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The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent… (More)

- Ben Calderhead, Mark A. Girolami, Neil D. Lawrence
- NIPS
- 2008

Identification and comparison of nonlinear dynamical system models using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian… (More)

- Ben Calderhead, Mark A. Girolami
- Computational Statistics & Data Analysis
- 2009

A Bayesian approach to model comparison based on the integrated or marginal likelihood is considered, and applications to linear regression models and nonlinear ordinary differential equation (ODE) models are used as the setting in which to elucidate and further develop existing statistical methodology. The focus is on two methods of marginal likelihood… (More)

- Ben Calderhead, Mark A. Girolami
- Interface focus
- 2011

Mechanistic models based on systems of nonlinear differential equations can help provide a quantitative understanding of complex physical or biological phenomena. The use of such models to describe nonlinear interactions in molecular biology has a long history; however, it is only recently that advances in computing have allowed these models to be set… (More)

The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The method provides a fully automated adaptation mechanism that circumvents the costly pilot runs required to tune proposal… (More)

- Ben Calderhead
- Proceedings of the National Academy of Sciences…
- 2014

Markov chain Monte Carlo methods (MCMC) are essential tools for solving many modern-day statistical and computational problems; however, a major limitation is the inherently sequential nature of these algorithms. In this paper, we propose a natural generalization of the Metropolis-Hastings algorithm that allows for parallelizing a single chain using… (More)

We explore probability modelling of discretization uncertainty for system states defined implicitly by ordinary or partial differential equations. Accounting for this uncertainty can avoid posterior under-coverage when likelihoods are constructed from a coarsely discretized approximation to system equations. A formalism is proposed for inferring a fixed but… (More)

The GLASSO algorithm has been proposed by Friedman, Hastie and Tibshirani in 2008 to solve the `1 regularized inverse covariance matrix estimation problem. The conditional dependency structure which is captured by the inverse of the covariance matrix is of interest in numerous applications and the publication of GLASSO has spurred the development of several… (More)

This paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that… (More)

This thesis presents novel Markov chain Monte Carlo methodology that exploits the natural representation of a statistical model as a Riemannian manifold. The methods developed provide generalisations of the Metropolisadjusted Langevin algorithm and the Hybrid Monte Carlo algorithm for Bayesian statistical inference, and resolve many shortcomings of existing… (More)