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.
Recent studies based on lattice Monte Carlo simulations of quantum chromodynamics (QCD)-the theory of strong interactions-have demonstrated that at high temperature there is a phase change from ...confined hadronic matter to a deconfined quark-gluon plasma in which quarks and gluons can travel distances that greatly exceed the size of hadrons. Here we show that the phase structure of such strongly interacting matter can be decoded by analysing particle production in high-energy nuclear collisions within the framework of statistical hadronization, which accounts for the thermal distribution of particle species. Our results represent a phenomenological determination of the location of the phase boundary of strongly interacting matter, and imply quark-hadron duality at this boundary.
This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate ...zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed Bayesian approach is particularly beneficial in applications where parameters are added to a conventional model such that a nonidentified model is obtained if maximum-likelihood estimation is applied. This approach is useful for measurement aspects of latent variable modeling, such as with confirmatory factor analysis, and the measurement part of structural equation modeling. Two application areas are studied, cross-loadings and residual correlations in confirmatory factor analysis. An example using a full structural equation model is also presented, showing an efficient way to find model misspecification. The approach encompasses 3 elements: model testing using posterior predictive checking, model estimation, and model modification. Monte Carlo simulations and real data are analyzed using Mplus. The real-data analyses use data from
Holzinger and Swineford's (1939)
classic mental abilities study, Big Five personality factor data from a British survey, and science achievement data from the National Educational Longitudinal Study of 1988.
Particle Markov chain Monte Carlo methods Andrieu, Christophe; Doucet, Arnaud; Holenstein, Roman
Journal of the Royal Statistical Society. Series B, Statistical methodology,
June 2010, Letnik:
72, Številka:
3
Journal Article
Recenzirano
Odprti dostop
Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov ...chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to build efficient high dimensional proposal distributions by using sequential Monte Carlo methods. This allows us not only to improve over standard Markov chain Monte Carlo schemes but also to make Bayesian inference feasible for a large class of statistical models where this was not previously so. We demonstrate these algorithms on a non-linear state space model and a Lévy-driven stochastic volatility model.
We present an information-theoretic approach to stochastic optimal control problems that can be used to derive general sampling-based optimization schemes. This new mathematical method is used to ...develop a sampling-based model predictive control algorithm. We apply this information-theoretic model predictive control scheme to the task of aggressive autonomous driving around a dirt test track, and compare its performance with a model predictive control version of the cross-entropy method.
A re-analysis of intraclass correlation (ICC) theory is presented together with Monte Carlo simulations of ICC probability distributions. A partly revised and simplified theory of the single-score ...ICC is obtained, together with an alternative and simple recipe for its use in reliability studies. Our main, practical conclusion is that in the analysis of a reliability study it is neither necessary nor convenient to start from an initial choice of a specified statistical model. Rather, one may impartially use all three single-score ICC formulas. A near equality of the three ICC values indicates the absence of bias (systematic error), in which case the classical (one-way random) ICC may be used. A consistency ICC larger than absolute agreement ICC indicates the presence of non-negligible bias; if so, classical ICC is invalid and misleading. An F-test may be used to confirm whether biases are present. From the resulting model (without or with bias) variances and confidence intervals may then be calculated. In presence of bias, both absolute agreement ICC and consistency ICC should be reported, since they give different and complementary information about the reliability of the method. A clinical example with data from the literature is given.
