George Kokolakis

Reliability analysis of a two-unit general parallel system with (n - 2) warm standbys

A parallel (2,n-2)-system is investigated here where two units start their operation simultaneously and any one of them is replaced instantaneously upon its failure by one of the (n-2) warm standbys. We assume availability of n non-identical, non-repairable units. The unit-lifetimes in full operational mode and in partial operational mode have general distribution functions Gi and respectively. The system reliability is evaluated by recursive relations.

Bayesian Statistical Analysis

Bayesian statistics has been considered, for quite a long time, as a branch of statistics; however, its role and impact on the development of the statistical inference is much more profound. Its philosophical base traces back to the very initial and rather subjective interpretation of the notion of probability during the Hellenistic period (323–146 BC). Nowadays, Bayesian statistics is considered as the study of uncertain events through the notion of probability. Its objective is the development of a coherent methodology for inductive mathematical reasoning. This article presents the basic principles of Bayesian inference together with the basic methodology applied to a variety of statistical problems, including estimation theory, hypothesis testing, model selection, and hierarchical models.

Asymptotics for the random coupon collector problem

We develop techniques of computing the asymptotics of the expected number of items that one has to check in order to detect all N existing kinds, as N → ∞. The occurring frequencies of the differend kinds are random variables.

Importance partitioning in micro-aggregation

One of the techniques of data holders for the protection of confidentiality of continuous data is that of micro-aggregation. Rather than releasing raw data (individual records), micro-aggregation releases the averages of small groups and thus reduces the risk of identity disclosure. At the same time the method implies loss of information and often distorts the data. Thus, the choice of groups is very crucial to minimize the information loss and the data distortion. No exact polynomial algorithms exist up to date for optimal micro-aggregation, and so the usage of heuristic methods is necessary. A heuristic algorithm, based on the notion of importance partitioning, is proposed and it is shown that compared with other micro-aggregation heuristics achieves improved performance.

A two-unit parallel system supported by ( n -2) standbys with general and non-identical lifetimes

This paper examines a functioning policy of a parallel system. We assume availability of n non-identical, non-repairable units for replacement or support. Two units start their operation simultaneously at times , and any one of them is replaced instantaneously upon its failure by one of the ( n − 2) standby units at random starting times Si ( ). Thus, with probability one, the system is functioning with two units up till the failure of the ( n − 1)th unit. Unit lifetimes Ti have a general joint distribution function F( t ). The system has to operate for a fixed period of time, c, and it stops functioning when all available units fail before c. The probability that the system is functioning for the required period of time c depends on the distribution of the unit lifetimes. The reliability of the system is evaluated by recursive relations. Independent unit lifetimes are considered as special cases.

Bregman divergences in the (m×k)-partitioning problem

A method of fixed cardinality partition is examined. This methodology can be applied on many problems, such as the confidentiality protection, in which the protection of confidential information has to be ensured, while preserving the information content of the data. The basic feature of the technique is to aggregate the data into m groups of small fixed size k, by minimizing Bregman divergences. It is shown that, in the case of non-uniform probability measures the groups of the optimal solution are not necessarily separated by hyperplanes, while with uniform they are. After the creation of an initial partition on a real data-set, an algorithm, based on two different Bregman divergences, is proposed and applied. This methodology provides us with a very fast and efficient tool to construct a near-optimum partition for the (mxk)-partitioning problem.

Random Multivariate Multimodal Distributions

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 multivatiate 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.

A martingale approach to the problem of dimensionality and performance of bayesian classifiers: asymptotic results

A martingale approach to the problem of performance of Bayesian classifiers with increasing feature dimensionality is applied here . Martingale limit theorems are also used to demonstrate that the expected probability of correct classification tends monotonically to unity for two general classification problems.

Bayesian classification based on multivariate binary data

Abstract Consider a disease which has associated with it d symptoms that are either present or absent. Several specific symptoms are known for an individual. The question is whether the person has the disease? This is a classification problem based on multivariate binary data. Our approach is Bayesian and involves the prediction of future d-vectors of binary responses. Underlying this problem is the implicit estimation of the corresponding 2d cell probabilities. This is difficult with low structure and with moderate or large d, unless the sample sizes for the training data are enormous. Our model incorporates a prior distribution on unknown parameters, and a ‘smoothing’ parameter that relates the cells to one another. The posterior is approximated in order to obtain cell probability estimates and an approximate predictive density. Consistency results are indicated, and the procedure is illustrated with data involving the diagnosis of a disease called ‘dry eyes’.

Priors on the Space of Unimodal Probability Measures

Construction of unimodal random probability measures on finite dimensional Euclidean space is considered. The approach based on Bayesian nonparametric models and Convexity Theory. Specifically, the proposed model makes use of the special properties of convex sets and Choquet’s theorem. As a result, we get random probability measures that admit derivatives almost everywhere in R d .