Ralph Gailis

On Localisation of a Radiological Point Source

The problem is to localise a source of gamma radiation using dose rate measurements taken with a gamma probe at various points in space. A statistical model of dose-rate counts is developed using experimental data recorded in a laboratory. The problem is then studied using the theoretical Cramer-Rao bound (CRB) analysis, which quantifies the accuracy with which it is possible to localise the source and estimate its intensity. Three estimation algorithms are implemented and their performance investigated by simulations. The algorithms are then applied to field trial radiological survey data. The maximum likelihood algorithm performs the best of the considered algorithms.

Bayesian likelihood-free localisation of a biochemical source using multiple dispersion models

Localisation of a source of a toxic release of biochemical aerosols in the atmosphere is a problem of great importance for public safety. Two main practical difficulties are encountered in this problem: the lack of knowledge of the likelihood function of measurements collected by biochemical sensors, and the plethora of candidate dispersion models, developed under various assumptions (e.g. meteorological conditions, terrain). Aiming to overcome these two difficulties, the paper proposes a likelihood-free approximate Bayesian computation method, which simultaneously uses a set of candidate dispersion models, to localise the source. This estimation framework is implemented via the Monte Carlo method and tested using two experimental datasets. HighlightsWe develop a statistical method for adaptive likelihood free Bayesian estimation and model selection.The method is developed in the context of localisation of an emitting source of toxic material in the atmosphere.Three atmospheric dispersion models are considered.Two real datasets are used to assess the performance of the proposed method.

Detecting disease outbreaks using a combined Bayesian network and particle filter approach

Evaluating whether a disease outbreak has occurred based on limited information in medical records is inherently a probabilistic problem. This paper presents a methodology for consistently analysing the probability that a disease targeted by a surveillance system has appeared in the population, based on the medical records of the individuals within the target population, using a Bayesian network. To enable the system to produce a probability density function of the fraction of the population that is infected, a mathematically consistent conjoining of Bayesian networks and particle filters is used. This approach is tested against the default algorithm of ESSENCE Desktop Edition (which adaptively uses Poisson, exponentially weighted moving average and linear regression techniques as needed), and is shown, for the simulated test data used, to give significantly shorter detection times at false alarm rates of practical interest. This methodology shows promise to greatly improve detection times for outbreaks in populations where timely electronic health records are available for data-mining.

Achievable accuracy in Gaussian plume parameter estimation using a network of binary sensors

Theoretical Cramer-Rao bounds derived for parameter estimation of an atmospheric dispersion model.The work important for hazard modelling in the context of toxic source localisation.Bounds derived for the binary sensor network, as well as for the non-quantised (analogue measurement) sensor network.Theoretical bounds examined as a function of the binary threshold, sensor placement, and prior uncertainty.A comparison of the theoretical bound with empirical RMS errors of an MCMC estimation technique provided as a validation. The Gaussian plume model is the core of most regulatory atmospheric dispersion models. The parameters of the model include the source characteristics (e.g. location, strength) and environmental parameters (wind speed, direction, atmospheric stability conditions). The paper presents a theoretical analysis of the best achievable accuracy in estimation of Gaussian plume parameters in the context of a continuous point-source release and using a binary sensor network for acquisition of measurements. The problem is relevant for automatic localisation of atmospheric pollutants with applications in public health and defence. The theoretical bounds of achievable accuracy provide a guideline for sensor network deployment and its performance under various environmental conditions. The bounds are compared with empirical errors obtained using a Markov chain Monte Carlo (MCMC) parameter estimation technique.

Achievable accuracy in parameter estimation of a Gaussian plume dispersion model

The Gaussian plume model is the core of most regulatory atmospheric dispersion models. The parameters of the model include the source characteristics (e.g. location, strength, size) and environmental parameters (wind speed, direction, atmospheric stability conditions). A sensor network is at disposal to measure the concentration of biological pathogen or chemical substance within the plume. This paper presents a theoretical analysis of the best achievable accuracy in estimation of Gaussian plume model parameters. Numerical results illustrate how parameter estimation accuracy depends on sensor measurement accuracy, the density of sensors and the quality of (prior) meteorological advice. The theoretical bounds are compared with empirical errors obtained using an importance sampling parameter estimation technique.

The Interference of Higher-Order Statistics of the Concentration Field Produced by Two Point Sources According to a Generalized Fluctuating Plume Model

The higher-order correlation functions for the concentrationfluctuations arising from a two-point-source configuration have beencalculated analytically within the context of the phenomenology of afluctuating plume model (viz., a meandering plume model that explicitlyincorporates internal fluctuations). Explicit expressions for thesecond-, third-, and fourth-order correlationfunctions between the concentrationfluctuations produced by two point sources are given in terms of the sourceseparation d and the five physically based parameters that define thegeneralized fluctuating plume model: namely, the absolute plume dispersion,σa, which determines the outer plume length scale; the relative plume dispersion, σr, which determines the inner plume length scale; the fluctuation intensity, ir, in relative coordinates, which determines the internal concentration fluctuation level; the correlation coefficient, r,between the positions of the centroids of the two interfering plumes; and,the correlation coefficient, r*, between the concentration fluctuationsof the two plumes in relative coordinates, which determines the degree ofinternal mixing of the two scalars. Furthermore, the form of the totalconcentration probability density function arising from the interferenceproduced by two point sources is presented. Predictions for the second-ordercorrelation function, ρ, and for the total concentration probabilitydensity function have been compared with some new experimental data fora two-point-source configuration in grid turbulence generated in awater-channel simulation. These results are in good agreement with the dataand suggest that the analytical model for the second-order correlationfunction and the total concentration probability density function canreproduce many qualitative trends in the interaction of plumes from twosources.

Managing uncertainty in early estimation of epidemic behaviors using scenario trees

The onset of an epidemic can be foreshadowed theoretically through observation of a number of syndromic signals, such as absenteeism or rising sales of particular pharmaceuticals. The success of such approaches depends on how well the uncertainty associated with the early stages of an epidemic can be managed. This article uses scenario trees to summarize the uncertainty in the parameters defining an epidemiological process and the future path the epidemic might take. Extensive simulations are used to generate various syndromic and epidemic time series, which are then summarized in scenario trees, creating a simple data structure that can be explored quickly at surveillance time without the need to fit models. Decisions can be made based on the subset of the uncertainty (the subtree) that best fits the current observed syndromic signals. Simulations are performed to investigate how well an underlying dynamic model of an epidemic with inhomogeneous mixing and noise fluctuations can capture the effects of social interactions. Two noise terms are introduced to capture the observable fluctuations in the social network connectivity and variation in some model parameters (e.g., infectious time). Finally, it is shown how the entire framework can be used to compare syndromic surveillance systems against each other; to evaluate the effect of lag and noise on accuracy; and to evaluate the impact that differences in syndromic behavior among susceptible and infected populations have on accuracy.