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- Cédric Archambeau, Dan Cornford, Manfred Opper, John Shawe-Taylor
- Gaussian Processes in Practice
- 2007

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)

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 multimodal. We propose a variational… (More)

- Lucy Bastin, Dan Cornford, +6 authors Matthew Williams
- Environmental Modelling and Software
- 2013

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)

- Edzer J. Pebesma, Dan Cornford, +6 authors Jon O. Skøien
- Computers & Geosciences
- 2011

INTAMAP is a Web Processing Service for the automatic spatial 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… (More)

- David J. Evans, Dan Cornford, Ian T. Nabney
- Neurocomputing
- 2000

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)

- Ian T. Nabney, Dan Cornford, Christopher K. I. Williams
- Neurocomputing
- 2000

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)

Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the expected tilted loss function. The integration required in learning is not analytically tractable so to speed up the… (More)

- Matthew Williams, Dan Cornford, Lucy Bastin, Richard Jones, Stephen Parker
- Computers & Geosciences
- 2011

6 Recent advances in technology have produced a significant increase in the avail7 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. Despite… (More)

- Xuchen Yang, Jonathan D. Blower, +6 authors Joanna Lumsden
- Philosophical transactions. Series A…
- 2013

Data quality is a difficult notion to define precisely, and different communities have different views and understandings of the subject. This causes confusion, a lack of harmonization of data across communities and omission of vital quality information. For some existing data infrastructures, data quality standards cannot address the problem adequately and… (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)