Improved algorithms for rare event simulation with heavy tails

The estimation of P(S-n > u) by simulation, where S, is the sum of independent. identically distributed random varibles Y-1,..., Y-n, is of importance in many applications. We propose two simulation estimators based upon the identity P(S-n > u) = nP(S, > u, M-n = Y-n), where M-n = max(Y-1,..., Y-n). One estimator uses importance sampling (for Y-n only), and the other uses conditional Monte Carlo conditioning upon Y1,..., Yn-1. Properties of the relative error of the estimators are derived and a numerical study given in terms of the M/G/1 queue in which n is replaced by an independent geometric random variable N. The conclusion is that the new estimators compare extremely favorably with previous ones. In particular, the conditional Monte Carlo estimator is the first heavy-tailed example of an estimator with bounded relative error. Further improvements are obtained in the random-N case, by incorporating control variates and stratification techniques into the new estimation procedures.

Quantitative integration of high-resolution hydrogeophysical data through Monte-Carlo-type conditional simulations

Geophysical techniques can help to bridge the inherent gap with regard to spatial resolution and the range of coverage that plagues classical hydrological methods. This has lead to the emergence of the new and rapidly growing field of hydrogeophysics. Given the differing sensitivities of various geophysical techniques to hydrologically relevant parameters and their inherent trade-off between resolution and range the fundamental usefulness of multi-method hydrogeophysical surveys for reducing uncertainties in data analysis and interpretation is widely accepted. A major challenge arising from such endeavors is the quantitative integration of the resulting vast and diverse database in order to obtain a unified model of the probed subsurface region that is internally consistent with all available data. To address this problem, we have developed a strategy towards hydrogeophysical data integration based on Monte-Carlo-type conditional stochastic simulation that we consider to be particularly suitable for local-scale studies characterized by high-resolution and high-quality datasets. Monte-Carlo-based optimization techniques are flexible and versatile, allow for accounting for a wide variety of data and constraints of differing resolution and hardness and thus have the potential of providing, in a geostatistical sense, highly detailed and realistic models of the pertinent target parameter distributions. Compared to more conventional approaches of this kind, our approach provides significant advancements in the way that the larger-scale deterministic information resolved by the hydrogeophysical data can be accounted for, which represents an inherently problematic, and as of yet unresolved, aspect of Monte-Carlo-type conditional simulation techniques. We present the results of applying our algorithm to the integration of porosity log and tomographic crosshole georadar data to generate stochastic realizations of the local-scale porosity structure. Our procedure is first tested on pertinent synthetic data and then applied to corresponding field data collected at the Boise Hydrogeophysical Research Site near Boise, Idaho, USA.

Testing multiple mapping conditioning mixing for Monte Carlo probability density function simulations

Mitarai [Phys. Fluids 17, 047101 (2005)] compared turbulent combustion models against homogeneous direct numerical simulations with extinction/recognition phenomena. The recently suggested multiple mapping conditioning (MMC) was not considered and is simulated here for the same case with favorable results. Implementation issues crucial for successful MMC simulations are also discussed.

Reducing noise associated with the Monte Carlo Independent Column Approximation for weather forecasting models

The Monte Carlo Independent Column Approximation (McICA) is a flexible method for representing subgrid-scale cloud inhomogeneity in radiative transfer schemes. It does, however, introduce conditional random errors but these have been shown to have little effect on climate simulations, where spatial and temporal scales of interest are large enough for effects of noise to be averaged out. This article considers the effect of McICA noise on a numerical weather prediction (NWP) model, where the time and spatial scales of interest are much closer to those at which the errors manifest themselves; this, as we show, means that noise is more significant. We suggest methods for efficiently reducing the magnitude of McICA noise and test these methods in a global NWP version of the UK Met Office Unified Model (MetUM). The resultant errors are put into context by comparison with errors due to the widely used assumption of maximum-random-overlap of plane-parallel homogeneous cloud. For a simple implementation of the McICA scheme, forecasts of near-surface temperature are found to be worse than those obtained using the plane-parallel, maximum-random-overlap representation of clouds. However, by applying the methods suggested in this article, we can reduce noise enough to give forecasts of near-surface temperature that are an improvement on the plane-parallel maximum-random-overlap forecasts. We conclude that the McICA scheme can be used to improve the representation of clouds in NWP models, with the provision that the associated noise is sufficiently small.

