori and a posteriori characteristics of each policyholder, extending the framework developed by Dionne and Vanasse (1989, 1992). This isachieved by employing GAMLSS modeling on all the frequency models consideredin this chapter, i.e. the Negative Binomial, Sichel and Poisson-Inverse Gaussianmodels. In the above setup optimality is achieved by minimizing the insurer's risk.The majority of optimal BMSs in force assign to each policyholder a premium basedon their number of claims disregarding their aggregate amount. In this way, apolicyholder who underwent an accident with a small size of loss will be unfairlypenalized in comparison to a policyholder who had an accident with a big size of loss.Motivated by this, the first objective of Chapter 4 is the integration of claim severityinto the optimal BMSs based on the a posteriori criteria of Chapter 3. For this purposewe consider that the losses are distributed according to a Pareto distribution,following the setup used by Frangos and Vrontos (2001). The second objective ofChapter 4 is the development of a generalized BMS with a frequency and a severitycomponent when both the a priori and the a posteriori rating variables are used. Forthe frequency component we assume that the number of claims is distributedaccording to the Negative Binomial Type I, Poisson Inverse Gaussian and SichelGAMLSS. For the severity component we consider that the losses are distributedaccording to a Pareto GAMLSS. This system is derived as a function of the years thatthe policyholder is in the portfolio, their number of accidents, the size of loss of eachof these accidents and of the statistically significant a priori rating variables for thenumber of accidents and for the size of loss that each of these claims incurred.Furthermore, we present a generalized form of the one obtained in Frangos andVrontos (2001). Finally, in Chapter 5 we give emphasis on both the analysis of theclaim frequency and severity components of an optimal BMS using finite mixtures ofdistributions and regression models (see Mclachlan and Peel, 2000 & Rigby andStasinopoulos, 2009) as these methods, with the exception of Lemaire(1995), have notbeen studied in the BMS literature. Specifically, for the frequency component weemploy a finite Poisson, Delaporte and Negative Binomial mixture, while for theseverity component we employ a finite Exponential, Gamma, Weibull andGeneralized Beta Type II (GB2) mixture, updating the posterior probability. We alsoconsider the case of a finite Negative Binomial mixture and a finite Pareto mixtureupdating the posterior mean. The generalized BMSs we propose adequately integraterisk classification and experience rating by taking into account both the a priori and aposteriori characteristics of each policyholder.
Adaptive designs in phase II clinical trials
(2013-09-23) Poulopoulou, Stavroula; Πουλοπούλου, Σταυρούλα; Athens University of Economics and Business. Department of Statistics; Karlis, Dimitrios; Dafni, Urania
Clinical trials play a very important role in the development process of new therapies. Recently there has been a rapid increase in theresearch and creation of new modern molecular agents, which makes necessary the development of more flexible and adaptive designs forthe implementation of clinical trials. The objective of adaptive designs is to ensure direct and dynamic control of the effectiveness and thesafety of a new treatment by allowing the adjustment of the elements of the study (i.e sample size), during the study, in such a way that wewill not sacrifice elements which are associated with the credibility of the study (i.e statistical power) and also issues which concern ethicalcharacteristics of the clinical trials.
Measuring and modeling income inequality in Greece
(2014-04-30) Chrissis, Kostas; Χρύσης, Κώστας; Athens University of Economics and Business, Department of Statistics; Λειβαδά, Αλεξάνδρα
Income inequality gains significance from its close relationship with social injustice, and it has, therefore, been the subject of voluminous research by philosophers, political scientists, sociologists and economists. This thesis concentrates on the empirical study of personal income distribution in Greece utilizing alternative data sources and employing several statistic and econometric approaches for the modeling of income inequality. The structure of this thesis is the following: Chapter 1 is the introduction, Chapter 2 presents a detailed literature review of income inequality in Greece. Data and methodology are illustrated in Chapter 3. Two are the main datasources: Income tax data (declared income of physical persons) and EU-SILC micro data. The statistical specification for grouped income tax data includes the utilization of interpolation methods according to Cowell and Mehta (1982). An alternative methodology for the estimation of top income shares from grouped tax data according to the Piketty (2001) approach is also employed. Moreover this Chapter includes the statistical specification for EUSILC micro data for the estimation of the inequality indices. The empirical findings are presented in Chapter 4. A section is dedicated to the impact ofeconomic crisis on income distribution. The econometric approach employed for studying the relationship of income inequality and macroeconomic activity is discussed in Chapter 5. Autoregressive Distributed Lag (ARDL) (or boundstesting) cointegration procedure is employed for the empirical analysis of thelong-run relationships and dynamic interaction among the variables of interest. Chapter 6 illustrates the empirical results of the composition of income inequality (decomposition of inequality indices by population subgroups and income sources) as well as the distributional effects of policy tools (such as taxes and social transfers). Finally, conclusions, policy implications and potential future research are presented in Chapter 7.
