Recent Advances in Stochastic Modeling and Data Analysis

The following sections are included:

• Preface

• Contents

Probability distributions are central tools for probabilistic modeling in data mining. In functional data analysis (FDA) they are weakly studied in the general case. In this paper we discuss a probability distribution law for functional data considered as stochastic process. We define first a new kind of stationarity linked to the Archimedean copulas, and then we build a probability distribution using jointly the Quasi-arithmetic means and the generators of Archimedean copulas. We also study some properties of this new mathematical tool.

In the case of the quantum generalization of random processes with the Hurst index H ≠ 1/2, expression for the quantum Hermitian generator of translations and its eigenfunctions are proposed. The normalization constant has been determined and its relation to the operator of momentum is shown. The interrelation between the momentum and the wave number has been generalized for the processes with a non-integer dimensionality α.

This study uses stochastic calculus to investigate the causes of the stock return stochastic volatility. The study aims to advance new explanations of stochastic volatility that hold also if the firm is unleveraged, and if the level of uncertainty about future business conditions does not change. Using the dividend discount model, I show that stock return volatility is admittedly stochastic if future dividends are affected by more than one stochastic state variable. Morever, I study how the mappings of state variables are related to stochastic return volatility. This study also investigates the effects of the discount rate and state variables' mutual correlation on the level of stock volatility and its fluctuation, finding substantial relationships therein.

In this paper, we intend to prove a result on the solvabillity of a class of backward stochastic differential equations by the McShane type. We will considered some more general conditions by the coefficient functions and prove a result on the existence and the pathwise uniqueness by the Nagumo type, extended the Athanassov results ([Athanassov, 1990]) for the ordinary differential equations. In final, we study the control of some electronic circuits in the presence of the stochastic resonance.

An extension of the univariate Waring distribution is proposed as an alternative to the UGWD for overdispersed count data in those cases in which the parameter estimates do not allow the properties of the UGWD to be used, such as the partition of the variance. Specifically, this model is applied to study the set of variables number of hotels per municipality in the Autonomous Region on Andalusia (Spain) from 1990 to 2003.

We present new characteristics of the central tendency and dispersion of data samples. They are constructed from estimates of parameters of underlying distributions and make possible an easy comparison of results obtained under different assumptions.

Our understanding of the input-output function of single neurons has been advanced by biophysically accurate multi-compartmental models. The large number of free parameters in these models requires the use of automated approaches for finding their optimal values in a very multi dimensional parameter-plane. Due to inherent noise in measuring equipment and surroundings determination of the accuracy of the obtained parameters is near impossible. Here we show that finding the parameters distribution via Monte Carlo approach simulations reveals the sensitivity of each parameter to noise. This method allows for the reduction of the complexity of the parameter-plane which in turn enables finding the sensitivity of the model to each parameter and the sensitivity of each parameter to noise.

We obtain in this paper stability and instability conditions for some single server queues with negative customers of batch or work removals. A negative customer removes a group of customers or an amount of work if present upon its arrival. Under general assumptions of stationary ergodic arrivals of negative customers or services of regular customers, we obtain sufficient stability conditions by strong coupling convergence of the process modeling the dynamics of the system to a stationary ergodic regime. We obtain also instability conditions by convergence in distribution to improper limiting distribution. The systems considered are of batch or amount of work removals, removals of customers from the tail of the queue, removals of customers in service, batches of arrivals and services of regular customers.

Bayesian nonparametric inference for unimodal and multimodal random probability measures on a finite dimensional Euclidean space is examined. After a short discussion on several concepts of multivariate unimodality, we introduce and study a new class of nonparametric prior distributions on the subspace of random multivariate multimodal distributions. This class in a way generalizes the very restrictive class of random unimodal distributions. A flexible constructional approach is developed using a variant of Khinchin's representation theorem for unimodal distributions. Results using our approach in a bivariate setting with a random draw from a Dirichlet process are presented.

We study a system maintained by means of imperfect repairs before a perfect repair. This model has been previously studied by Biswas and Sarkar (2000), which calculated the availability of the system when the operational and repair times were exponential. We extend the model considering these times phase-type distributed. Performance measures are calculated in stationary regime.

Using the principle of minimax and Bayesian approach the method of synthesis of asymptotically robust (AR) algorithms for detection and recognition of signals with unknown parameters on the background of independent noise and signal-like interference is developed. According to this method the asymptotically robust algorithm is sought in the class of algorithms of correlation type with the threshold depending on the observed sampling. For synthesis of a robust algorithm using this class no requirements are imposed on energy parameter of a signal, it is different from the known class of algorithms of M-type.

In this paper, we consider the estimation of the three-parameter Weibull distribution. We construct numerical algorithms to estimate the location, scale and shape parameters by maximal likelihood and simplified analytical methods. Convergence of these algorithms is studied theoretically and by computer modeling. Computer modeling results confirm practical applicability of estimates proposed. Recommendations for implementation of the estimates are discussed, too. Results from simulation studies assessing the performance of our proposed method are included.

