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Showing papers in "Journal of the Royal Statistical Society in 2011"


Journal Article
TL;DR: The methodology proposed automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density, and substantial improvements in the time‐normalized effective sample size are reported when compared with alternative sampling approaches.
Abstract: 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 the costly pilot runs that are required to tune proposal densities for Metropolis-Hastings or indeed Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms. This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain. The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. The performance of these Riemann manifold Monte Carlo methods is rigorously assessed by performing inference on logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. Substantial improvements in the time-normalized effective sample size are reported when compared with alternative sampling approaches. MATLAB code that is available from http://www.ucl.ac.uk/statistics/research/rmhmc allows replication of all the results reported.

1,031 citations


Journal Article
TL;DR: A multiscale adaptive regression model (MARM) is proposed to integrate the propagation-separation approach with statistical modeling at each voxel for spatial and adaptive analysis of neuroimaging data from multiple subjects and significantly outperforms conventional analyses of imaging data.
Abstract: Neuroimaging studies aim to analyse imaging data with complex spatial patterns in a large number of locations (called voxels) on a two-dimensional surface or in a three-dimensional volume. Conventional analyses of imaging data include two sequential steps: spatially smoothing imaging data and then independently fitting a statistical model at each voxel. However, conventional analyses suffer from the same amount of smoothing throughout the whole image, the arbitrary choice of extent of smoothing and low statistical power in detecting spatial patterns. We propose a multiscale adaptive regression model to integrate the propagation- separation approach with statistical modelling at each voxel for spatial and adaptive analysis of neuroimaging data from multiple subjects. The multiscale adaptive regression model has three features: being spatial, being hierarchical and being adaptive. We use a multiscale adaptive estimation and testing procedure to utilize imaging observations from the neighbouring voxels of the current voxel to calculate parameter estimates and test statistics adaptively. Theoretically, we establish consistency and asymptotic normality of the adaptive parameter estimates and the asymptotic distribution of the adaptive test statistics. Our simulation studies and real data analysis confirm that the multiscale adaptive regression model significantly outperforms conventional analyses of imaging data.

62 citations


Journal Article
TL;DR: A new class of dynamic multiscale models for spatiotemporal processes arising from Gaussian areal data is introduced that uses nested geographical structures to decompose the original process intoMultiscale coefficients which evolve through time following state space equations.
Abstract: We introduce a new class of dynamic multiscale models for spatiotemporal processes arising from Gaussian areal data. Specifically, we use nested geographical structures to decompose the original process into multiscale coefficients which evolve through time following state space equations. Our approach naturally accommodates data that are observed on irregular grids as well as heteroscedasticity. Moreover, we propose a multiscale spatiotemporal clustering algorithm that facilitates estimation of the nested geographical multiscale structure. In addition, we present a singular forward filter backward sampler for efficient Bayesian estimation. Our multiscale spatiotemporal methodology decomposes large data analysis problems into many smaller components and thus leads to scalable and highly efficient computational procedures. Finally, we illustrate the utility and flexibility of our dynamic multiscale framework through two spatiotemporal applications. The first example considers mortality ratios in the state of Missouri whereas the second example examines agricultural production in Espirito Santo State, Brazil.

3 citations


Journal Article
TL;DR: This work formally proves that the thick pen transform is a discriminatory statistic for two Gaussian time series with distinct correlation structures, and derives the asymptotic distribution of the test statistic.
Abstract: Traditional visualization of time series data often consists of plotting the time series values against time and ‘connecting the dots'. We propose an alternative, multiscale visualization technique, motivated by the scale-space approach in computer vision. In brief, our method also ‘connects the dots' but uses a range of pens of varying thicknesses for this. The resulting multiscale map, which is termed the thick pen transform, corresponds to viewing the time series from a range of distances. We formally prove that the thick pen transform is a discriminatory statistic for two Gaussian time series with distinct correlation structures. Further, we show interesting possible applications of the thick pen transform to measuring cross-dependence in multivariate time series, classifying time series and testing for stationarity. In particular, we derive the asymptotic distribution of our test statistic and argue that the test is applicable to both linear and non-linear processes under low moment assumptions. Various other aspects of the methodology, including other possible applications, are also discussed.

2 citations


Journal Article
TL;DR: In this paper, the authors give a brief review of the basic idea and some history and then discuss some developments since the original paper on regression shrinkage and selection via the lasso.
Abstract: In the paper I give a brief review of the basic idea and some history and then discuss some developments since the original paper on regression shrinkage and selection via the lasso.

1 citations