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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
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
Multilevel Particle Filters for L\'evy-driven stochastic differential equations
We develop algorithms for computing expectations of the laws of models
associated to stochastic differential equations (SDEs) driven by pure L\'evy
processes. We consider filtering such processes and well as pricing of path
dependent options. We propose a multilevel particle filter (MLPF) to address
the computational issues involved in solving these continuum problems. We show
via numerical simulations and theoretical results that under suitable
assumptions of the discretization of the underlying driving L\'evy proccess,
our proposed method achieves optimal convergence rates. The cost to obtain MSE
scales like for our method, as compared with
the standard particle filter
Relative abundance and size composition of subtidal abalone, Haliotis spp., sea urchin, Strongylocentrotus spp., and abundance of sea stars off Fitzgerald marine reserve, September 1993
Data were collected at twenty-six dive stations at seven discrete latitudes along Fitzgerald Marine Reserve (FMR). Dive stations were targeted at three stratified depth zones: shallow (6.1 m), medium (10.7 m), and deep (16.8 m) in six of the seven locations. Two types of line
transects, emergent and invasive, were completed by separate dive teams at each dive station. The area surveyed totalled 1,510 m2 for emergent and 560 m2 for invasive transects.
Reef habitat dominated all depth zones, with moveable boulder and cobble increasing at medium and shallow depths. Encrusting coraline and surface algae dominated (49%), followed by turf (37%), sub-canopy (11.2%), and rare canopy (0.2%). Canopy was found only at shallow depths. Turf and sub-canopy decreased with depth.
Only two species of abalone, red, Haliotis rufescens, and flat, H. walallensis, were found. Flat abalone were extremely rare with only two found on invasive transects (0.004 abalone m-2). Red abalone densities were low at both emergent (0.02 abalone m-2, s.e.=O.Ol) and
invasive (0.07 abalone m-2, s.e.=0.03 ) transects. Red abalone concentrations differed significantly by depth and location. No abalone were found at deep depths and only one
sport-legal (178 mm shell length) abalone was found at medium depth. One commercial legal (198 mm shell length) abalone was found on the entire survey. Most sport-legal abalone were located in cryptic habitat in shallow invasive transects (38%), compared to 7% on emergent transects. The only evidence of recruitment was found on invasive transects where three young-of-the-year (<=31 mm shell length) red abalone were found. Evidence from our survey and other sources suggests that sport and commercial fisheries are not sustainable off the San Mateo coast.
Red urchin, Stongylocentrotus franciscanus, were more abundant than purple urchin, S. purpuratus, or red abalone. Red urchin densities were lower in emergent (1.08 urchin m-2,s.e.=0.04) than invasive (1.52, s.e.=0.06 m-2) transects. Densities of red urchin at deep stations in areas of lower algal abundance and potentially greater commercial fishing pressure were about one-half the densities at medium and shallow depths. ANOVA showed significant differences by depth and location. Mean Test Diameter (MTD) increased from deep to medium to shallow depths, while juvenile (<=50 mm) MTD showed an inverse
relationship with depth. Shallow-depth invasive transects revealed a missing mode of 83 mm red urchin. This size mode was not found in emergent transects, probably due to cryptic habitat.
Purple urchin were found at low densities at all three depth strata. Purple urchin densities were comparable in emergent (0.11 urchin m-2, s.e.=0.02 ) and invasive (0.09 urchin m-2,s.e.=0.03) transects. ANOVA showed densities varied significantly by location but not depth. 'Juvenile' purple urchin abundance showed an inverse relation to juvenile red urchin, increasing from deep to shallow depths. Purple urchin MTD of 84 mm (s.d.=23) was larger
than reported for intertidal areas off FMR.
Sea stars were found in high abundance off FMR. Bat stars, Asterina minata, had the highest densities (0.79 sea stars m-2, s.e.=0.03) followed by Pisaster sp. (0.47 sea stars m-2,s.e.=0.03 ), and sunflower stars, Pycnopodia helianthoides, (0.11 sea stars m-2, s.e.=0.04).
Pisaster sp. was the only group of sea stars where differences in density were significant by depth or location. (30pp.
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