Financial analysis of demographic ageing effect on pharmaceutical expenditure of Greece
(2014-07) Politi, Anastasia S.; Πολίτη, Αναστασία, Σ.; Athens University of Economics and Business, Department of Statistics; Φράγκος, Νικόλαος
The study aims to take a thorough look at the generating process of Greece’s pharmaceutical expenditure volatility taking into consideration latent cost synthesis differentiations among distinct morbidity areas. It uses frequency-severity models that decompose pharmaceutical demand of prescription drugs (Rxs) into a frequency component (claim frequency counts) and a severity component (claim size). It encompasses linear stochastic forms that treat health expenditure as an age-dependent branching process. The models also comprise the therapeutic category of Rxs as a controllable factor of population morbidity.Motivated by official population statistics which signal the impending serious growth of seniors’ portion within the following decades, globally and particularly in Greece, this dissertation presents estimating results of demographic senescence effects on pharmaceutical expenditure in the long run, through the implementation of projections for distinct therapeutic areas.Up to date literature review does not show any frequency – severity analysis conducted for pharmaceutical care data, neither at an international level, nor at the national level where the integrated information systems were developed with delay in relation to European systems. This study focused on this specific methodology and attempted to fill this knowledge gap in theVIdomain of healthcare by producing not only general estimates for the entire study population but also analytical results for sub-populations with distinct morbidity characteristics. As regards the principal aim of this study, namely, the estimation of the impact of aging on pharmaceutical expenditure, it is suggested that this study can bring substantial contribution to this cognitive field, as it includes the assessment of relevant results for sub-populations with distinct morbidity characteristics, which to the knowledge of the author, is a novel approach according to up to date literature data regarding Greece.According to the results, frequency effects play the key role towards severity ones in the generating process of pharmaceutical claim and loss intensity, this norm does not however apply within each therapeutic category. Pharmaceutical spending associated especially with the reimbursement of drugs for the genito-urinary system, the ophthalmological diseases, the antineoplastic and immunomodulating agents and the respiratory system, is more susceptible to the advent of the demographic aging risk.
Application of hidden Markov and related models to earthquake studies
(2015) Orfanogiannaki, Aikaterini M.; Ορφανογιαννάκη, Αικατερίνη Μ.; Athens University of Economics and Business, Department of Statistics; Karlis, Dimitrios
Discrete valued hidden Markov Models (HMMs) are used to model time series of event counts in several scientific fields like genetics, engineering, seismology and finance. In its general form the model consists of two parts: the observation sequence and an unobserved sequence of hidden states that underlies the data and consist a Markov chain. Each state is characterized by a specific distribution and the progress of the hidden process from state to state is controlled by a transition probability matrix. We extend the theory of HMMs to the multivariate case and apply them to seismological data fromdifferent seismotectonic environments. This extension is not straightforward and it is achieved gradually by assuming different multivariate distributions to describe each state of the model.
Applications of stochastic analysis in sensitivity analysis and insurance mathematics
(2016-10-13) Roumelioti, Eleni E.; Ρουμελιώτη, Ελένη Ε.; Athens University of Economics and Business, Department of Statistics; Zazanis, M.
This thesis deals primarily with the use of Malliavin calculus techniques in estimatingthe sensitivity of functionals of diffusion processes.
