Colin Fox

Bio: Colin Fox is an academic researcher from University of Otago. The author has contributed to research in topics: Markov chain Monte Carlo & Bayesian inference. The author has an hindex of 24, co-authored 96 publications receiving 2355 citations. Previous affiliations of Colin Fox include University of Auckland.

On the Oblique Reflexion and Transmission of Ocean Waves at Shore Fast Sea Ice

Abstract: A mathematical model is reported describing the oblique reflexion and penetration of ocean waves into shore fast sea ice. The arbitrary depth model allows all velocity potentials occurring in the open water region to be matched precisely to their counterparts in the ice-covered region. Matching is done using a preconditioned conjugate gradient technique which allows the complete solution to be found to a predefined precision. The model enables the reflexion and transmission coefficients at the ice edge to be found, and examples are reported for ice plates of different thicknesses. A critical angle is predicted beyond which no travelling wave penetrates the ice sheet; in this case the deflexion of the ice is due only to evanescent modes. Critical angle curves are provided for various ice thicknesses on deep, intermediate and shallow water. The strain field which is set up within the ice sheet due to the incoming waves is also discussed; principal strains are provided as are the strains normal to the ice edge. Finally the spreading function within the ice cover, and some consequences of this function to unimodal seas with realistic open water spreading functions, are reported with the aim of generalizing the work to model the effect of shore fast ice on an incoming directional wave spectrum of specified structure.

Markov Chain Monte Carlo Using an Approximation

Abstract: This article presents a method for generating samples from an unnormalized posterior distribution f(·) using Markov chain Monte Carlo (MCMC) in which the evaluation of f(·) is very difficult or computationally demanding. Commonly, a less computationally demanding, perhaps local, approximation to f(·) is available, say f**x(·). An algorithm is proposed to generate an MCMC that uses such an approximation to calculate acceptance probabilities at each step of a modified Metropolis–Hastings algorithm. Once a proposal is accepted using the approximation, f(·) is calculated with full precision ensuring convergence to the desired distribution. We give sufficient conditions for the algorithm to converge to f(·) and give both theoretical and practical justifications for its usage. Typical applications are in inverse problems using physical data models where computing time is dominated by complex model simulation. We outline Bayesian inference and computing for inverse problems. A stylized example is given of recove...

Reflection and transmission characteristics at the edge of shore fast sea ice

Abstract: The reflection and transmission of ocean waves at a sea ice boundary is reconsidered. The sea ice is modelled as a continuous, thin elastic plate of uniform thickness, floating on water of arbitrary constant depth. Unlike earlier solutions, matching of potentials between the free surface domain and the ice-covered domain is done at all depths; previous solutions were incompletely matched, as the potentials in each domain were deficient. In the present solution a number of the infinity of evanescent modes, which were hitherto ignored, are included in the solution and allow matching to be carried out by minimization of an integrated error term from surface to seafloor. Reflection and transmission are found to be markedly influenced by the inclusion of these modes, suggesting that conclusions based on the incomplete potentials may be substantially in error.

A general purpose sampling algorithm for continuous distributions (the t-walk)

Abstract: We develop a new general purpose MCMC sampler for arbitrary continuous distributions that requires no tuning. We call this MCMC the t-walk. The t-walk maintains two independent points in the sample space, and all moves are based on proposals that are then accepted with a standard Metropolis-Hastings acceptance probability on the product space. Hence the t-walk is provably convergent under the usual mild requirements. We restrict proposal distributions, or `moves', to those that produce an algorithm that is invariant to scale, and approximately invariant to affine transformations of the state space. Hence scaling of proposals, and effectively also coordinate transformations, that might be used to increase efficiency of the sampler, are not needed since the t-walk's operation is identical on any scaled version of the target distribution. Four moves are given that result in an effective sampling algorithm. We use the simple device of updating only a random subset of coordinates at each step to allow application of the t-walk to high-dimensional problems. In a series of test problems across dimensions we find that the t-walk is only a small factor less efficient than optimally tuned algorithms, but significantly outperforms general random-walk M-H samplers that are not tuned for specific problems. Further, the t-walk remains effective for target distributions for which no optimal affine transformation exists such as those where correlation structure is very different in differing regions of state space. Several examples are presented showing good mixing and convergence characteristics, varying in dimensions from 1 to 200 and with radically different scale and correlation structure, using exactly the same sampler. The t-walk is available for R, Python, MatLab and C++ at http://www.cimat.mx/~jac/twalk/

Bayesian calibration of a large-scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm

Abstract: [1] The aim of this research is to estimate the parameters of a large-scale numerical model of a geothermal reservoir using Markov chain Monte Carlo (MCMC) sampling, within the framework of Bayesian inference. All feasible parameters that are consistent with the measured data are summarized by the posterior distribution, and hence parameter estimation and uncertainty quantification are both given by calculating expected values of statistics of interest over the posterior distribution. It appears to be computationally infeasible to use the standard Metropolis-Hastings algorithm (MH) to sample the high dimensional computationally expensive posterior distribution. To improve the sampling efficiency, a new adaptive delayed-acceptance MH algorithm (ADAMH) is implemented to adaptively build a stochastic model of the error introduced by the use of a reduced-order model. This use of adaptivity differs from existing adaptive MCMC algorithms that tune proposal distributions of the Metropolis-Hastings algorithm (MH), though ADAMH also implements that technique. For the 3-D geothermal reservoir model we present here, ADAMH shows a great improvement in the computational efficiency of the MCMC sampling, and promising results for parameter estimation and uncertainty quantification are obtained. This algorithm could offer significant improvement in computational efficiency when implementing sample-based inference in other large-scale inverse problems.