Checking Assumptions in Latent Class Regression Models via a Markov Chain Monte Carlo Estimation Approach: An Application to Depression and Socio-Economic Status

Latent class regression models are useful tools for assessing associations between covariates and latent variables. However, evaluation of key model assumptions cannot be performed using methods from standard regression models due to the unobserved nature of latent outcome variables. This paper presents graphical diagnostic tools to evaluate whether or not latent class regression models adhere to standard assumptions of the model: conditional independence and non-differential measurement. An integral part of these methods is the use of a Markov Chain Monte Carlo estimation procedure. Unlike standard maximum likelihood implementations for latent class regression model estimation, the MCMC approach allows us to calculate posterior distributions and point estimates of any functions of parameters. It is this convenience that allows us to provide the diagnostic methods that we introduce. As a motivating example we present an analysis focusing on the association between depression and socioeconomic status, using data from the Epidemiologic Catchment Area study. We consider a latent class regression analysis investigating the association between depression and socioeconomic status measures, where the latent variable depression is regressed on education and income indicators, in addition to age, gender, and marital status variables. While the fitted latent class regression model yields interesting results, the model parameters are found to be invalid due to the violation of model assumptions. The violation of these assumptions is clearly identified by the presented diagnostic plots. These methods can be applied to standard latent class and latent class regression models, and the general principle can be extended to evaluate model assumptions in other types of models.

COVARIATE-ADJUSTED NONPARAMETRIC ANALYSIS OF MAGNETIC RESONANCE IMAGES USING MARKOV CHAIN MONTE CARLO

Permutation tests are useful for drawing inferences from imaging data because of their flexibility and ability to capture features of the brain that are difficult to capture parametrically. However, most implementations of permutation tests ignore important confounding covariates. To employ covariate control in a nonparametric setting we have developed a Markov chain Monte Carlo (MCMC) algorithm for conditional permutation testing using propensity scores. We present the first use of this methodology for imaging data. Our MCMC algorithm is an extension of algorithms developed to approximate exact conditional probabilities in contingency tables, logit, and log-linear models. An application of our non-parametric method to remove potential bias due to the observed covariates is presented.

A comparison of variational and Markov chain Monte Carlo methods for inference in partially observed stochastic dynamic systems

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the Variational Gaussian Process Smoother with an exact solution computed using a Hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while conditional variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother. © 2008 Springer Science + Business Media LLC.

Evaluating tests for convergence of economic series using Monte Carlo methods with an application to real GDP's per head.

Doutoramento em Economia.

On The Consistency Of Monte Carlo Track Structure Dna Damage Simulations.

Monte Carlo track structures (MCTS) simulations have been recognized as useful tools for radiobiological modeling. However, the authors noticed several issues regarding the consistency of reported data. Therefore, in this work, they analyze the impact of various user defined parameters on simulated direct DNA damage yields. In addition, they draw attention to discrepancies in published literature in DNA strand break (SB) yields and selected methodologies. The MCTS code Geant4-DNA was used to compare radial dose profiles in a nanometer-scale region of interest (ROI) for photon sources of varying sizes and energies. Then, electron tracks of 0.28 keV-220 keV were superimposed on a geometric DNA model composed of 2.7 × 10(6) nucleosomes, and SBs were simulated according to four definitions based on energy deposits or energy transfers in DNA strand targets compared to a threshold energy ETH. The SB frequencies and complexities in nucleosomes as a function of incident electron energies were obtained. SBs were classified into higher order clusters such as single and double strand breaks (SSBs and DSBs) based on inter-SB distances and on the number of affected strands. Comparisons of different nonuniform dose distributions lacking charged particle equilibrium may lead to erroneous conclusions regarding the effect of energy on relative biological effectiveness. The energy transfer-based SB definitions give similar SB yields as the one based on energy deposit when ETH ≈ 10.79 eV, but deviate significantly for higher ETH values. Between 30 and 40 nucleosomes/Gy show at least one SB in the ROI. The number of nucleosomes that present a complex damage pattern of more than 2 SBs and the degree of complexity of the damage in these nucleosomes diminish as the incident electron energy increases. DNA damage classification into SSB and DSB is highly dependent on the definitions of these higher order structures and their implementations. The authors' show that, for the four studied models, different yields are expected by up to 54% for SSBs and by up to 32% for DSBs, as a function of the incident electrons energy and of the models being compared. MCTS simulations allow to compare direct DNA damage types and complexities induced by ionizing radiation. However, simulation results depend to a large degree on user-defined parameters, definitions, and algorithms such as: DNA model, dose distribution, SB definition, and the DNA damage clustering algorithm. These interdependencies should be well controlled during the simulations and explicitly reported when comparing results to experiments or calculations.

Monte Carlo Simulation Of The Response Functions Of Cdte Detectors To Be Applied In X-ray Spectroscopy.

