Details of Grant 

EPSRC Reference:	EP/N000188/1
Title:	Unbiased Inference for Complex Models
Principal Investigator:	Vollmer, Dr S
Other Investigators:
Researcher Co-Investigators:
Project Partners:	University of Warwick
Department:	Statistics
Organisation:	University of Oxford
Scheme:	First Grant - Revised 2009
Starts:	01 October 2015	Ends:	30 September 2017	Value (£):	98,893
EPSRC Research Topic Classifications:	Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 16 Jun 2015 EPSRC Mathematics Prioritisation Panel June 2015 Announced
Summary on Grant Application Form
Large scale mathematical models play an essential role in many applications throughout science. A prime example of an application of a complex continuous model is the research on climate change. The climate is usually modelled as a non-linear mathematical-physical system based on the coupling of a model of the atmosphere and an ocean circulation model. Both of these models involve a big set of state variables, such as the temperature, humidity, the wind, flow speed and pressure, to name but a few. The state of the system is modelled as the collection of these parameters for every grid cell. The evolution of these parameters arises as a discretisation of the underlying continuous model. In order to make inference about the climate, the model needs to be run at a fixed discretisation. The accuracy of the inference depends on the number of times the model can be simulated under a finite computational budget which thus influences the level of the discretisation. This trade-off results in a widening gap between the models that we can simulate and the ones for which we can make sound statistical inference. Bayesian methods are ubiquitous in statistical modelling and machine learning for the analysis of data. The aim is to model the posterior distribution which is in most cases only available indirectly as an appropriate limit of a sequence of probability measures. The most prominent technique to access the posterior distribution is via MCMC algorithms. MCMC algorithms are fully flexible and generally applicable. However, they require simulations of the full complex model on each step which limits the number of steps that are possible for a fixed computational budget, thus requiring huge computational budgets if we want to keep a high level of accuracy. For this reason Monte Carlo methods are often neglected, even though they are the only methods targeting the correct posterior. For a wide range of applications, for example in weather prediction, nuclear waste management and quantitative finance, the quantity to be inferred is often only given indirectly as an appropriate limit of distributions. The conventional approach to such an indirect representation requires a truncation. In most cases, the choice is to either run the MCMC only for a sufficiently long time, to fix a finite discretisation or to incorporate only a certain number of terms in the series expansion. However, all of these truncations lead to a systematic bias in the modelling of the target distribution and the exact accuracy of this bias is highly application-specific and very difficult to analyse. The main motivation of this proposal is to establish, extend and improve schemes for direct unbiased inference and thus to remove systematic bias in Bayesian inference for complex models. In particular, it aims at improving established inference methods by an incorporation of a new class of unbiased estimators and to develop new inference algorithms that yield unbiased estimators for Bayesian inference. This approach naturally allows the distribution of computations across different discretisations which results in great computational gain which is beneficial for a wide range of applications. The BBC has, for example, recently reported on the possibility to use the mobile phone records in Western Africa in order to predict the spreading of Ebola. Mathematical models have also become a factor for the strategic planning of the Metropolitan police in London to predict crime and to identify the areas of high probabilities of certain crimes in order to increase the presence of the police accordingly. Many more of these very recent examples in the press can be found undermining the importance of the use of accurate models around us. In the medium term, a sound statistical method, allowing an unbiased evaluation of complex models would therefore optimise a wide range of production processes in industry, politics and medicine to name just a few.
Key Findings
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Potential use in non-academic contexts
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Organisation Website:	http://www.ox.ac.uk