Insurance companies have to build a reserve for their future payments which is usually done by deterministic methods giving only a point estimate. In this paper two semi-stochastic methods are presented along with a more sophisticated hierarchical Bayesian model containing MCMC technique. These models allow us to determine quantiles and confidence intervals of the reserve which can be more reliable as just a point estimate. A sort of cross-validation technique is also used to test the models.

The paper is about stochastic modelling risk capital requirements to cover equity risk for an insurance company by using copulas. We have tried to find the best portfolio structure with copula model and simulation using risk measure VAR. The result is compared with equity shock model given in Solvency II documents.

Aim of the paper is the analysis of the behaviour of risk filters connected to the demographic risk drivers for a portfolio of life annuities. The model, easily suitable to the case of pension annuities, involves the evolution in time of the mortality rates, taking into account the randomness of the financial scenario. Within this context, the uncertainty in the choice of the demographic scenario is measured and the analysis is also supported by the VaR sensitivity to this risk source.

Our aim was to examine the territorial dependence of risk for household insurances. Besides the classical risk factors such as type of wall, type of building, etc., we consider the location associated to each contract. A Markov random field model seems to be appropriate to describe the spatial effect. Basically there are two ways of fitting the model; we fit a GLM to the counts of claims with the classical risk factors and regarding their effects as fixed we fit the spatial model. Alternatively we can estimate the effects of all covariates (including location) jointly. Although this latter approach may seem to be more accurate, its high complexity and computational demands makes it unfeasible in our case. To overcome the disadvantages of the distinct estimation of the classical and the spatial risk factors proceed as follows: use first a GLM for the non-spatial covariates, and then fit the spatial model by MCMC. Refit next the GLM with keeping the obtained spatial effect fixed and afterwards refit the spatial model, too. Iterate this procedure several times. We achieve much better fit by performing eight iterations.

Latent, that is Incurred But Not Reported (IBNR) claims influence heavily the calculation of the reserves of an insurer, necessitating an accurate estimation of such claims. The highly diverse estimations of the latent claim amount produced by the traditional estimation methods (chain-ladder, etc.) underline the need for more sophisticated modelling. We are aimed at predicting the number of latent claims, not yet reported. This means the continuation the so called run-off triangle by filling in the lower triangle of the delayed claims matrix. In order to do this the dynamics of claims occurrence and reporting tendency is specified in a hierarchical Bayesian model. The complexity of the model building requires an algorithmic estimation method, that we carry out along the lines of the Bayesian paradigm using the MCMC technique. The predictive strength of the model against the future disclosed claims is analysed by cross validation. Simulations serve to check model stability. Bootstrap methods are also available as we have full record of the individual claims at our disposal. Those methods are used for assessing the variability of the estimated structural parameters.

Markov chain modelling has been previously used for hospital and community care systems, where the states in hospital care are described as phases, such as acute, rehabilitation, or long-stay and likewise social care in the community may be modelled using phases such as dependent, convalescent, or nursing home. This approach allows us to adopt a unified approach to health and community care modelling and management rather than focusing on the improvement of part of the system to the possible detriment of other components. We here extend this approach to show how the non-homogeneous Markov framework can be used to extract various metrics of interest. In particular, we use time-dependent covariates to obtain the mean and variance of the number of spells spent by a patient in hospital and in the community, and the expected total lengths of time in hospital and in the community.

Previous research introduced Conditional Phase-type distributions (C-Ph) consisting of a Coxian phase-type distribution conditioned on a BN where the phase-type distribution represents a continuous survival variable, the duration of time until a particular event occurs and the BN represents a network of inter-related variables. The C-Ph model has proved to be a suitable technique for modeling patient duration of stay in hospital characterized by the patient's characteristics on admission to hospital. This paper expands upon this technique to form a family of DC-Ph models of which the C-Ph is a member and applies the models to modeling patient stay in hospital based a set of inter-related discrete covariates.

This paper considers the analysis of waiting times in a hospital Accident and Emergency department, in particular the waiting time from the clinician's decision to admit until actual ward admission. A model is developed which employs a nave Bayes classifier for identification of patients who will require admission to ospital and thus experience such a waiting time. Such waiting times are found to be adequately represented by a lognormal model. Potential exists to expand such a model to include patient covariates.

The aim of this paper is to analyse the total length of time spent by a group of patients in an Accident and Emergency (A&E) department using a multi-stage Markov model. A patient's pathway through A&E consists of a sequence of stages, such as triage, examination, and a decision of whether to admit to hospital or not. Using Coxian phase-type distributions, this paper models these stages and illustrates the difference in the distribution of the time spent in A&E for those patients who are admitted to hospital, and those patients who are not. A theoretical approach to modelling the costs accumulated by a group of patients in A&E is also presented. The data analysed refers to the time spent by 53,213 patients in the A&E department of a hospital in Northern Ireland over a one year period.

