Enhancing statistical moment calculations for stochastic Galerkin solutions with Monte Carlo techniques

2018 ◽  
Vol 374 ◽  
pp. 1017-1030
Author(s):  
Kenny Chowdhary ◽  
Cosmin Safta ◽  
Habib N. Najm
Keyword(s):  
Monte Carlo ◽  
Statistical Moment ◽  
Monte Carlo Techniques ◽  
Stochastic Galerkin

Bayesian Estimation of DSGE Models

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Likelihood Function ◽  
Academic Research ◽  
Dynamic Stochastic General Equilibrium ◽  
Computational Techniques ◽  
Dsge Models ◽  
Monte Carlo Techniques ◽  
Dynamic Stochastic ◽  
Theoretical Foundations

Dynamic stochastic general equilibrium (DSGE) models have become one of the workhorses of modern macroeconomics and are extensively used for academic research as well as forecasting and policy analysis at central banks. This book introduces readers to state-of-the-art computational techniques used in the Bayesian analysis of DSGE models. The book covers Markov chain Monte Carlo techniques for linearized DSGE models, novel sequential Monte Carlo methods that can be used for parameter inference, and the estimation of nonlinear DSGE models based on particle filter approximations of the likelihood function. The theoretical foundations of the algorithms are discussed in depth, and detailed empirical applications and numerical illustrations are provided. The book also gives invaluable advice on how to tailor these algorithms to specific applications and assess the accuracy and reliability of the computations. The book is essential reading for graduate students, academic researchers, and practitioners at policy institutions.

Neutron dose evaluation of Elekta Linac at two energies (10 & 18 MV) by MCNP code and comparison with experimental measurements

2014 ◽  
Vol 6 (1) ◽  
pp. 1006-1015
Author(s):  
Negin Shagholi ◽  
Hassan Ali ◽  
Mahdi Sadeghi ◽  
Arjang Shahvar ◽  
Hoda Darestani ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Measurement Data ◽  
Calculated Data ◽  
High Energy ◽  
Neutron Dose ◽  
Dose Assessment ◽  
Photon Flux ◽  
Dose Equivalent ◽  
Monte Carlo Techniques ◽  
Neutron Dose Equivalent

Medical linear accelerators, besides the clinically high energy electron and photon beams, produce other secondary particles such as neutrons which escalate the delivered dose. In this study the neutron dose at 10 and 18MV Elekta linac was obtained by using TLD600 and TLD700 as well as Monte Carlo simulation. For neutron dose assessment in 2020 cm2 field, TLDs were calibrated at first. Gamma calibration was performed with 10 and 18 MV linac and neutron calibration was done with 241Am-Be neutron source. For simulation, MCNPX code was used then calculated neutron dose equivalent was compared with measurement data. Neutron dose equivalent at 18 MV was measured by using TLDs on the phantom surface and depths of 1, 2, 3.3, 4, 5 and 6 cm. Neutron dose at depths of less than 3.3cm was zero and maximized at the depth of 4 cm (44.39 mSvGy-1), whereas calculation resulted  in the maximum of 2.32 mSvGy-1 at the same depth. Neutron dose at 10 MV was measured by using TLDs on the phantom surface and depths of 1, 2, 2.5, 3.3, 4 and 5 cm. No photoneutron dose was observed at depths of less than 3.3cm and the maximum was at 4cm equal to 5.44mSvGy-1, however, the calculated data showed the maximum of 0.077mSvGy-1 at the same depth. The comparison between measured photo neutron dose and calculated data along the beam axis in different depths, shows that the measurement data were much more than the calculated data, so it seems that TLD600 and TLD700 pairs are not suitable dosimeters for neutron dosimetry in linac central axis due to high photon flux, whereas MCNPX Monte Carlo techniques still remain a valuable tool for photonuclear dose studies.

scholarly journals Stochastic Order and Generalized Weighted Mean Invariance

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 662
Author(s):  
Mateu Sbert ◽  
Jordi Poch ◽  
Shuning Chen ◽  
Víctor Elvira
Keyword(s):  
Monte Carlo ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Arithmetic Mean ◽  
Stochastic Orders ◽  
Arithmetic Means ◽  
Increasing Convex Order ◽  
Monte Carlo Techniques ◽  
Multiple Importance Sampling ◽  
Invariance Properties

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

scholarly journals Random Sampling Many-Dimensional Sets Arising in Control

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 580
Author(s):  
Pavel Shcherbakov ◽  
Mingyue Ding ◽  
Ming Yuchi
Keyword(s):  
Monte Carlo ◽  
Random Sampling ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Computational Mathematics ◽  
Closed Form Solutions ◽  
Monte Carlo Techniques ◽  
Control Optimization ◽  
Point Representation ◽  
Hit And Run

Various Monte Carlo techniques for random point generation over sets of interest are widely used in many areas of computational mathematics, optimization, data processing, etc. Whereas for regularly shaped sets such sampling is immediate to arrange, for nontrivial, implicitly specified domains these techniques are not easy to implement. We consider the so-called Hit-and-Run algorithm, a representative of the class of Markov chain Monte Carlo methods, which became popular in recent years. To perform random sampling over a set, this method requires only the knowledge of the intersection of a line through a point inside the set with the boundary of this set. This component of the Hit-and-Run procedure, known as boundary oracle, has to be performed quickly when applied to economy point representation of many-dimensional sets within the randomized approach to data mining, image reconstruction, control, optimization, etc. In this paper, we consider several vector and matrix sets typically encountered in control and specified by linear matrix inequalities. Closed-form solutions are proposed for finding the respective points of intersection, leading to efficient boundary oracles; they are generalized to robust formulations where the system matrices contain norm-bounded uncertainty.

