There is uncertainty introduced when a cortical surface based model derived from an anatomical MRI is used to reconstruct neural activity with MEG data. This is a specific case of a problem with uncertainty in paramet...
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There is uncertainty introduced when a cortical surface based model derived from an anatomical MRI is used to reconstruct neural activity with MEG data. This is a specific case of a problem with uncertainty in parameters on which M/EEG lead fields depend non-linearly. Here we present a general mathematical treatment of any such problem with a particular focus on co-registration. We use a metropolis search followed by Bayesian Model Averaging over multiple sparse prior source inversions with different headlocation/orientation parameters. Based on MEG data alone we can locate the cortex to within 4 mm at empirically realistic signal to noise ratios. We also show that this process gives improved posterior distributions on the estimated current distributions, and can be extended to make inference on the locations of local maxima by providing confidence intervals for each source. (c) 2012 Elsevier Inc. All rights reserved.
In this paper we suggest the use of simulation techniques to extend the applicability of the usual Gaussian state space filtering and smoothing techniques to a class of non-Gaussian time series models. This allows a f...
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In this paper we suggest the use of simulation techniques to extend the applicability of the usual Gaussian state space filtering and smoothing techniques to a class of non-Gaussian time series models. This allows a fully Bayesian or maximum likelihood analysis of some interesting models, including outlier models, discrete Markov chain components, multiplicative models and stochastic variance models. Finally we discuss at some length the use of a non-Gaussian model to seasonally adjust the published money supply figures.
We introduce a form of Rao-Blackwellization for Markov chains which uses the transition distribution for conditioning. We show that for reversible Markov chains, this form of Rao-Blackwellization always reduces the as...
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We introduce a form of Rao-Blackwellization for Markov chains which uses the transition distribution for conditioning. We show that for reversible Markov chains, this form of Rao-Blackwellization always reduces the asymptotic variance, and derive two explicit forms of the variance reduction obtained through repeated Rao-Blackwellization. The result applies to many Markov chain Monte Carlo methods used in practice. In particular, we discuss an application to data augmentation and give some simulation results for Ising model samplers. (C) 2000 Elsevier Science B.V. All rights reserved.
In this work, the thermodynamic and magnetic properties such as total and partial magnetizations, magnetic susceptibility, internal energy, total specific heat, magnetic hysteresis loops and compensation temperature o...
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In this work, the thermodynamic and magnetic properties such as total and partial magnetizations, magnetic susceptibility, internal energy, total specific heat, magnetic hysteresis loops and compensation temperature of a ferrimagnetic mixed spins-3/2 and spins-5/2 hexagonal Ising nanowire, have been determined by using Monte Carlo method based on the metropolis algorithm. The effects of the longitudinal crystal field, the exchange interactions and the temperature on the magnetic properties and hysteresis loops are examined in detail for different values of the system parameters. Moreover, different interesting magnetic phenomena were obtained, such as the seven and triple hysteresis loops at low temperatures, the tricritical point and compensation behavior under certain physical parameters were detected. Our results are also compared with some experimental and theoretical results.
The Malawi Demographic and Health Survey conducted in 1992 collected the retrospective birth histories for a national sample of 4,878 women aged between 15 and 49 years. The sample was randomly selected by a two-stage...
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The Malawi Demographic and Health Survey conducted in 1992 collected the retrospective birth histories for a national sample of 4,878 women aged between 15 and 49 years. The sample was randomly selected by a two-stage sampling design. The data consist of biological, demographic, and social variables collected for each birth. This article models the infant and early childhood survival using family and community random effect multipliers on the fixed effect proportional hazards model, which allows the dependence between observations in the same family and community into the model. 4 Markov chain Monte Carlo sample from the posterior distribution of the parameters given the data is found. The standard errors of the fixed effect estimates are more correct than those found from the standard model, which are underestimated because of the ignored correlation structure.
Structure and dynamics of interface in three dimensional Ising model on a simple cubic lattice has been studied. Lattice is placed in an inhomogeneous external field, of specific profile, and field is translating with...
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Structure and dynamics of interface in three dimensional Ising model on a simple cubic lattice has been studied. Lattice is placed in an inhomogeneous external field, of specific profile, and field is translating with velocity V-f. For small V-f,V- magnetization interface generated by the field is pinned to the field interface. As V-f is increased magnetization interface detaches from field interface. For small V-f, the local slope of the interface locks in to one of many possible rational values which most closely approximates field profile. Accordingly, in two dimensional Ising model, plot of orientation of field interface vs. most probable local slope of magnetization interface has a staircase structure. In present case of three dimensional Ising model, these steps are manifested as patches in graphical representation. Effect of V-f on this patch structure has been studied.
We critically analyze a recent numerical method due to the first author, Rechnitzer, and van Rensburg, which attempts to detect amenability in a finitely generated group by numerically estimating its asymptotic cogrow...
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We critically analyze a recent numerical method due to the first author, Rechnitzer, and van Rensburg, which attempts to detect amenability in a finitely generated group by numerically estimating its asymptotic cogrowth rate. We identify two potential sources of error. We then propose a modification of the method that enables it to easily compute surprisingly accurate estimates for initial terms of the cogrowth sequence.
We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian st...
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We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and statistical mechanics. We provide lower bounds on the spectral gaps of parallel and simulated tempering. These bounds imply a single set of sufficient conditions for rapid mixing of both techniques. A direct consequence of our results is rapid mixing of parallel and simulated tempering for several normal mixture models, and for the mean-field Ising model.
Equi-energy sampling (EES, for short) is a method to speed up the convergence of the metropolis chain, when the latter is slow. We show that there are still models like the mean-field Potts model, where EES does not c...
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Equi-energy sampling (EES, for short) is a method to speed up the convergence of the metropolis chain, when the latter is slow. We show that there are still models like the mean-field Potts model, where EES does not converge rapidly in certain temperature regimes. Indeed we will show that EES is slowly mixing on the mean-field Potts model, in a regime below the critical temperature. Though we will concentrate on the Potts model with three colors, our arguments remain valid for any number of colors q >= 3, if we adapt the temperature regime. For the situation of the mean-field Potts model this answers a question posed in Hua and Kou (2011 Stat. Sin. 21 1687-711).
Background: A common approach to the protein folding problem involves computer simulation of folding using lattice models of amino acid sequences. Key factors for good performance in such models are the correct choice...
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Background: A common approach to the protein folding problem involves computer simulation of folding using lattice models of amino acid sequences. Key factors for good performance in such models are the correct choice of the temperature and the average interaction energy between residues. In order to push the lattice approach to its limit it is important to have a method to adjust these parameters for optimal folding that is not limited by our ability to successfully simulate folding in a reasonable time. Results: In this study, we adopt a simple cubic-lattice model and present a method for calculating the free energy of a chain as a function of the number of native contacts. This does not require that we are able to fold the sequence by simulation and it provides a method of estimating the folding transition temperature. For a given set of parameters, the free energy analysis also allows an estimate of foldability. By applying the method to sequences with 27 and 125 residues, we show that optimal folding occurs near the folding transition temperature and at either zero or small negative average interaction energy. We find ourselves able to fold only 125-mers that have significant short-range native contacts. Conclusions: A free energy analysis during unfolding is a useful tool for the study of foldability and should be applicable to a variety of folding models. In this way we are able to fold some 125-mer designed sequences and our results confirm the finding that short-range contacts contribute to foldability.
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