In this paper the periodicity of a perturbed non homogeneous Markov system (P-NHMS) is studied. More specifically, the concept of a periodic P-NHMS is introduced, when the sequence of the total transition matrices does not converge, but oscillates among several different matrices, which are rather close to a periodic matrix Q, with period equal to d. It is proved that under this more realistic assumption, the sequence of the relative population structures splits into d subsequences that converge in norm, as t → ∞. Moreover, the asymptotic variability of the system is examined using the vector of means, variances and covariances of the state sizes, μ(t). More specifically, we prove that the vector μ(t) also splits into d subsequences that converge, as t → ∞, and we give the limits in an elegant closed analytic form.

In the present paper we study the evolution of a discrete-time homogeneous Markov system (HMS) with a finite state capacity. In order to examine the variability of the state sizes, their moments are evaluated for any time point, and recursive formulae for their computation are derived. Also a recursive formula is provided for the moments of the overflow size due to the finite state's capacity. The p.d.f. of the overflow size follows directly by means of the moments.

There are more and more recent copula models aimed at describing the behavior of multivariate data sets. However, no effective methods are known for checking the validity of these models, especially for the case of higher dimensions.

Our approach is based on the multivariate probability integral transformation of the joint distribution, which reduces the multivariate problem to one dimension. We compare the above goodness of fit tests to those, which are based on the copula density function. We present the background of the methods as well as simulations for their power.

In the present paper, the classical semi-Markov model in discrete time is examined under the assumption of a fuzzy state space. The definition of a semi-Markov model with fuzzy states is provided. Basic equations for the interval transition probabilities are given for the homogeneous and non homogeneous case. The definitions and results for the fuzzy model are provided by means of the basic parameters of the classical semi-Markov model.

Importance Sampling (IS) is a well-known Monte Carlo method which is used in order to estimate expectations with respect to a target distribution π, using a sample from another distribution g and weighting properly the output. Here, we consider IS from a different point of view. By considering the weights as sojourn times until the next jump, we associate a jump process with the weighted sample. Under certain conditions, the associated jump process is an ergodic semi-Markov process with stationary distribution π. Besides its theoretical interest, the proposed point of view has also interesting applications. Working along the lines of the above approach, we are allowed to run more convenient Markov Chain Monte Carlo algorithms. This can prove to be very useful when applied in conjunction with a discretization of the state space.

For the classical semi-Markov model, either time homogeneous or non-homogeneous, an examination of the convergence of the interval transition probabilities P_ij(s,t) as t → ∞ is presented using an approximation method provided by [R. De Dominics and R. Manca 1984]. Especially, we examine the dependence of the accuracy of the respective numerical method on the various values of the step h, in finding the transition interval probabilities, and we investigate the complexity of this algorithm.

Some models of probabilities are described by generalised stochastic equations. These models lead to the resolution of boundary problems for random distributions (generalized equations). We are interested in the equation Lx = f in S ⊂ IR^d where L is a linear operator, f is a random distribution and to the class of boundary conditions on the frontier Γ = ∂S in order to define for the corresponding boundary conditions. The resolution of boundary problems for random distributions lead to the Markov property for the solution of these equations.

The hidden Markov chain (HMC) model is a couple of random sequences (X, Y), in which X is an unobservable Markov chain, and Y is its observable noisy version. Classically, the distribution p(y∣x) is simple enough to ensure the Markovianity of p(x∣y), that enables one to use different Bayesian restoration techniques. HMC model has recently been extended to "triplet Markov chain" (TMC) model, which is obtained by adding a third chain U and considering the Markovianity of the triplet T = (X, U, Y). When U is not too complex, X can still be recovered from Y. In particular, a semi-Markov hidden chain is a particular TMC. Otherwise, the recent triplet partially Markov chain (TPMC) is a triplet T = (X,U,Y) such that p(x,u∣y) is a Markov distribution, which still allows one to recover X from Y.

The aim of this paper is to introduce, using a particular TPMC, semi-Markov chains hidden with long dependence noise. The general iterative conditional estimation (ICE) method is then used to estimate the model parameters, and the interest of the new model in unsupervised data segmentation is validated through experiments.

Non-parametric and parametric explicit decompositions of the classical Pearson, Pearson-Fisher, Hsuan-Robson-Mirvaliev and other tests on a sum of asymptotically independent chi-squared random variables with one degree of freedom in case of non-equiprobable cells are discussed. The parametric decompositions can be used for constructing more powerful tests, and can be considered as alternative proofs of limit theorems for some chi-squared type goodness-of-fit statistics.

Suppose the random vector (X, Y) satisfies the heteroscedastic regression model Y = m(X) + σ(X)ε, where m(·) = E(Y∣·), σ²(·) = Var(Y∣·) and ε (with mean zero and variance one) is independent of X. The response Y is subject to random right censoring and the covariate X is completely observed. New goodness-of-fit testing procedures for m and σ²(·) are proposed. They are based on a modified integrated regression function technique which uses the method of [Heuchenne and Van Keilegom, 2006b] to construct new versions of functions of the data points. Asymptotic representations of the processes are obtained and weak convergence to gaussian processes is deduced.

