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Islamic financial outlook and the influence of religion on the law
This presentation was given as part of the Islamic Law and International Law Conference 2011 by Professor Javaid Rehman from Brunel Law School. The conference was hosted by the Brunel Law School on the 9th September 2011
Proposals which speed-up function-space MCMC
Inverse problems lend themselves naturally to a Bayesian formulation, in
which the quantity of interest is a posterior distribution of state and/or
parameters given some uncertain observations. For the common case in which the
forward operator is smoothing, then the inverse problem is ill-posed.
Well-posedness is imposed via regularisation in the form of a prior, which is
often Gaussian. Under quite general conditions, it can be shown that the
posterior is absolutely continuous with respect to the prior and it may be
well-defined on function space in terms of its density with respect to the
prior. In this case, by constructing a proposal for which the prior is
invariant, one can define Metropolis-Hastings schemes for MCMC which are
well-defined on function space, and hence do not degenerate as the dimension of
the underlying quantity of interest increases to infinity, e.g. under mesh
refinement when approximating PDE in finite dimensions. However, in practice,
despite the attractive theoretical properties of the currently available
schemes, they may still suffer from long correlation times, particularly if the
data is very informative about some of the unknown parameters. In fact, in this
case it may be the directions of the posterior which coincide with the (already
known) prior which decorrelate the slowest. The information incorporated into
the posterior through the data is often contained within some
finite-dimensional subspace, in an appropriate basis, perhaps even one defined
by eigenfunctions of the prior. We aim to exploit this fact and improve the
mixing time of function-space MCMC by careful rescaling of the proposal. To
this end, we introduce two new basic methods of increasing complexity,
involving (i) characteristic function truncation of high frequencies and (ii)
hessian information to interpolate between low and high frequencies
Solution of systems of nonlinear equations Final report
Algorithm and computer program of diagonal discrimination method for computing nonlinear and transcendental function
Parenting, partnerships and a pandemic. In conversation with Abi Locke
A conversation with Abi Locke about her keynote at Psychology of Women and Equalities 2022 Conference
The experience of being a working mum with young children
Presentation of the findings from Master's project
The experience of being a working mum with young children. MSc project
Presentation of the Master's project, 26th May 2022
Deterministic Mean-field Ensemble Kalman Filtering
The proof of convergence of the standard ensemble Kalman filter (EnKF) from
Legland etal. (2011) is extended to non-Gaussian state space models. A
density-based deterministic approximation of the mean-field limit EnKF
(DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given
a certain minimal order of convergence between the two, this extends
to the deterministic filter approximation, which is therefore asymptotically
superior to standard EnKF when the dimension . The fidelity of
approximation of the true distribution is also established using an extension
of total variation metric to random measures. This is limited by a Gaussian
bias term arising from non-linearity/non-Gaussianity of the model, which exists
for both DMFEnKF and standard EnKF. Numerical results support and extend the
theory
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