18,406 research outputs found
Bayesian near-boundary analysis in basic macroeconomic time series models
Several lessons learnt from a Bayesian analysis of basic macroeconomic time series models are presented for the situation where some model parameters have substantial posterior probability near the boundary of the parameter region. This feature refers to near-instability within dynamic models, to forecasting with near-random walk models and to clustering of several economic series in a small number of groups within a data panel. Two canonical models are used: a linear regression model with autocorrelation and a simple variance components model. Several well-known time series models likeunit root and error correction models and further state space and panel data models are shown to be simple generalizations of these two canonical models for the purpose of posterior inference. A Bayesian model averaging procedure is presented in order to deal with models with substantial probability both near and at the boundary of the parameter region. Analytical, graphical and empirical results using U.S. macroeconomic data, in particular on GDP growth, are presented.MCMC;Bayesian model averaging;Gibbs sampler;autocorrelation;error correction models;nonstationarity;random effects panel data models;reduced rank models;state space models
Application of Multicanonical Multigrid Monte Carlo Method to the Two-Dimensional -Model: Autocorrelations and Interface Tension
We discuss the recently proposed multicanonical multigrid Monte Carlo method
and apply it to the scalar -model on a square lattice. To investigate
the performance of the new algorithm at the field-driven first-order phase
transitions between the two ordered phases we carefully analyze the
autocorrelations of the Monte Carlo process. Compared with standard
multicanonical simulations a real-time improvement of about one order of
magnitude is established. The interface tension between the two ordered phases
is extracted from high-statistics histograms of the magnetization applying
histogram reweighting techniques.Comment: 49 pp. Latex incl. 14 figures (Fig.7 not included, sorry) as
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Spin glass overlap barriers in three and four dimensions
For the Edwards-Anderson Ising spin-glass model in three and four dimensions
(3d and 4d) we have performed high statistics Monte Carlo calculations of those
free-energy barriers which are visible in the probability density
of the Parisi overlap parameter . The calculations rely on the
recently introduced multi-overlap algorithm. In both dimensions, within the
limits of lattice sizes investigated, these barriers are found to be
non-self-averaging and the same is true for the autocorrelation times of our
algorithm. Further, we present evidence that barriers hidden in dominate
the canonical autocorrelation times.Comment: 20 pages, Latex, 12 Postscript figures, revised version to appear in
Phys. Rev.
Ergodic Properties of Microcanonical Observables
The problem of the existence of a Strong Stochasticity Threshold in the
FPU-beta model is reconsidered, using suitable microcanonical observables of
thermodynamic nature, like the temperature and the specific heat. Explicit
expressions for these observables are obtained by exploiting rigorous methods
of differential geometry. Measurements of the corresponding temporal
autocorrelation functions locate the threshold at a finite value of the energy
density, that results to be indipendent of the number of degrees of freedom.Comment: 19 pages, 6 figure
Biased Metropolis Sampling for Rugged Free Energy Landscapes
Metropolis simulations of all-atom models of peptides (i.e. small proteins)
are considered. Inspired by the funnel picture of Bryngelson and Wolyness, a
transformation of the updating probabilities of the dihedral angles is defined,
which uses probability densities from a higher temperature to improve the
algorithmic performance at a lower temperature. The method is suitable for
canonical as well as for generalized ensemble simulations. A simple
approximation to the full transformation is tested at room temperature for
Met-Enkephalin in vacuum. Integrated autocorrelation times are found to be
reduced by factors close to two and a similar improvement due to generalized
ensemble methods enters multiplicatively.Comment: Plenary talk at the Los Alamos conference, The Monte Carlo Method in
Physical Sciences: Celebrating the 50th Anniversary of the Metropolis
Algorithm, to appear in the proceedings, 11 pages, 4 figures, one table.
Inconsistencies corrected and references adde
Dynamic and static properties of the invaded cluster algorithm
Simulations of the two-dimensional Ising and 3-state Potts models at their
critical points are performed using the invaded cluster (IC) algorithm. It is
argued that observables measured on a sub-lattice of size l should exhibit a
crossover to Swendsen-Wang (SW) behavior for l sufficiently less than the
lattice size L, and a scaling form is proposed to describe the crossover
phenomenon. It is found that the energy autocorrelation time tau(l,L) for an
l*l sub-lattice attains a maximum in the crossover region, and a dynamic
exponent z for the IC algorithm is defined according to tau_max ~ L^z.
Simulation results for the 3-state model yield z=.346(.002) which is smaller
than values of the dynamic exponent found for the SW and Wolff algorithms and
also less than the Li-Sokal bound. The results are less conclusive for the
Ising model, but it appears that z<.21 and possibly that tau_max ~ log L so
that z=0 -- similar to previous results for the SW and Wolff algorithms.Comment: 21 pages with 12 figure
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