Monte Carlo Strategies in Scientific Computing

Liu, Jun S.

doi:10.1007/978-0-387-76371-2

Cited by 1,805 publications

(2,439 citation statements)

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“…A standard local Markov-Chain Monte-Carlo (MC) based method (see Binder and Heermann (1997) and Brémaud (2001)) would be the simplest of sampling strategies: one picks a state variable at a randomly-chosen time slice t k , and proposes a new configuration for it. The cost function of the new configuration is compared to the old cost function; the difference in the cost functions will determine whether to accept or reject using the standard Metropolis algorithm (see Liu (2002) for details on the Metropolis algorithm).…”

Section: The Path Integral Methodsmentioning

confidence: 99%

“…Since (1) is not a proper probability distribution (the normalization is most likely unknown), a number of sampling techniques have been developed to circumvent this issue. One of these is Markov Chain Monte Carlo sampling scheme (MCMC) (see Liu (2002) and Chen et al (2000) for some background on Monte Carlo and its use in the Bayesian setting). Simple MCMC is computationally expensive and the path integral method PIMC constructed with this sampler will be slow to converge statistically.…”

Section: Introductionmentioning

confidence: 99%

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A path integral method for data assimilation

Restrepo

2008

Physica D: Nonlinear Phenomena

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Described here is a path integral, sampling-based approach for data assimilation, of sequential data and evolutionary models. Since it makes no assumptions on linearity in the dynamics, or on Gaussianity in the statistics, it permits consideration of very general estimation problems. The method can be used for such tasks as computing a smoother solution, parameter estimation, and data/model initialization.Speedup in the Monte Carlo sampling process is essential if the path integral method has any chance of being a viable estimator on moderately large problems.Here a variety of strategies are proposed and compared for their relative ability to improve the sampling efficiency of the resulting estimator. Provided as well are details useful in its implementation and testing.The method is applied to a problem in which standard methods are known to fail, an idealized flow/drifter problem, which has been used as a testbed for assimilation strategies involving Lagrangian data. It is in this kind of context that the method may prove to be a useful assimilation tool in oceanic studies.

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Section: The Path Integral Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A path integral method for data assimilation

Restrepo

2008

Physica D: Nonlinear Phenomena

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show abstract

“…This consists in building a Markov chain, whose stationary distribution is the joint posterior pdf (6), by sequentially generating random samples from the full conditional pdfs of all the unknown parameters and hyper-parameters; see (Liu, 2001;Robert, 2001) for a general introduction to MCMC.…”

Section: Gibbs Sampling Algorithmmentioning

confidence: 99%

A fully Bayesian approach to the parcel-based detection-estimation of brain activity in fMRI

Idier²,

et al. 2008

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Within-subject analysis in fMRI essentially addresses two problems, i.e., the detection of activated brain regions in response to an experimental task and the estimation of the underlying dynamics, also known as the characterisation of Hemodynamic response function (HRF). So far, both issues have been treated sequentially while it is known that the HRF model has a dramatic impact on the localisation of activations and that the HRF shape may vary from one region to another. In this paper, we conciliate both issues in a region-based joint detection-estimation framework that we develop in the Bayesian formalism. Instead of considering function basis to account for spatial variability, spatially adaptive General Linear Models are built upon region-based non-parametric estimation of brain dynamics. Regions are first identified as functionally homogeneous parcels in the mask of the grey matter using a specific procedure [Thirion, B., Flandin, G., Pinel, P., Roche, A., Ciuciu, P., Poline, J.-B., August 2006. Dealing with the shortcomings of spatial normalization: Multi-subject parcellation of fMRI datasets. Hum. Brain Mapp. 27 (8), 678-693.]. Then, in each parcel, prior information is embedded to constrain this estimation. Detection is achieved by modelling activating, deactivating and nonactivating voxels through mixture models within each parcel. From the posterior distribution, we infer upon the model parameters using Markov Chain Monte Carlo (MCMC) techniques. Bayesian model comparison allows us to emphasize on artificial datasets first that inhomogeneous gamma-Gaussian mixture models outperform Gaussian mixtures in terms of sensitivity/specificity trade-off and second that it is worthwhile modelling serial correlation through an AR(1) noise process at low signal-to-noise (SNR) ratio. Our approach is then validated on an fMRI experiment that studies habituation to auditory sentence repetition. This phenomenon is clearly recovered as well as the hierarchical temporal organisation of the superior temporal sulcus, which is directly derived from the parcel-based HRF estimates. © 2008 Elsevier Inc. All rights reserved.Keywords: Bayesian modelling; fMRI; Gamma-Gaussian mixture model; Detection-estimation; Markov Chain Monte Carlo methods; Bayes factor; Model comparison IntroductionSince the first report of the BOLD effect in human (Ogawa et al., 1990), functional magnetic resonance imaging (fMRI) has represented a powerful tool to non-invasively study the relation between cognitive stimulus and the hemodynamic (BOLD) response. Within-subject analysis in fMRI is usually addressed using a hypothesis-driven approach that actually postulates a model for the HRF and enable voxelwise inference in the General Linear Model (GLM) framework. In this formulation, the modelling of the BOLD response i.e., the definition of the design matrix is crucial. In its simplest form, this matrix relies on a spatially invariant temporal model of the BOLD signal across the brain meaning that the expected response to each stimulus is modelled by ...

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“…These methods have their origin in motif-finding methods, such as meme and bioprospector, that were developed to identify regulatory elements in co-expressed genes [8][9][10][11][12][13]. The statistical search does not always converge to the correct binding site.…”

Section: Introductionmentioning

confidence: 99%

Decoding transcriptional regulatory interactions

Liu

Bader

2006

Physica D: Nonlinear Phenomena

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Transcription factor proteins control the temporal and spatial expression of genes by binding specific regulatory elements, or motifs, in DNA. Mapping a transcription factor to its motif is an important step towards defining the structure of transcriptional regulatory networks and understanding their dynamics. The information to map a transcription factor to its DNA binding specificity is in principle contained in the protein sequence. Nevertheless, methods that map directly from protein sequence to target DNA sequence have been lacking, and generation of regulatory maps has required experimental data. Here we describe a purely computational method for predicting transcription factor binding. The method calculates the free energy of binding between a transcription factor and possible target DNA sequences using thermodynamic integration. Approximations of additivity (each DNA basepair contributes independently to the binding energy) and linear response (the DNAprotein and DNA-solvent couplings are linear in an effective reaction coordinate representing the basepair character at a specific position) make the computations feasible and can be verified by more detailed simulations. Results obtained for MAT-α2, a yeast homeodomain transcription factor, are in good agreement with known results. This method promises to provide a general, computationally feasible route from a genome sequence to a gene regulatory network.

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Monte Carlo Strategies in Scientific Computing

Cited by 1,805 publications

References 0 publications

A path integral method for data assimilation

A path integral method for data assimilation

A fully Bayesian approach to the parcel-based detection-estimation of brain activity in fMRI

Decoding transcriptional regulatory interactions

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