Search results for "Computation"
showing 10 items of 7362 documents
Posterior moments and quantiles for the normal location model with Laplace prior
2021
We derive explicit expressions for arbitrary moments and quantiles of the posterior distribution of the location parameter η in the normal location model with Laplace prior, and use the results to approximate the posterior distribution of sums of independent copies of η.
Triply Factorised Groups and the Structure of Skew Left Braces
2021
The algebraic structure of skew left brace has proved to be useful as a source of set-theoretic solutions of the Yang–Baxter equation. We study in this paper the connections between left and right $$\pi $$ -nilpotency and the structure of finite skew left braces. We also study factorisations of skew left braces and their impact on the skew left brace structure. As a consequence of our study, we define a Fitting-like ideal of a left brace. Our approach depends strongly on a description of a skew left brace in terms of a triply factorised group obtained from the action of the multiplicative group of the skew left brace on its additive group.
Sparse kernel methods for high-dimensional survival data
2008
Abstract Sparse kernel methods like support vector machines (SVM) have been applied with great success to classification and (standard) regression settings. Existing support vector classification and regression techniques however are not suitable for partly censored survival data, which are typically analysed using Cox's proportional hazards model. As the partial likelihood of the proportional hazards model only depends on the covariates through inner products, it can be ‘kernelized’. The kernelized proportional hazards model however yields a solution that is dense, i.e. the solution depends on all observations. One of the key features of an SVM is that it yields a sparse solution, dependin…
MCMC methods to approximate conditional predictive distributions
2006
Sampling from conditional distributions is a problem often encountered in statistics when inferences are based on conditional distributions which are not of closed-form. Several Markov chain Monte Carlo (MCMC) algorithms to simulate from them are proposed. Potential problems are pointed out and some suitable modifications are suggested. Approximations based on conditioning sets are also explored. The issues are illustrated within a specific statistical tool for Bayesian model checking, and compared in an example. An example in frequentist conditional testing is also given.
Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations
2010
During the last decade, lattice-Boltzmann (LB) simulations have been improved to become an efficient tool for determining the permeability of porous media samples. However, well known improvements of the original algorithm are often not implemented. These include for example multirelaxation time schemes or improved boundary conditions, as well as different possibilities to impose a pressure gradient. This paper shows that a significant difference of the calculated permeabilities can be found unless one uses a carefully selected setup. We present a detailed discussion of possible simulation setups and quantitative studies of the influence of simulation parameters. We illustrate our results b…
Componentwise adaptation for high dimensional MCMC
2005
We introduce a new adaptive MCMC algorithm, based on the traditional single component Metropolis-Hastings algorithm and on our earlier adaptive Metropolis algorithm (AM). In the new algorithm the adaption is performed component by component. The chain is no more Markovian, but it remains ergodic. The algorithm is demonstrated to work well in varying test cases up to 1000 dimensions.
Pseudo-Cut Strategies for Global Optimization
2011
Motivated by the successful use of a pseudo-cut strategy within the setting of constrained nonlinear and nonconvex optimization in Lasdon et al. (2010), we propose a framework for general pseudo-cut strategies in global optimization that provides a broader and more comprehensive range of methods. The fundamental idea is to introduce linear cutting planes that provide temporary, possibly invalid, restrictions on the space of feasible solutions, as proposed in the setting of the tabu search metaheuristic in Glover (1989), in order to guide a solution process toward a global optimum, where the cutting planes can be discarded and replaced by others as the process continues. These strategies can…
Model comparison and selection for stationary space–time models
2007
An intensive simulation study to compare the spatio-temporal prediction performances among various space-time models is presented. The models having separable spatio-temporal covariance functions and nonseparable ones, under various scenarios, are also considered. The computational performance among the various selected models are compared. The issue of how to select an appropriate space-time model by accounting for the tradeoff between goodness-of-fit and model complexity is addressed. Performances of the two commonly used model-selection criteria, Akaike information criterion and Bayesian information criterion are examined. Furthermore, a practical application based on the statistical ana…
Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter
2013
Markov chain Monte Carlo (MCMC) methods are powerful computational tools for analysis of complex statistical problems. However, their computational efficiency is highly dependent on the chosen proposal distribution, which is generally difficult to find. One way to solve this problem is to use adaptive MCMC algorithms which automatically tune the statistics of a proposal distribution during the MCMC run. A new adaptive MCMC algorithm, called the variational Bayesian adaptive Metropolis (VBAM) algorithm, is developed. The VBAM algorithm updates the proposal covariance matrix using the variational Bayesian adaptive Kalman filter (VB-AKF). A strong law of large numbers for the VBAM algorithm is…
Bayesian analysis of a Gibbs hard-core point pattern model with varying repulsion range
2014
A Bayesian solution is suggested for the modelling of spatial point patterns with inhomogeneous hard-core radius using Gaussian processes in the regularization. The key observation is that a straightforward use of the finite Gibbs hard-core process likelihood together with a log-Gaussian random field prior does not work without penalisation towards high local packing density. Instead, a nearest neighbour Gibbs process likelihood is used. This approach to hard-core inhomogeneity is an alternative to the transformation inhomogeneous hard-core modelling. The computations are based on recent Markovian approximation results for Gaussian fields. As an application, data on the nest locations of Sa…