Stochastic modeling of time series with intermittency, persistence and extreme variability, with application to spatio-temporal averages of rainfall fields
(2018-06-21) Chronis, George A.; Χρόνης, Γεώργιος Α.; Athens University of Economics and Business, Department of Statistics; De Michele, Carlo; Picek, Jan; Dellaportas, Petros; Karlis, Dimitrios; Zazanis, Michael; Ioannidis, Evaggelos; Pavlopoulos, Charalampos
Motivated by rainfall research, this thesis contributes new insights on mechanisms of precipitation. This is accomplished through a stochastic modelling approach of time series representing intermittency and variability of precipitation cumulatively at large spatial scales. Our objective is to obtain a parsimonious but flexible stochastic model that can capture adequately the spectral power distribution and the marginal probability distribution of time series of spatio-temporal averages of rain rate (STARR) at such large spatial scales, presumably under stationarity conditions. The model conceived and presented in this thesis treats intermittency and variability as two stochastically independent multiplicative components, each contributing partially to the overall persistence of memory or dependence of the model. Specifically, we model intermittency by a stationary renewal process in discrete time, where instants of renewals are marked with the value {1} and otherwise the process attains the value {0}. In particular, we model the probability distribution of waiting (discrete) time between successive renewals by the family of Riemann's zeta-distributions, whose parameter allows for the possibility of heavy tails (i.e. infinite variance), which in turn is an event associated with persistence (i.e. long memory) of the renewal process. Subsequently, conditionally on raining, the overall amount of rain is modelled as a log-infinitely divisible noise process, independent of the zeta-renewal process. Specifically, positive values of STARR during spells of successive renewals are modelled as exponential values of (unitary-lag) stationary increments of a self-similar process known as Linear Fractional Stable Motion, which is obtained by stochastic integration of a certain deterministic kernel with respect to a suitable alpha-stable random measure. That is, conditionally on raining, log-STARR is modelled as Linear Fractional Stable Noise. The contemporaneous product of the stationary zeta-renewal process with the stationary log-LFSN process, provides the stationary model proposed in this dissertation.
Statistical methods for population ecology with applications in the Mediterranean
(2020-03-31) Νησιώτης, Κωνσταντίνος-Συμεών; Nisiotis, Constantinos-Symeon; Athens University of Economics and Business, Department of Statistics; Βασδέκης, Βασίλειος; Κόκκορης, Γεώργιος; Κυριακίδης, Επαμεινώνδας; Κωστάκη, Αναστασία; Buckland, Stephen; Halley, John; Μπεσμπέας, Παναγιώτης
Δομικό στοιχείο της Οικολογίας αποτελεί η γνώση του πληθυσμιακού μεγέθους των ζώντων οργανισμών. Ο υπολογισμός αυτός εμφανίζει μεγάλο επιστημονικό ενδιαφέρον που γίνεται ακόμα πιο έντονο όταν εκτός από τις πρακτικές δυσκολίες απογραφής, επιπλέον ιδιαίτερα χαρακτηριστικά του υπό μελέτη πληθυσμού οδηγούν σε έμμεση παρατήρηση του.Μεταξύ των πλέον διαδεδομένων τεχνικών εκτίμησης πληθυσμιακών μεγεθών (πλήθος ή/και πυκνότητα) είναι οι distance sampling τεχνικές. Η conventional distance sampling (CDS), ένα μείγμα design και model-based τεχνικής, αποτελεί την πλέον απλή και διαδεδομένη. Η γενίκευση αυτής, Multiple Covariate Distance Sampling (MCDS), δίνει τη δυνατότητα για ερμηνεία της παρατηρούμενης μεταβλητότητας μέσω διαφόρων παραγόντων. Εναλλακτικά, οι ιεραρχικές τεχνικές distance sampling (HDS) δύναται να χρησιμοποιηθούν για την αντιμετώπιση παρόμοιων προβλημάτων. Τα μοντέλα αυτά είναι πλήρως model-based και έχουν μεγαλύτερες δυνατότητες ερμηνείας της παρατηρούμενης μεταβλητότητας.Αδημοσίευτα δεδομένα από έρευνα οικολογίας για τον πληθυσμό του κόκκινου ελαφιού της Πάρνηθας (ανατολική/βόρειο-ανατολική Μεσόγειο, WWF Ελλάς) χρησιμοποιήθηκαν για την εκτεταμένη εφαρμογή των distance sampling τεχνικών, (M-)CDS και HDS, με στόχο την εκτίμηση των πληθυσμιακών μεγεθών του καταγεγραμμένου βιοδηλωτικού χαρακτηριστικού. Επιπλέον σε αυτά, αποδεικνύεται ότι οι δύο διαφορετικές προσεγγίσεις, (M-)CDS και HDS, κάτω από συγκεκριμένες υποθέσεις ταυτίζονται, οδηγώντας σε κοινά αποτελέσματα.Για την ολοκλήρωση των ερευνών οικολογίας με έμμεσες καταγραφές και την εξαγωγή συμπερασμάτων για τον ζώντα οργανισμό, απαιτείται η εφαρμογή μίας μεθοδολογίας συσχέτισης των έμμεσων καταγραφών και του οργανισμού ενδιαφέροντος. Υπάρχει μία σειρά από προτεινόμενες μεθόδους, οι οποίες και εφαρμόζονται εδώ. Επιπρόσθετα σε αυτές, μία νέα, ολοκληρωμένη μεθοδολογία προτείνεται, απαραίτητη για την εκτίμηση των πληθυσμιακών μεγεθών του ζώντος οργανισμού από τα αντίστοιχα των έμμεσων καταγραφών. Αποδεικνύεται η άμεση σχέση της προτεινόμενης μεθόδου με την μέχρι τώρα επικρατούσα, αλλά και με άλλες υπάρχουσες, ενώ αναδεικνύονται τα ανώτερα χαρακτηριστικά αυτής.