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Flexible paleoclimate age-depth models using an autoregressive gamma process

Abstract: Radiocarbon dating is routinely used in paleoecology to build chronolo- gies of lake and peat sediments, aiming at inferring a model that would relate the sediment depth with its age. We present a new approach for chronology building (called \Bacon") that has received enthusiastic attention by paleoecologists. Our methodology is based on controlling core accumulation rates using a gamma au- toregressive semiparametric model with an arbitrary number of subdivisions along the sediment. Using prior knowledge about accumulation rates is crucial and in- formative priors are routinely used. Since many sediment cores are currently ana- lyzed, using difierent data sets and prior distributions, a robust (adaptive) MCMC is very useful. We use the t-walk (Christen and Fox, 2010), a self adjusting, robust MCMC sampling algorithm, that works acceptably well in many situations. Out- liers are also addressed using a recent approach that considers a Student-t model for radiocarbon data. Two examples are presented here, that of a peat core and a core from a lake, and our results are compared with other approaches. Past climates and environments can be reconstructed from deposits such as ocean or lake sediments, ice sheets and peat bogs. Within a vertical sediment proflle (core), mea- surements of microfossils, macrofossils, isotopes and other variables at a range of depths serve as proxy estimates or \proxies" of climate and environmental conditions when the sediment of those depths was deposited. It is crucial to establish reliable relationships between these depths and their ages. Age-depth relationships are used to study the evolution of climate/environmental proxies along sediment depth and therefore through time (e.g., Lowe and Walker 1997). Age-depth models are constructed in various ways. For sediment depths containing organic matter, and for ages younger than c. 50,000 years, radiocarbon dating is often used to create an age-depth model. Cores are divided into slices and some of these are radiocarbon dated. A curve is fltted to the radiocarbon data and interpolated to obtain an age estimate for every depth of the core. The flrst restriction to be considered is that age should be increasing monotonically with depth, because sediment can never have accumulated backwards in time (extraordinary events leading to mixed or reversed sediments are, most of the time, noticeable in the stratigraphy and therefore such cores are ruled out from further analyses). Moreover, cores may have missing sections, leading to ∞at parts in the age depth models.

Handbook of Markov Chain Monte Carlo

Abstract: Foreword Stephen P. Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng Introduction to MCMC, Charles J. Geyer A short history of Markov chain Monte Carlo: Subjective recollections from in-complete data, Christian Robert and George Casella Reversible jump Markov chain Monte Carlo, Yanan Fan and Scott A. Sisson Optimal proposal distributions and adaptive MCMC, Jeffrey S. Rosenthal MCMC using Hamiltonian dynamics, Radford M. Neal Inference and Monitoring Convergence, Andrew Gelman and Kenneth Shirley Implementing MCMC: Estimating with confidence, James M. Flegal and Galin L. Jones Perfection within reach: Exact MCMC sampling, Radu V. Craiu and Xiao-Li Meng Spatial point processes, Mark Huber The data augmentation algorithm: Theory and methodology, James P. Hobert Importance sampling, simulated tempering and umbrella sampling, Charles J.Geyer Likelihood-free Markov chain Monte Carlo, Scott A. Sisson and Yanan Fan MCMC in the analysis of genetic data on related individuals, Elizabeth Thompson A Markov chain Monte Carlo based analysis of a multilevel model for functional MRI data, Brian Caffo, DuBois Bowman, Lynn Eberly, and Susan Spear Bassett Partially collapsed Gibbs sampling & path-adaptive Metropolis-Hastings in high-energy astrophysics, David van Dyk and Taeyoung Park Posterior exploration for computationally intensive forward models, Dave Higdon, C. Shane Reese, J. David Moulton, Jasper A. Vrugt and Colin Fox Statistical ecology, Ruth King Gaussian random field models for spatial data, Murali Haran Modeling preference changes via a hidden Markov item response theory model, Jong Hee Park Parallel Bayesian MCMC imputation for multiple distributed lag models: A case study in environmental epidemiology, Brian Caffo, Roger Peng, Francesca Dominici, Thomas A. Louis, and Scott Zeger MCMC for state space models, Paul Fearnhead MCMC in educational research, Roy Levy, Robert J. Mislevy, and John T. Behrens Applications of MCMC in fisheries science, Russell B. Millar Model comparison and simulation for hierarchical models: analyzing rural-urban migration in Thailand, Filiz Garip and Bruce Western

Heat and Mass Transfer

Abstract: Thermophysical Properties Research Literature Retrieval Guide Edited by Y. S. Touloukian, J. K. Gerritsen and N. Y. Moore Second edition, revised and expanded. Book 1: Pp. xxi + 819. Book 2: Pp.621. Book 3: Pp. ix + 1315. (New York: Plenum Press, 1967.) n.p.

Inositol Trisphosphate Receptor Ca2+ Release Channels

Abstract: The inositol 1,4,5-trisphosphate (InsP3) receptors (InsP3Rs) are a family of Ca2+ release channels localized predominately in the endoplasmic reticulum of all cell types. They function to release Ca2+ into the cytoplasm in response to InsP3 produced by diverse stimuli, generating complex local and global Ca2+ signals that regulate numerous cell physiological processes ranging from gene transcription to secretion to learning and memory. The InsP3R is a calcium-selective cation channel whose gating is regulated not only by InsP3, but by other ligands as well, in particular cytoplasmic Ca2+. Over the last decade, detailed quantitative studies of InsP3R channel function and its regulation by ligands and interacting proteins have provided new insights into a remarkable richness of channel regulation and of the structural aspects that underlie signal transduction and permeation. Here, we focus on these developments and review and synthesize the literature regarding the structure and single-channel properties of the InsP3R.