Research on Monte Carlo Perturbation Calculation Methods Applied in Reactor Physics

2009 ◽  
Author(s):  
Ze-guang Li ◽  
Kan Wang ◽  
Gang-lin Yu
Keyword(s):  
Monte Carlo ◽  
Differential Operator ◽  
Sampling Method ◽  
Perturbation Methods ◽  
Calculation Model ◽  
Perturbation Calculation ◽  
Reactor Physics ◽  
Tracking Method ◽  
Monte Carlo Techniques ◽  
Sensitivity Studies

In the reactor design and analysis, there is often a need to calculate the effects caused by perturbations of temperature, components and even structure of reactors on reactivity. And in sensitivity studies, uncertainty analysis of target quantities and unclear data adjustment, perturbation calculations are also widely used. To meet the need of different types of reactors (complex, multidimensional systems), Monte Carlo perturbation methods have been developed. In this paper, several kinds of perturbation methods are investigated. Specially, differential operator sampling method and correlated tracking method are discussed in details. MCNP’s perturbation calculation capability is discussed by calculating certain problems, from which some conclusions are obtained on the capabilities of the differential operator sampling method used in the perturbation calculation model of MCNP. Also, a code using correlated tracking method has been developed to solve certain problems with cross-section changes, and the results generated by this code agree with the results generated by straightforward Monte Carlo techniques.

Grid and Slot Scan Scatter Reduction in Mammography: Comparison by Using Monte Carlo Techniques

Radiology ◽  
2002 ◽  
Vol 222 (2) ◽  
pp. 519-527 ◽  
Author(s):  
John M. Boone ◽  
J. Anthony Seibert ◽  
Cha-Mei Tang ◽  
Steve M. Lane
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Techniques ◽  
Scatter Reduction

scholarly journals Multivariate Error Covariance Estimates by Monte Carlo Simulation for Assimilation Studies in the Pacific Ocean

2005 ◽  
Vol 133 (8) ◽  
pp. 2310-2334 ◽  
Author(s):  
Anna Borovikov ◽  
Michele M. Rienecker ◽  
Christian L. Keppenne ◽  
Gregory C. Johnson
Keyword(s):  
Monte Carlo ◽  
Data Assimilation ◽  
Forecast Error ◽  
Independent Set ◽  
Velocity Fields ◽  
Optimal Interpolation ◽  
Model Errors ◽  
Error Statistics ◽  
Practical Applications ◽  
Monte Carlo Techniques

Abstract One of the most difficult aspects of ocean-state estimation is the prescription of the model forecast error covariances. The paucity of ocean observations limits our ability to estimate the covariance structures from model–observation differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross covariances between different model variables used. Here a comparison is made between a univariate optimal interpolation (UOI) scheme and a multivariate OI algorithm (MvOI) in the assimilation of ocean temperature profiles. In the UOI case only temperature is updated using a Gaussian covariance function. In the MvOI, salinity, zonal, and meridional velocities as well as temperature are updated using an empirically estimated multivariate covariance matrix. Earlier studies have shown that a univariate OI has a detrimental effect on the salinity and velocity fields of the model. Apparently, in a sequential framework it is important to analyze temperature and salinity together. For the MvOI an estimate of the forecast error statistics is made by Monte Carlo techniques from an ensemble of model forecasts. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross covariances between the fields of different physical variables constituting the model-state vector, at the same time incorporating the model’s dynamical and thermodynamical constraints as well as the effects of physical boundaries. Only temperature observations from the Tropical Atmosphere–Ocean array have been assimilated in this study. To investigate the efficacy of the multivariate scheme, two data assimilation experiments are validated with a large independent set of recently published subsurface observations of salinity, zonal velocity, and temperature. For reference, a control run with no data assimilation is used to check how the data assimilation affects systematic model errors. While the performance of the UOI and MvOI is similar with respect to the temperature field, the salinity and velocity fields are greatly improved when the multivariate correction is used, as is evident from the analyses of the rms differences between these fields and independent observations. The MvOI assimilation is found to improve upon the control run in generating water masses with properties close to the observed, while the UOI fails to maintain the temperature and salinity structure.

Experimental and Numerical Analyses of a Pressurized Air Receiver for Solar-Driven Gas Turbines

2010 ◽  
Author(s):  
Illias Hischier ◽  
Pascal Leumann ◽  
Aldo Steinfeld
Keyword(s):  
Power Generation ◽  
Monte Carlo ◽  
Steady State ◽  
Gas Turbines ◽  
Porous Ceramic ◽  
Operating Pressure ◽  
Radiative Fluxes ◽  
Monte Carlo Techniques ◽  
Concentrated Solar Radiation ◽  
Solar Receiver

A high-temperature pressurized air-based receiver for power generation via solar-driven gas turbines is experimentally and theoretically examined. It consists of an annular reticulate porous ceramic (RPC) foam concentric with an inner cylindrical cavity-receiver exposed to concentrated solar radiation. Absorbed heat is transferred by combined conduction, radiation, and convection to the pressurized air flowing across the RPC. The governing steady-state mass, momentum and energy conservation equations are formulated and solved numerically by coupled Finite Volume and Monte Carlo techniques. Validation is accomplished with experimental results using a 1 kW solar receiver prototype subjected to average solar radiative fluxes in the range 1870–4360 kW m−2. Experimentation was carried out with air and helium as working fluids, heated from ambient temperature up to 1335 K at an absolute operating pressure of 5 bars.

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