We develop a kernel smoothing based test of a parametric mean-regression model against a nonparametric alternative when the response variable is right-censored. The new test statistic is inspired by the synthetic data approach for estimating the parameters of a (non)linear regression model under censoring. The asymptotic critical values of our tests are given by the quantiles of the standard normal law. The test is consistent against any fixed alternative, against local Pitman alternatives and uniformly over alternatives in Hölder classes of functions of known regularity.

In this paper the regression models used for description and forecasting of the inland rail passenger conveyances of the regions of Latvia were considered. Two estimation approaches were compared: the classical linear regression model and the single index model. Various tests for hypothesis of explanatory variables insignificance and model correctness have been lead, and the cross-validation approach has been carried out as well. The analysis has shown obvious preference of the single index model.

Technological change is a dynamic and multidimensional phenomenon involving substitution and diffusion of technologies. In this process new technologies are entered into the market while the old ones are displaced. Various models have been constructed to explore the principles of technology substitutions. In general there are two approaches in tackling the problem. The first approach is using the replacing factor as the measure of technology substitution assuming that it is a function of market share captured by the technology or/and the time elapsed since technology introduction into the economic system. The second approach models the competitive technologies penetration separately where their intrinsic and competitive effects are explicitly represented into the relevant models. The purpose of this paper is to review the existent modeling approaches of technology substitution and analyze the factors affecting the interrelationship between the competing technologies. Finally, the models under review will be used to describe the substitution of the dial-up by the broadband technology for internet connectivity purposes and the models' fitting and forecasting performance is illustrated.

This paper explores the chaotic properties of an advection system expressed in difference equations form. In the beginning the Aref's blinking vortex system is examined. Then several new lines are explored related to the sink problem (one central sink, two symmetric sinks, eccentric sink and others). Chaotic forms with or without space contraction are presented, analyzed and simulated. Several chaotic objects are formulated especially when special rotation angles or a complex sinus rotation angle are introduced in the rotation-translation difference equations. Very interesting chaotic forms arise when elliptic rotation-translation equations are applied. The simulated chaotic images and attractors express several vortex-like forms resulting in various situations and especially in fluid dynamics.

In a previous work by the authors, maximum likelihood estimators (MLEs) were obtained for the drift and diffusion coefficients characterizing 2D lognormal diffusion models involving exogenous factors affecting the drift term. Such models are well-known to describe properly the behaviour of real phenomena of interest, for instance, in geophysical and environmental studies. The present paper provides the distribution of these MLEs, the Fisher information matrix, and the solution to some likelihood ratio tests of interest for hypotheses on the parameters weighting the relative effect of the exogenous factors.

The Cartographical Modeling belongs to the system of common scientific methods we use in search of new knowledge and its proving. The study of spatial relations is based on a map providing the most complete description and comprehension of any territorial problems.

A map gives a new information of more high order on mapping phenomena which is hidden in an initial figures. This new information one have got due to generalization of statistics is of particular value to scientific research and practical needs. The process of generalization results in discovery of the cartographical structures forming a certain system. Analysis of these structures enables the revelation of spatial regularities in disposition, proportion, combination and dynamics of sociodemographic and socioeconomical processes and phenomena.

Besides, the cartographical modeling provides the transition from discrete to continuous knowledge. This is the only method to obtain the continuous picture of spatially unbroken phenomena on the basis of discrete factual information (Aslanicashvili A., 1974). The importance of uninterrupted knowledge contained in the cartographical model is conditioned not only by its possibility to reveal the changes of investigated process or phenomena "from place to place" but also by its potentialities to bring to light a significant spatial relations between them and other social and natural processes and phenomena represented in the given model (map). The new knowledge obtained in the course of modeling serves as a basis for working out of the management decisions.

The comparison of identical models for a few years in succession gives us the notion about the nature and rate of changes and development of spatial structures. The cartographical modeling may be regarded as one of the modification of latent structure analysis which pursues an object to reveal and distinguish the latent groups of population with peculiar social organization, material and cultural consumption, goals, preferences and behaviour.

The permanent observation of current statistical information during a long time creates the necessary grounds for organization of data base. The collection of statistical data, their standardization and compiling of series of relevant maps are integral parts of monitoring as a system of supervision and control after the processes of spatial behaviour of population.

The scientific programme of monitoring includes also the working out of prognoses concerning eventual changes in the course of spatial self-organization of people, providing it with necessary information about possible unfavourable consequences, appraisals of regulation decisions and their efficiency.

Present paper contains the analysis of a spatial behaviour of rural population in Ukraine since the seventies, carried out by means of cartographical modeling of statistical data in the monitoring regime.