The generalized waring process - statistical inference and applications
(2021) Zografi, Mimoza S.; Ζωγράφη, Μιμόζα; Athens University of Economics and Business. Department of Statistics; Teugels, Jef; Dimaki, A.; Zazanis, Michael; Zografos, Constantinos; Balakrishnan, Narayanaswamy; Katti, S. K.; Xekalaki, Evdokia
Σ’ αυτήν την διατριβή αναπτύσσουμε μια θεωρία της Γενικευμένης Ανέλιξης Waring που σχετίζεται με μια μεγάλη ποικιλία εφαρμογών. Ειδικότερα, ορίζουμε πρώτα την Γενικευμένη Ανέλιξη Waring στην πραγματική ευθεία ως στατική, αλλά μη ομοιογενή ανέλιξη Markov. Παρέχεται μία εφαρμογή στο πλαίσιο μοντελοποίησης της πρόσβασης στο διαδίκτυο και εφαρμόζεται σε πραγματικά δεδομένα. Στην συνέχεια κατασκευάζουμε την Γενικευμένη Ανέλιξη Waring σε έναν πλήρη διαχωρίσιμο μετρικό χώρο. Η Γενικευμένη Ανέλιξη Waring ορίζεται στον Rd . Αποδεικνύοντας ένα αριθμό ιδιοτήτων της όπως προσθετικότητα, στασιμότητα, εργοδικότητα και διαταξιμότητα, επιδεικνύουμε ότι η νέα ανέλιξη είναι απολύτως ικανοποιητική για στατιστικές εφαρμογές.
Bayesian modeling and estimation for complex multiparameter problems with real applications
(2021) Koki, Constandina; Κοκή, Κωνσταντίνα; Athens University of Economics and Business, Department of Statistics; Meligkotsidou, Loukia; Karlis, Dimitrios; Dellaportas, Petros; Kypraios, Theodore; Fouskakis, Dimitris; Kalogeropoulos, Kostas; Vrontos, Ioannis
In the big data era, the study of complex multiparameter problems is more than necessary. The development of Machine Learning techniques enhanced the inferentialability of statistical models. In this direction, by leveraging Machine Learning techniques, we propose a new predictive Hidden Markov model with exogenous variables, within a Bayesian framework, for joint inference and variable selection. Wepropose a computational Markov Chain Monte Carlo algorithm that offers improved forecasting and variable selection performance, compared to existing benchmarkmodels. Our methodology is applied in various simulated and real datasets, such as realized volatility data and cryptocurrency return series. Furthermore, we exploit the Bayesian methodology in implementing the X-ray luminosity function of the ActiveGalactic Nuclei under the assumption of Poisson errors in the determination of X-ray fluxes and estimation uncertainties.
