Search results for "algorithm"
showing 10 items of 4887 documents
Efficient spatial designs using Hausdorff distances and Bayesian optimization
2021
An iterative Bayesian optimisation technique is presented to find spatial designs of data that carry much information. We use the decision theoretic notion of value of information as the design criterion. Gaussian process surrogate models enable fast calculations of expected improvement for a large number of designs, while the full-scale value of information evaluations are only done for the most promising designs. The Hausdorff distance is used to model the similarity between designs in the surrogate Gaussian process covariance representation, and this allows the suggested algorithm to learn across different designs. We study properties of the Bayesian optimisation design algorithm in a sy…
Cluster Monte Carlo algorithms
1990
Abstract The Swendsen-Wang and Wolff Monte Carlo algorithms are described in some detail, using the Potts model as an example. Various generalizations are then reviewed and some applications are discussed. Two complete Fortran programs for the algorithms are provided.
Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo
2020
We consider importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution. In the context of Bayesian latent variable models, the MCMC typically operates on the hyperparameters, and the subsequent weighting may be based on IS or sequential Monte Carlo (SMC), but allows for multilevel techniques as well. The IS approach provides a natural alternative to delayed acceptance (DA) pseudo-marginal/particle MCMC, and has many advantages over DA, including a straightforward parallelisation and additional flexibility in MCMC implementation. We detail minimal conditions which ensure strong consistency of the sug…
Multiple smoothing parameters selection in additive regression quantiles
2021
We propose an iterative algorithm to select the smoothing parameters in additive quantile regression, wherein the functional forms of the covariate effects are unspecified and expressed via B-spline bases with difference penalties on the spline coefficients. The proposed algorithm relies on viewing the penalized coefficients as random effects from the symmetric Laplace distribution, and it turns out to be very efficient and particularly attractive with multiple smooth terms. Through simulations we compare our proposal with some alternative approaches, including the traditional ones based on minimization of the Schwarz Information Criterion. A real-data analysis is presented to illustrate t…
Generalized Symmetry Models for Hypercubic Concordance Tables
2000
Summary Frequency data obtained classifying a sample of 'units' by the same categorical variable repeatedly over 'components', can be arranged in a hypercubic concordance table (h.c.t.). This kind of data naturally arises in a number of different areas such as longitudinal studies, studies using matched and clustered data, item-response analysis, agreement analysis. In spite of the substantial diversity of the mechanisms that can generate them, data arranged in a h.c.t. can all be analyzed via models of symmetry and quasi-symmetry, which exploit the special structure of the h.c.t. The paper extends the definition of such models to any dimension, introducing the class of generalized symmetry…
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.
Splitting the dynamics of large biochemical interaction networks
2003
This article is inscribed in the general motivation of understanding the dynamics on biochemical networks including metabolic and genetic interactions. Our approach is continuous modeling by differential equations. We address the problem of the huge size of those systems. We present a mathematical tool for reducing the size of the model, master-slave synchronization, and fit it to the biochemical context.
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.
Criteria for Bayesian model choice with application to variable selection
2012
In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first formalize the most general and compelling of the various criteria that have been suggested, together with a new criterion. We then illustrate the potential of these criteria in determining objective model selection priors by considering their application to the problem of variable selection in normal linear models. This results in a new model selection objective prior with a number of compelling properties.