ABSTRACT We present a robust measurement and analysis of the rest-frame ultraviolet (UV) luminosity functions at z = 4-8. We use deep Hubble Space Telescope imaging over the Cosmic Assembly ...Near-infrared Deep Extragalactic Legacy Survey/GOODS fields, the Hubble Ultra Deep Field, and the Hubble Frontier Field deep parallel observations near the Abell 2744 and MACS J0416.1-2403 clusters. The combination of these surveys provides an effective volume of 0.6-1.2 × 106 Mpc3 over this epoch, allowing us to perform a robust search for faint 18) and bright (M 21) high-redshift galaxies. We select candidate galaxies using a well-tested photometric redshift technique with careful screening of contaminants, finding a sample of 7446 candidate galaxies at 3.5 8.5, with >1000 galaxies at 6-8. We measure both a stepwise luminosity function for candidate galaxies in our redshift samples, and a Schechter function, using a Markov Chain Monte Carlo analysis to measure robust uncertainties. At the faint end, our UV luminosity functions agree with previous studies, yet we find a higher abundance of UV-bright candidate galaxies at 6. Our best-fit value of the characteristic magnitude is consistent with −21 at 5, which is different than that inferred based on previous trends at lower redshift, and brighter at ∼2 significance than previous measures at z = 6 and 7. At z = 8, a single power law provides an equally good fit to the UV luminosity function, while at z = 6 and 7 an exponential cutoff at the bright end is moderately preferred. We compare our luminosity functions to semi-analytical models, and find that the lack of evolution in is consistent with models where the impact of dust attenuation on the bright end of the luminosity function decreases at higher redshift, although a decreasing impact of feedback may also be possible. We measure the evolution of the cosmic star-formation rate (SFR) density by integrating our observed luminosity functions to , correcting for dust attenuation, and find that the SFR density declines proportionally to (1 ) at 4, which is consistent with observations at 9. Our observed luminosity functions are consistent with a reionization history that starts at 10, completes at 6, and reaches a midpoint (x 0.5) at 6.7 9.4. Finally, using a constant cumulative number density selection and an empirically derived rising star-formation history, our observations predict that the abundance of bright z = 9 galaxies is likely higher than previous constraints, although consistent with recent estimates of bright 10 galaxies.
ABSTRACT Precise and accurate parameters for late-type (late K and M) dwarf stars are important for characterization of any orbiting planets, but such determinations have been hampered by these ...stars' complex spectra and dissimilarity to the Sun. We exploit an empirically calibrated method to estimate spectroscopic effective temperature (Teff) and the Stefan-Boltzmann law to determine radii of 183 nearby K7-M7 single stars with a precision of 2%-5%. Our improved stellar parameters enable us to develop model-independent relations between Teff or absolute magnitude and radius, as well as between color and Teff. The derived Teff-radius relation depends strongly on Fe/H, as predicted by theory. The relation between absolute KS magnitude and radius can predict radii accurate to 3%. We derive bolometric corrections to the and Gaia passbands as a function of color, accurate to 1%-3%. We confront the reliability of predictions from Dartmouth stellar evolution models using a Markov chain Monte Carlo to find the values of unobservable model parameters (mass, age) that best reproduce the observed effective temperature and bolometric flux while satisfying constraints on distance and metallicity as Bayesian priors. With the inferred masses we derive a semi-empirical mass-absolute magnitude relation with a scatter of 2% in mass. The best-agreement models overpredict stellar Teff values by an average of 2.2% and underpredict stellar radii by 4.6%, similar to differences with values from low-mass eclipsing binaries. These differences are not correlated with metallicity, mass, or indicators of activity, suggesting issues with the underlying model assumptions, e.g., opacities or convective mixing length.
Ten events per variable (EPV) is a widely advocated minimal criterion for sample size considerations in logistic regression analysis. Of three previous simulation studies that examined this minimal ...EPV criterion only one supports the use of a minimum of 10 EPV. In this paper, we examine the reasons for substantial differences between these extensive simulation studies.
The current study uses Monte Carlo simulations to evaluate small sample bias, coverage of confidence intervals and mean square error of logit coefficients. Logistic regression models fitted by maximum likelihood and a modified estimation procedure, known as Firth's correction, are compared.
The results show that besides EPV, the problems associated with low EPV depend on other factors such as the total sample size. It is also demonstrated that simulation results can be dominated by even a few simulated data sets for which the prediction of the outcome by the covariates is perfect ('separation'). We reveal that different approaches for identifying and handling separation leads to substantially different simulation results. We further show that Firth's correction can be used to improve the accuracy of regression coefficients and alleviate the problems associated with separation.
The current evidence supporting EPV rules for binary logistic regression is weak. Given our findings, there is an urgent need for new research to provide guidance for supporting sample size considerations for binary logistic regression analysis.
We report diffusion quantum Monte Carlo calculations of the interlayer binding energy of bilayer graphene. We find the binding energies of the AA-and AB-stacked structures at the equilibrium ...separation to be 11.5(9) and 17.7(9) meV/atom, respectively. The out-of-plane zone-center optical phonon frequency predicted by our binding-energy curve is consistent with available experimental results. As well as assisting the modeling of interactions between graphene layers, our results will facilitate the development of van der Waals exchange-correlation functionals for density functional theory calculations.
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