A data-driven approach for modeling volatility dynamics and comovements in financial markets is introduced. Special emphasis is given to multivariate conditionally heteroscedastic factor models in which the volatilities of the latent factors depend on their past values, and the parameters are driven by regime switching in a latent state variable. We propose an innovative indirect estimation method based on the generalized EM algorithm principle combined with a structured variational approach, that can handle models with large cross-sectional dimensions. Extensive Monte Carlo simulations and preliminary experiments with financial data show promising results.

In 2006, a set of new correlation functions named combined ODACF and ODCCF was proposed for detecting nonlinear correltionships. In the present study, a new validation method which is based on the nonlinear correlation tests is proposed to check the quality of NARMAX data smoothers without detailed prior knowledge of the actual noise. A simulation example is implemented to demonstrate the effectiveness and efficiency of the new method.

Based on an existing kernel survival function estimate that admits censored data, we develop confidence intervals to help assess the validity of the estimate. Practical issues of estimation are discussed and then the developments are applied to a real data set. The results are analyzed and discussed further.

We propose two methods of analysis of chaotic processes to be applied in sensory analysis. These methods may be used off-line in clinics e.g. for analysis of biosignals registered during sleep, or implemented into new sensor systems e.g. for drivers' vigilance monitoring in real time; they may also be applied in new type of hybrid models of circulatory and respiratory systems.

In this article we will prove existence and uniqueness conditions for stochastic fractal interpolation functions. As application we will study the normal and pathological human body temperature control.

A modeling approach to Life Table Data sets is proposed. The method is based on a stochastic methodology and the derived first exit time probability density function. The Health State Function of a population is modeled as the mean value of the health states of the individuals. The form for the health state function suggested here is relatively simple compared to previous attempts but the application results are quite promising. The model proposed is a three parameter model and it is compared to the three parameter Weibull model. Both models are applied to the Life Table Data for males and females in Greece from 1992 to 2000. The results indicate that the proposed model fits better to the data than the Weibull model. The methodology for the model building and the model proposed could be used in several cases in population studies in biology, ecology and in other fields.

In previous papers a dynamic model expressing the human life table data by using the first-passage-time theory for a stochastic process was formulated. It was also proposed a model for the health state function of a population and it was applied to the data of some countries.

In this paper we propose a quadratic and an extended form for the health state function and we introduce this form to the density function derived by using the first-passage-time theory for a stochastic process for the number of annual deaths of a population. The Health State Function H(t) is assumed to be close to zero at the time of birth and then increasing to a maximum health level and gradually decreases to a zero level at the time of death. The form of the density function includes also the high level of deaths occurring the first years of the childhood. Another very interesting feature of the extended quadratic health state function is that the resulting density function could fit quite reasonably the raw life table data provided by the Bureau of the Census. The use of a simple quadratic model and an extended quadratic model provides the researcher with a quite good explanatory tool with implications to pension funds and option theory.

We consider n agents displayed on S choosing one by one a standard A or B according to a local assignment rule. There is no asymptotics in space or in time, since the scan of the network is unique. We study the final behaviour by simulations. The main goal of this work is to evaluate the effect of an initial dumping on the final configuration.

This paper provides estimates of labor productivity growth in Italian mechanical sector during the period 1997-2002 analyzing its determinants with particular attention to the role played by turnover (exits and entrants) and company size. Data come from the longitudinal company accounts database of Research Centre of Unioncamere. The analysis put in evidence the global slowdown of productivity and the positive impact on productivity growth given by gross firm turnover. Transition matrices reveal a relevant degree of persistence in the period and a positive relation of this persistence with firm size. We apply the decomposition of [Baily et al., 1996] to analyse the role of turnover: survivors account in negative of overall growth, on the contrary, the contribution of entrants and exits is positive and very high.

This paper examines the economic performance of CSP-1, under specified outgoing quality limit (AOQL) and a realistic assumption of linearly variable acceptance cost. A mathematical programming model is developed to determine the unique combination of the plan's parameters (i*, f*) for which minimum total cost, per item produced, is achieved. Extended sensitivity analysis explores the behavior of the proposed model and validates its satisfying adaptation to real quality control conditions.

We present a dynamic programming model for the optimal operation of a flexible machine tool, to find a sequence of cutting speeds for the successive tools used in a cutting operation, in order to minimize expected makespan. The expected tool life decreases with cutting speed and each tool takes a setup time to install. We compare the optimal dynamic policies with well-known static policies.

Real-time estimation and short-term prediction of traffic conditions is one of major concern of traffic managers and ITS-oriented systems. Model-based methods appear now as very promising ways in order to reach this purpose. Such methods are already used in process control (Kalman filtering, Luenberger observers). In the application presented in this paper, due to the high non linearity of the traffic models, particle filter (PF) approach is applied in combination with the well-known first order macroscopic traffic model. Not only shall we show that travel time prediction is successfully realized, but also that we are able to estimate, in real time, the motorway traffic conditions, even on points with no measurement facilities, having, in a way, designed a virtual sensor.

