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Stochastic differential equations arise naturally in a range of contexts, from financial to environmental modeling. Current solution methods are limited in their representation of the posterior process in the presence of data. In this work, we present a novel Gaussian process approximation to the posterior measure over paths for a general class of(More)
A conventional neural network approach to regression problems approximates the conditional mean of the output vector. For mappings which are multi-valued this approach breaks down, since the average of two solutions is not necessarily a valid solution. In this article Mixture Density Networks, a principled method for modelling conditional probability(More)
6 Recent advances in technology have produced a significant increase in the avail-7 ability of free sensor data over the Internet. With affordable weather monitoring 8 stations now available to individual meteorology enthusiasts, a reservoir of real 9 time data such as temperature, rainfall and wind speed can now be obtained for 10 most of the world.(More)
In many problems in spatial statistics it is necessary to infer a global problem solution by combining local models. A principled approach to this problem is to develop a global probabilistic model for the relationships between local variables and to use this as the prior in a Bayesian inference procedure. We use a Gaussian process with hyper-parameters(More)
Models are central tools for modern scientists and decision makers, and there are many existing frameworks to support their creation, execution and composition. Many frameworks are based on proprietary interfaces, and do not lend themselves to the integration of models from diverse disciplines. Web based systems, or systems based on web services, such as(More)
Diffusion processes are a family of continuous-time continuous-state stochastic processes that are in general only partially observed. The joint estimation of the forcing parameters and the system noise (volatility) in these dynamical systems is a crucial, but non-trivial task, especially when the system is nonlinear and multi-modal. We propose a(More)
INTAMAP is a Web Processing Service for the automatic interpolation of measured point data. Requirements were (i) using open standards for spatial data such as developed in the context of the Open Geospatial Consortium (OGC), (ii) using a suitable environment for statistical modelling and computation, and (iii) producing an integrated, open source solution.(More)
Web-based distributed modelling architectures are gaining increasing recognition as potentially useful tools to build holistic environmental models, combining individual components in complex workflows. However, existing web-based modelling frameworks currently offer no support for managing uncertainty. On the other hand, the rich array of modelling(More)
Proofs subject to correction. Not to be reproduced without permission. Confidential until read to the Society. Contributions to the discussion must not exceed 400 words. Contributions longer than 400 words will be cut by the editor. Summary. The retrieval of wind vectors from satellite scatterometer observations is a non-linear inverse problem. A common(More)
The retrieval of wind vectors from satellite scatterometers is a non-linear inverse problem. A common approach to solving inverse problems is to adopt a Bayesian framework and infer the posterior distribution of the parameters of interest given the observations using a likelihood model relating the observations to the parameters, and a prior distribution(More)