an analytic expression of its asymptotic variance. Simulation results, based on Monte-Carlo realisations, are presented in order to show the validity of the theoretical derivations. 1.

triaxial halo model, we compute expected distributions of large Einstein radii. To assess the cosmic variance, we generate a number of Monte-Carlo realisations of all-sky catalogues of massive clusters. We find that the expected largest Einstein radius in the universe is sensitive to parameters

of evolution itself. This paper outlines a method of Monte Carlo realisation which does this, and hence allows an estimation of the distribution of key parameters in SETI, as well as allowing a quantification of their errors (and the level of ignorance therein). Furthermore, it provides a means for competing

(projected distance)× (radial velocity) 2 /G over the sample. However, it applies to the commonest case of all, when the tracer population does not follow the overall dark matter density. The method is verified against simulated datasets drawn from Monte Carlo realisations of exact solutions

We motivate the use of convergence diagnostic techniques for Markov Chain Monte Carlo algorithms and review various methods proposed in the MCMC literature. A common notation is established and each method is discussed with particular emphasis on implementational issues and possible extensions

for parameters of the Ising model given a particular lattice realisation.

and filaments, together with the assumption that formation history depends on when these barriers are crossed. We implement both these extensions in a generalised excursion set method, and run large Monte Carlo realisations to quantify the effects. Our results suggest that effects as large as those found

We present efficient Monte Carlo algorithms for performing Bayesian inference in a broad class of models: those in which the distributions of interest may be represented by time marginals of continuoustime jump processes conditional on a realisation of some noisy observation sequence

are presented for generation of random realisations from the joint smoothing distribution and for MAP estimation of the state sequence. Realisations of the smoothing distribution are generated in a forward-backward procedure, while the MAP estimation procedure can be performed in a single forward pass

. That is, we verify that under certain assumptions, signal realisations of the MFC model converge to a Gaussian process and thereafter compute the Gaussian process ’ covariance matrix, which is needed to construct Gaussian pro-cess signal realisations. The obtained Gaussian process model is under certain