Modelling the human behaviour in the market of the exchange rate was always an important challenge for the researchers. Financial markets are influenced by many economical, political and even psychological factors and so it is very difficult to forecast the movement of future values. Many traditional methods were used to help forecasting short-term foreign exchange rates. In their effort to achieve better results many researchers started to use soft computing techniques over the last years. In this paper a neuro-fuzzy model is presented. The model uses a time series data of daily quotes of the euro/dollar exchange rate in order to calculate the probability of the trend prediction as far as exchange rate. The data is divided into the training data, checking data and testing data. The model is trained using the training data and then the testing data is used for model validation.

The paper examines the organizational structure of Greek libraries, in the context of continuing change. It seeks the influence of the information technology and the new complex procedures that are necessary.

Management turns to a more vertical hierarchy transferring decision-making and responsibilities to the lower levels.

What that means is that library staff has to participate to decision making, problem solving, risk undertaking, innovation transferring. The most active role of human resources of the libraries ensures the effectiveness and efficiency of the management of library change. Consequently, the team working has characterized as the most effective working model.

Importance Sampling is a variance reduction technique possessing the potential of zero-variance estimators in its optimal case. It has been successfully applied in a variety of settings ranging from Monte Carlo methods for static models to simulations of complex dynamical systems governed by stochastic processes. We demonstrate the applicability of Importance Sampling to the simulation of coupled molecular reactions constituting biological or genetic networks. This fills a gap between great efforts spent on enhanced trajectory generation and the largely neglected issue of reduced variance among trajectories in the context of biological and genetic networks.

We propose an asymptotically unbiased and consistent estimate of the bispectrum of a stationary continuous-time process X = {X(t)}_t∈ℝ. The estimate is constructed from observations obtained by a random sampling of the time by {X(τ_k)}_k∈ℤ, where {τ_k}_k∈ℤ is a sequence of real random variables, generated from a Poisson counting process. Moreover, we establish the asymptotic normality of the constructed estimate.

This paper proposes a new numerical optimization technique, Search via Probability (SP) algorithm, for single-objective optimization problems. The SP algorithm uses probabilities to control the process of searching for optimal solutions. We calculate probabilities of the appearance of a better solution than the current one on each iteration, and on the performance of SP algorithm we create good conditions for its appearance. We test this approach by implementing the SP algorithm on some test single-objective optimization problems, and we find very stable results.

The aim of this study is to present a Genetic Algorithm (GA) for solving the Capacitated Single Allocation Hub Location Problem (CSAHLP) and to demonstrate its robustness and effectiveness for solving this problem. The appropriate objective function is correcting infeasible individuals to be feasible. These corrections are frequent in the initial population, so that in the subsequent generations genetic operators slightly violate the feasibility of individuals and the necessary corrections are rare. The solutions of proposed GA method are compared with the best solutions presented in the literature by considering various problem sizes of the AP data set.

Non-uniqueness of solutions and sensitivity to erroneous data are common problems to large-scale data clustering tasks. In order to avoid poor quality of solutions with partitioning-based clustering methods, robust estimates (that are highly insensitive to erroneous data values) are needed and initial cluster prototypes should be determined properly. In this paper, a robust density estimation initialization method that exploits the spatial median estimate to the prototype update is presented. Besides being insensitive to noise and outliers, the new method is also computationally comparable with other traditional methods. The methods are compared by numerical experiments on a set of synthetic and real-world data sets. Conclusions and discussion on the results are given.

In many psychological questionnaires (i.e., personnel selection surveys and diagnostic tests) the collected samples often include fraudulent records. This confronts the researcher with the crucial problem of biases yielded by the usage of standard statistical models. In this paper we generalize a recent combinatorial perturbation procedure, called SGR (Sample Generation by Replacements; [Lombardi et at., 2004]), to the analysis of structured malingering scenarios for dichotomous data. Combinatorial aspects of the approach are discussed and an application to a simple data set on the drug addiction domain is presented. Finally, the close relationships with Monte Carlo simulation studies are explored.

Distinct coefficients can give the degree of agreement between two raters. Some of them, such as π, κ, β and AC1, use the same concept of proportion of observed agreement but they use different measures of Agreement Expected by Chance (P_C).

This study analyses the effect of P_C on agreement indices when two raters classify subjects in two categories. Several examples are shown in which the degree of agreement and their respective P_C are calculated. These show that if the same number of observed agreements go from being equally distributed – in both categories - to being concentrated in only one category (1) π and κ decrease and their respective P_C increases (2) β and its P_C remain constant, and (3) AC1 increases and its P_C decreases.

Last years the amount of information about data of Libraries' management is increasing rapidly. This fact is making very difficult the analysis that is concerning decision making about improvement of services.

A new methodology for the quality analysis of Greek libraries is described in this paper. The goal is the recognition current state of resources management and the achievement of an effective and efficient decision-making and strategic planning.