Self-starting methods in Bayesian statistical process control and monitoring
(2021-10-26) Bourazas, Konstantinos; Μπουραζάς, Κωνσταντίνος; Ntzoufras, Ioannis; Demiris, Nikolaos; Psarakis, Stelios; Capizzi, Giovanna; Colosimo, Bianca Maria; Chakraborti, Subhabrata; Tsiamyrtzis, Panagiotis
In this dissertation, the center of attention is in the research area of Bayesian Statistical Process Control and Monitoring (SPC/M) with emphasis in developing self-starting methods for short horizon data. The aim is in detecting a process disorder as soon as it occurs, controlling the false alarm rate, and providing reliable posterior inference for the unknown parameters. Initially, we will present two general classes of methods for detecting parameter shifts for data that belong to the regular exponential family. The first, named Predictive Control Chart (PCC), focuses on transient shifts (outliers) and the second, named Predictive Ratio CUSUM (PRC), in persistent shifts. In addition, we present an online change point scheme available for both univariate or multivariate data, named Self-starting Shiryaev (3S). It is a generalization of the well-known Shiryaev’s procedure, which will utilize the cumulative posterior probability that a change point has been occurred. An extensive simulation study along with a sensitivity analysis evaluate the performance of the proposed methods and compare them against standard alternatives. Technical details, algorithms and general guidelines for all methods are provided to assist in their implementation, while applications to real data illustrate them in practice.
An econometric analysis of high-frequency financial data
(2021-12-09) Lamprinakou, Fiori; Λαμπρινάκου, Φιόρη; Athens University of Economics and Business, Department of Statistics; Papaspiliopoulos, Omiros; Demiris, Nikolaos; Pedeli, Xanthi; Papastamoulis, Panagiotis; Tsionas, Mike; Damien, Paul; Dellaportas, Petros
We present and compare observation driven and parameter driven models for predictinginteger price changes of high-frequency financial data. We explore Bayesian inferencevia Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) for the observationdriven model activity-direction-size (ADS), introduced by Rydberg and Shephard [1998a,2003]. We extend the ADS model by proposing a parameter driven model and use a Bernoulligeneralized linear model (GLM) with a latent process in the mean. We propose a new decompositionmodel that uses trade intervals and is applied on data that allow three possible tickmovements: one tick up price change, one tick down price change, or no price change. Wemodel each component sequentially using a Binomial generalized linear autoregressive movingaverage (GLARMA) model, as well as a GLM with a latent process in the mean. We perform asimulation study to investigate the effectiveness of the proposed parameter driven models usingdifferent algorithms within a Bayesian framework. We illustrate the analysis by modelling thetransaction-by-transaction data of of E-mini Standard and Poor’s (S&P) 500 index futures contracttraded on the Chicago Mercantile Exchange’s Globex platformbetween May 16th 2011 andMay 24th 2011. In order to assess the predictive performance, we compare the mean square error(MSE) and mean absolute error (MAE) criterion, as well as four scalar performance measures,namely, accuracy, sensitivity, precision and specificity derived from the confusion matrix.
Some statistical models in ecology and epidemiology
(2021-12-13) Kondakis, Marios; Κονδάκης, Μάριος; Athens University of Economics and Business, Department of Statistics; Ντζούφρας, Ιωάννης; Κυριακίδης, Επαμεινώνδας; Παππά, Μαρία; Κυπραίος, Θεόδωρος; Γιαννακόπουλος, Αθανάσιος; Καλογερόπουλος, Κωνσταντίνος; Δεμίρης, Νικόλαος
This dissertation focuses on statistically modelling specific biological processes from a Bayesian standpoint and it can divided into four components. The first component is concerned with ecological models that account for uncertainty and describe the fitness of insects, as explained by deterministic and stochastic demographic models, in order to understand the population performance of invasive species. The second component involves the investigation of non-linear statistical models based on popular ecological functions that describe the developmental process of arthropods as it is affected by temperature. Statistical modelling may provide insights into the population evolution of arthropod pests, which is important for ecology. Moreover, we investigate various computation techniques in order to not only derive robust estimates of the parameters of interest, but also to compare different models and computation methods. The third component entails modelling predator-prey systems to account for changes in prey population consumption over time as well as inter-individual interactions within the same species. Hence, we study statistical models that generate data using the Binomial distribution while prey density change in real time is described via ordinary differential equations (ode) ecological models. To address the possibility of noise, we propose that the probability of being consumed be linked to a stochastic process that is centered and reduced to (in the absence of diffusion) the instantaneous ratio of consumed prey density (which is the default link). The fourth section differs from the previous sections in that it focuses on modeling and detection of the spread of Vector-borne diseases (VBDs), as well as the development of a semi-automatic early warning system for the prevention of these diseases in the context of epidemiology. A generic observation running throughout this work is that detailed and robust modelling may assist greatly in more accurate and cautious conclusions drawn when interpreting the data.

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