In this work, the energy response functions of a CdTe detector were obtained by Monte Carlo (MC) simulation in the energy range from 5 to 160keV, using the PENELOPE code. In the response calculations the carrier transport features and the detector resolution were included. The computed energy response function was validated through comparison with experimental results obtained with (241)Am and (152)Eu sources. In order to investigate the influence of the correction by the detector response at diagnostic energy range, x-ray spectra were measured using a CdTe detector (model XR-100T, Amptek), and then corrected by the energy response of the detector using the stripping procedure. Results showed that the CdTe exhibits good energy response at low energies (below 40keV), showing only small distortions on the measured spectra. For energies below about 80keV, the contribution of the escape of Cd- and Te-K x-rays produce significant distortions on the measured x-ray spectra. For higher energies, the most important correction is the detector efficiency and the carrier trapping effects. The results showed that, after correction by the energy response, the measured spectra are in good agreement with those provided by a theoretical model of the literature. Finally, our results showed that the detailed knowledge of the response function and a proper correction procedure are fundamental for achieving more accurate spectra from which quality parameters (i.e., half-value layer and homogeneity coefficient) can be determined.

Analyzing the n→π* Electronic Transition of Formaldehyde in Water. A Sequential Monte Carlo/Time-Dependent Density Functional Theory

The n→π* absorption transition of formaldehyde in water is analyzed using combined and sequential classical Monte Carlo (MC) simulations and quantum mechanics (QM) calculations. MC simulations generate the liquid solute-solvent structures for subsequent QM calculations. Using time-dependent density functional theory in a localized set of gaussian basis functions (TD-DFT/6-311++G(d,p)) calculations are made on statistically relevant configurations to obtain the average solvatochromic shift. All results presented here use the electrostatic embedding of the solvent. The statistically converged average result obtained of 2300 cm-1 is compared to previous theoretical results available. Analysis is made of the effective dipole moment of the hydrogen-bonded shell and how it could be held responsible for the polarization of the solvent molecules in the outer solvation shells.

Combining Monte Carlo simulation and density-functional theory to describe the spectral changes of Na(2) in liquid helium

Spectral changes of Na(2) in liquid helium were studied using the sequential Monte Carlo-quantum mechanics method. Configurations composed by Na(2) surrounded by explicit helium atoms sampled from the Monte Carlo simulation were submitted to time-dependent density-functional theory calculations of the electronic absorption spectrum using different functionals. Attention is given to both line shift and line broadening. The Perdew, Burke, and Ernzerhof (PBE1PBE, also known as PBE0) functional, with the PBE1PBE/6-311++G(2d,2p) basis set, gives the spectral shift, compared to gas phase, of 500 cm(-1) for the allowed X (1)Sigma(+)(g) -> B (1)Pi(u) transition, in very good agreement with the experimental value (700 cm(-1)). For comparison, cluster calculations were also performed and the first X (1)Sigma(+)(g) -> A (1)Sigma(+)(u) transition was also considered.

Liquid polymorphism, order-disorder transitions and anomalous behavior: A Monte Carlo study of the Bell-Lavis model for water

The Bell-Lavis model for liquid water is investigated through numerical simulations. The lattice-gas model on a triangular lattice presents orientational states and is known to present a highly bonded low density phase and a loosely bonded high density phase. We show that the model liquid-liquid transition is continuous, in contradiction with mean-field results on the Husimi cactus and from the cluster variational method. We define an order parameter which allows interpretation of the transition as an order-disorder transition of the bond network. Our results indicate that the order-disorder transition is in the Ising universality class. Previous proposal of an Ehrenfest second order transition is discarded. A detailed investigation of anomalous properties has also been undertaken. The line of density maxima in the HDL phase is stabilized by fluctuations, absent in the mean-field solution. (C) 2009 American Institute of Physics. [doi:10.1063/1.3253297]

Combined Monte Carlo and quantum mechanics study of the solvatochromism of phenol in water. The origin of the blue shift of the lowest pi-pi* transition

A combined and sequential use of Monte Carlo simulations and quantum mechanical calculations is made to analyze the spectral shift of the lowest pi-pi* transition of phenol in water. The solute polarization is included using electrostatic embedded calculations at the MP2/aug-cc-pVDZ level giving a dipole moment of 2.25 D, corresponding to an increase of 76% compared to the calculated gas-phase value. Using statistically uncorrelated configurations sampled from the MC simulation,first-principle size-extensive calculations are performed to obtain the solvatochromic shift. Analysis is then made of the origin of the blue shift. Results both at the optimized geometry and in room-temperature liquid water show that hydrogen bonds of water with phenol promote a red shift when phenol is the proton-donor and a blue shift when phenol is the proton-acceptor. In the case of the optimized clusters the calculated shifts are in very good agreement with results obtained from mass-selected free jet expansion experiments. In the liquid case the contribution of the solute-solvent hydrogen bonds partially cancels and the total shift obtained is dominated by the contribution of the outer solvent water molecules. Our best result, including both inner and outer water molecules, is 570 +/- 35 cm(-1), in very good agreement with the small experimental shift of 460 cm(-1) for the absorption maximum.