The study examines the library operation, its services to users, management of the library's internal procedures, human resources and the cost effective manner to allocate the budget.

Usage and analysis by an efficient way of all types of data that are involved in Library's operation, usage of evaluation indexes about quality of services in Libraries and the combination of their results gives very important conclusions for their structure. This fact leads to establish an efficient strategic planning in any occasion.

The term "structure" of a Library includes not only the internal organization of offered services to users, but also the organization of all the procedures in the Library. Also, includes efficient management of human resources and efficient planning and management of budget allocation.

This paper describes ways of data and knowledge mining from a large amount of operational data that are used in services and organization of modern Libraries. The purpose is the extraction of useful conclusions from data mining's procedure that will cause improvement of all offered services and the efficient organization and operation of modern Libraries (e.g. improvement of collection's material, improvement of services in specific types of users, strategic planning of efficient budget allocation for material's acquisition).

Implementations of this methodology refers to evaluation of Library's collection in connection to material's subject categories, departments that are served, type of resources, type of users and studying interests of them.

Another implementation of this method refers to the effects that can be appeared in case of disproportionate fluctuation of one part of Library's collection (e.g. growth of electronic resources in relation with printed resources, or growth of one subject category in comparison with others), These effects are influencing sometimes not only Library's internal organization but also offered services to users and staffs practice and knowledge in new activities.

To investigate the similarity of natural languages, we use the following motivation: when a listener hears for the first time a language, it is plausible that he can distinguish and individualize syllables; due to this fact, he is able to say to which language or to which family of languages the language he hears is similar to. In order to investigate more rigorous the above hypothesi, a statistical analyze of common syllables excerpted from the representative vocabularies of seven Romance languages is presented.

If grouping of languages in linguistic families is generally accepted, the relations between the languages belonging to the same family periodically attracts the researchers' attention. We investigate the similarity of Romance languages based on the syllables excerpted from the representative vocabularies of seven Romance languages (Latin, Romanian, Italian, Spanish, Catalan, French and Portuguese languages) In the statistical approach we consider as random variables the seven Romance languages and as cases the common syllables in the representative vocabularies of the languages. A descriptive statistics of the data is given and also graphically depicted as a box and whisker plot. The purpose of our approach is, given these data, to find out if the Romance languages form "natural" clusters that can be labelled in a meaningful manner. To answer this question we perform a joining analysis (tree clustering, hierarchical clustering) on this data. In this setting, every language (i.e. variable) represents a singleton cluster. At each of the N - 1 steps (i.e. N = 7 the number of the Romance languages taken into consideration) the closest two (least dissimilar) clusters are merged into a single cluster, producing one less cluster at the next higher level. We also display the dendogram obtained by clustering the Romance languages using the nearest-neighbor technique.

The aim of this work is to define a clustering method starting from the pretopological results related to the minimal closed subset concepts which provide us the view of relations between groups in its structure; then, we consider this result as the pre-treatment for some classical clustering algorithms. Especially, k-means philosophy is observed by its remarkable benefits. Thus we propose a new clustering method in two processes such as structuring process and clustering one. This method allows us to: obtain a data clustering for both of categorical and numeric data - exclude the limit in determination of cluster number a priori - and attain well-shaped clusters whose shapes are not influenced on existence of outliers.

Functional logistic regression is one of the methods that have raised great interest in the emerging statistical field of functional data analysis and particularly the one of functional regression analysis when the predictor is functional and the response is binary. The aim of this paper is to generalize the solutions exposed in the literature to the different problems that arise in the functional logit model (as multicollinearity), to the multinomial case where the response variable has a finite set of categories bigger than two.

In this paper, we introduce a volatility-based method for clustering analysis of financial time series. Using the generalized autoregressive conditional heteroskedasticity (GARCH) models we estimate the distances between the stock return volatilities. The proposed method uses the volatility behavior of the time series and solves the problem of different lengths. As an illustrative example, we investigate the similarities among major international stock markets using daily return series with different sample sizes from 1966 to 2006. The data were divided into two sample periods: previous and subsquent to the terrorist attack on September 11, 2001. From cluster analysis in the period before 9-11, most European markets countries, United States and Canada appear close together, and most Asian/Pacific markets and the South/Middle American markets appear in a distinct cluster. After 9-11, the European stock markets have become more homogenous, and North American markets, Japan and Australia seem to come closer.

The article describes problems of mathematical description of longevity and ageing processes in living organisms. These problems are similar to the problems considered in reliability theory but need development of additional methods to account for the living organisms specificity. The article describes methods for assessment of heterogeneity phenomenon in population, for analysis of stress experiments, for modeling of survival in changing environment. Results of analysis for longevity experiments with warms C.elegans and mediterranean fruitflies Ceratitis capitata are presented. Application of the new methods and results, obtained in biodemography, can be profitable in investigation of technical systems under nonstandard conditions and extreme conditions.

