Managing uncertainty in complex stochastic models: design and emulation of a Rabies model

In this paper we present a novel method for emulating a stochastic, or random output, computer model and show its application to a complex rabies model. The method is evaluated both in terms of accuracy and computational efficiency on synthetic data and the rabies model. We address the issue of experimental design and provide empirical evidence on the effectiveness of utilizing replicate model evaluations compared to a space-filling design. We employ the Mahalanobis error measure to validate the heteroscedastic Gaussian process based emulator predictions for both the mean and (co)variance. The emulator allows efficient screening to identify important model inputs and better understanding of the complex behaviour of the rabies model.

Approximately optimal experimental design for heteroscedastic Gaussian process models

This paper presents a greedy Bayesian experimental design criterion for heteroscedastic Gaussian process models. The criterion is based on the Fisher information and is optimal in the sense of minimizing parameter uncertainty for likelihood based estimators. We demonstrate the validity of the criterion under different noise regimes and present experimental results from a rabies simulator to demonstrate the effectiveness of the resulting approximately optimal designs.

Viruses and the eye

About 60% of human infections diseases are caused by viruses,including such important diseases as AIDS, polio, rabies and certain forms of cancer. A few groups of viruses are important to optometrists because they either cause a primary eye infection or a systemic viral infection with ocular complications.

Bacterial associations with salmonid eggs

Rainbow trout eggs Salmo gairdneri, Richardson, were incubated under a range of different environmental conditions. Recovery of bacteria from egg surfaces revealed that increased water temperature, slow water flow rates and high egg density all significantly increased egg surface bacterial populations. Live eggs were mainly colonized by Cytophaga sp., pseudomonas fluorescens and Aeromonas hydrophila. In contrast, dead eggs supported considerable numbers of fluorescent Pseudomonas sp. Analysis of potential nutrient sources for bacteria colonizing live egg surfaces revealed that small amounts of amino acids, phosphate and potassium may be lost by incubating eggs. Subsequently these nutrients were shown to be capable of supporting limited bacterial growth and reproduction. Dead eggs `leaked' increased amounts of the above nutrients which in turn supported higher bacterial numbers. In addition, biochemical analysis of eggs revealed amino acids and fatty acids that might be utilized by bacteria colonizing dead egg surfaces. Assessment of adhesion properties of bacteria frequently recovered from egg surfaces revealed high cell surface hydrophobicity as an important factor in successful egg colonization. Analysis of egg mortalities from groups of rainbow trout and brown trout (S.trutta L.) eggs maintained under two different incubation systems revealed that potentially a close correlation existed between egg surface bacterial numbers and mortalities in the egg during incubation. Innoculation of newly-fertilized eggs with bacteria demonstrated that groups of eggs supporting high numbers of P.fluorescens suffered significantly higher mortalities during the early part of their incubation. Exposure of incubating eggs to oxolinic acid, chlortetracycline and chloramphenicol demonstrated that numbers of bacteria on egg surfaces could be significantly reduced. However, as no corresponding increase in egg hatching success was revealed, the treatment of incubating eggs with antibiotics or antimicrobial compounds can not be recommended. In commercial hatcheries bacteria are only likely to be responsible for egg deaths during incubation when environmental conditions are unfavourable. High water temperatures, slow water flow rates and high egg density all lead to increased bacterial number of egg surfaces, reduced water circulation and low levels of dissolved oxygen. Under such circumstances sufficient amounts of dissolved oxygen may not be available to support developing embryos.

An efficient screening method for computer experiments

Computer simulators of real-world processes are often computationally expensive and require many inputs. The problem of the computational expense can be handled using emulation technology; however, highly multidimensional input spaces may require more simulator runs to train and validate the emulator. We aim to reduce the dimensionality of the problem by screening the simulators inputs for nonlinear effects on the output rather than distinguishing between negligible and active effects. Our proposed method is built upon the elementary effects (EE) method for screening and uses a threshold value to separate the inputs with linear and nonlinear effects. The technique is simple to implement and acts in a sequential way to keep the number of simulator runs down to a minimum, while identifying the inputs that have nonlinear effects. The algorithm is applied on a set of simulated examples and a rabies disease simulator where we observe run savings ranging between 28% and 63% compared with the batch EE method. Supplementary materials for this article are available online.