Martin Bøgsted Hansen

Bayesian inversion of geoelectrical resistivity data

Enormous quantities of geoelectrical data are produced daily and often used for large scale reservoir modelling. To interpret these data requires reliable and efficient inversion methods which adequately incorporate prior information and use realistically complex modelling structures. We use models based on random coloured polygonal graphs as a powerful and flexible modelling framework for the layered composition of the Earth and we contrast our approach with earlier methods based on smooth Gaussian fields. We demonstrate how the reconstruction algorithm may be efficiently implemented through the use of multigrid Metropolis-coupled Markov chain Monte Carlo methods and illustrate the method on a set of field data. Copyright 2003 Royal Statistical Society.

A Bayesian approach to crack detection in electrically conducting media

In this paper, we review powerful new computational techniques which facilitate the Bayesian approach to statistical inference and discuss how they may be used to solve general inverse problems. Their power and flexibility is illustrated by the problem of detecting a finite set of linear non-intersecting perfectly insulating cracks in a homogeneously electrically conducting medium. In this case, efficient algorithms only exist if the number of cracks is known a priori. However, in this paper we demonstrate how uncertainty about the number of cracks can be incorporated into the modelling process and assessed together with crack locations.

Multiplicative censoring: density estimation by a series expansion approach

Abstract We consider the linear inverse problem of recovering the density function for a sample of multiplicatively censored random variables. This is a problem arising in, e.g. estimation of waiting time distributions of renewal processes. The purpose of this paper is to present an approach to this problem using a singular value decomposition of the desired density. We establish conditions under which the rate of convergence of the mean integrated square error of the estimator is optimal. An empirical method for determining the order of expansion is suggested. Finite sample properties of the estimation procedure are studied on a simulated data example.

QRP01-5: Quantitative Analysis of Access Strategies to Remote Information in Network Services

Remote access to dynamically changing information elements is a required functionality for various network services, including routing and instances of context-sensitive networking. Three fundamentally different strategies for such access are investigated in this paper: (1) a reactive approach initiated by the requesting entity, and two versions of proactive approaches in which the entity that contains the information element actively propagates its changes to potential requesters, either (2) periodically or triggered by changes of the information element (3). This paper first develops a set of analytic models to compute different performance metrics for these approaches, with special focus on the so-called mismatch probability. The results of the analytic models allow for design decisions on which strategy to implement for specific input parameters (change rate of the information element, network delay characterization) and specific requirements on mismatch probability, traffic overhead, and access delay. Finally, the analysis is applied to the use-case of context-sensitive service discovery.

Asymptotic inference for waiting times and patiences in queues with abandonment

Motivated by applications in call center management, we propose a framework based on empirical process techniques for inference about waiting time and patience distributions in multiserver queues with abandonment. The framework rigorises heuristics based on survival analysis of independent and identically distributed observations by allowing correlated waiting times. Assuming a regenerative structure of offered waiting times, we establish asymptotic properties of estimators of limiting distribution functions and derived functionals. We discuss construction of bootstrap confidence intervals and statistical tests, including a simple bootstrap two-sample test for comparing patience distributions. A small simulation study and a real data example are presented.

Adaptive Caching Strategies for Context Management Systems

Efficient access strategies to dynamically changing context information is an important functionality in many scenarios of context-sensitive networking. Access delay requirements and bounded communication overhead can be achieved via caching of the remotely available context information; meeting such QoS constraints is particularly relevant for wireless settings. However, caching increases the probability that the used context information does not correspond to its true value at the remote node. The paper develops a quantitative analytic model to calculate mismatch probability, mean access delay, and network overhead as a function of the cache lifetimes, network delays, request rates, and properties of the dynamically changing context information. Parametric studies of these performance metrics provide insights into the impact of different distribution types and parameter choices on these performance metrics. Due to monotonicity properties, the choice of optimal cache durations can be reduced to numerical solutions of the analytic equations. Results for two optimality criterions are presented and discussed. The quantitative models presented in this paper allow to implement adaptive caching strategies for context-sensitive networking functionalities.

Nonparametric estimation of the chord length distribution

The distribution of the length of a typical chord of a stationary random set is an interesting feature of the sets whole distribution. We give a nonparametric estimator of the chord length distribution and prove its strong consistency. We report on a simulation experiment in which our estimator compared favourably to a reduced sample estimator. Both estimators are illustrated by applying them to an image sample from a yoghurt ferment. We briefly discuss the closely related problem of estimation of the linear contact distribution. We show by a simulation experiment that a transformation of our estimator of the chord length distribution is more efficient than a Kaplan-Meier type estimator of the linear contact distribution.

Estimation of first contact distribution functions for spatial patterns in S-PLUS

An important tool in the exploratory analysis of random patterns are the so called first contact distribution functions. These functions give the distribution of first contact for increasing test sets contained in the void, and provide thereby important information on the “pore” space between particles. An introduction to the use of first contact statistics for exploratory analysis and statistical inference is e.g. given in Stoyan et al. (1987). The statistical aspects of the edge correction techniques presented here are mainly due to Baddeley & Gill (1993), Hansen et al. (1995, 1996) and Chiu & Stoyan (1994).

Nonparametric estimation of the stationary M/G /1 workload distribution function

In this paper, it is demonstrated how a nonparametric estimator of the stationary workload distribution function of the M/G/1-queue can be obtained by systematic sampling the workload process. Weak convergence results and bootstrap methods for empirical distribution functions for stationary associated sequences are used to derive asymptotic results and bootstrap methods for inference about the workload distribution function. The potential of the method is illustrated by a simulation study of the M/D/1 model.