Undoubtedly, a distinguished increasing volume of mobile applications, nowadays, may have some impacts toward mobile IT-business. It is, therefore, of interest that the mobile applications among city people are examined as to obtain noticeable ideas worth for mobile IT-business development. Concerning investigation on mobile applications, sample data are primarily collected in Bangkok in-bound districts by interviewing with questionnaires, basing on stratification and proportional allocation. As for data-analysis, the descriptions of interesting variables in the four-main groups of mobile applications are, firstly, made. The first category consists of basic applications whereas the second one is composed of sending and receiving messages. The applications available for people's activities are categorized in the third one. The fourth represents communication-technology and device-transfer. As to make inferences for the true characteristics of interesting variables, estimations are performed and, subsequently followed by hypothesis-testings with appropriate parametric and nonparametric procedures. Relating the associations between variables concerning mobile-application types and mobile-user characteristics togetherwith their attitudes toward mobile technology, the association level and significance test are determined by Cramer's and Goodman-and-Kruskal-tau Statistics. Then, Regression is employed as to investigate the relationship between an interesting response variable with independent variables. However, in case of binary response-variable, Logistic Regression is applied.

Air pollution is a widely preoccupation which needs the development of control strategies. To reach this goal, pollution sources have to be precisely identified. Principal component analysis is a possible response to this problem. Indeed this factorial method enables to detect sources, that is to have a qualitative description of them. In this work, techniques of rotation are a useful help for the association of variables with factors. We highlight the fact that the rotation must be applied to the standardized principal components, so as to keep good interpretation properties. This methodology has then been applied to a problem of air pollution on a french site.

I present a path integral formulation of the density matrix for Rényi and Tsallis-Havrda-Charvát statistics. As a practical application I derive the associated option pricing formula generalizing the Black-Scholes analysis for Gaussian stock fluctuations. Perturbation expansion around the Black–Scholes formula is performed and properties of the ensuing expansion are discussed.

Suppose we observe a time series that alternates between different autoregressive processes. We give conditions under which it has a stationary version, derive a characterization of efficient estimators for differentiable functionals of the model, and use it to construct efficient estimators for the autoregression parameters and the innovation distributions. We also study the cases of equal autoregression parameters and of equal innovation densities.

We propose a recursive method for estimating an Hilbert Moving Average process of order 1. Under some assumptions this problem is equivalent to resolution of a non linear equation in an Hilbert space. Our method consist in resolving a non-linear equation recursively, from functional analysis results, and determine a recursive sequence of operators which converges to the solution of our equation.

This paper proposes a (stochastic) Langevin-type formulation to modelize the continuous time evolution of the state of a biological reactor. We adapt the classical technique of asymptotic observer commonly used in the deterministic case, to design a Monte–Carlo procedure for the estimation of an unobserved reactant. We illustrate the relevance of this approach by numerical simulations.

In this paper generalized barrier options of American type in discrete time are studied. Instead of a barrier, a domain of knock out type is considered. To find the optimal time of exercising the contract, or stopping a Markov price process, an optimal stopping domain can be constructed. To determine the optimal stopping domain Monte Carlo simulation is used. Probabilities of classification errors when determining the structure of the optimal stopping domain are analyzed.

The performance of image denoising algorithms using the Double Tree Complex Wavelet Transform, DT CWT, followed by a local adaptive bishrink filter can be improved by reducing the sensitivity of that filter with the local marginal variance of the wavelet coefficients. In this paper is proposed a solution for the sensitivity reduction based on enhanced diversity.

In order to evaluate the characteristics of a tandem queueing network, we propose a study, taking into account the qualitative properties of distributions. For this, we consider different bounds (lower and upper bounds) for different classes of nonparametric distributions. These bounds are computed while applying the QNA method (Queuing Network Analyser). To verify whether the proposed intervals include(contain) the approximate values, we have considered some approximations as those corresponding to KLB (Kramer Langenbach Benz) and simulation methods. Two algorithms have been constructed for programming the methods, and implemented for under the assumption that the inter-arrival distribution of the network is parametric or nonparametric.

This paper presents the method of assessment of groundwater quality monitoring network taking into account quantity of information, which can be delivered to the control system. This study was carried out on groundwater monitoring network of post-flotation waste disposal site, called "Zelazny Most". This paper shows the pilot study going to reorganization of existing groundwater quality monitoring network. Farther, different scenarios of verification the existing monitoring network are proposed. The density of monitoring network surrounded the reservoir are also considered. The values of transinformation were used to evaluation the amount of information providing by groundwater quality monitoring network.

Simultaneous tests of a huge number of hypotheses is a core issue in high flow experimental methods. In the central debate about the type I error rate, [Benjamini and Hochberg, 1995] have provided a procedure that controls the now popular False Discovery Rate (FDR).

The present paper focuses on the type II error rate. The proposed strategy improves the power by means of moderated test statistics integrating external information available in a double-sampling scheme. The small sample distribution of the test statistics is provided. Finally, the present method is implemented on transcriptomic data.

The following sections are included:

• Author Index