The Experts below are selected from a list of 4698 Experts worldwide ranked by ideXlab platform
Christian P. Robert - One of the best experts on this subject based on the ideXlab platform.
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Riemann Sums for MCMC estimation and convergence monitoring
Statistics and Computing, 2001Co-Authors: Anne Philippe, Christian P. RobertAbstract:This paper develops an extension of the Riemann Sum techniques of Philippe (J. Statist. Comput. Simul. 59: 295–314) in the setup of MCMC algorithms. It shows that these techniques apply equally well to the output of these algorithms, with similar speeds of convergence which improve upon the regular estimator. The restriction on the dimension associated with Riemann Sums can furthermore be overcome by Rao–Blackwellization methods. This approach can also be used as a control variate technique in convergence assessment of MCMC algorithms, either by comparing the values of alternative versions of Riemann Sums, which estimate the same quantity, or by using genuine control variate, that is, functions with known expectations, which are available in full generality for constants and scores.
Anne Philippe - One of the best experts on this subject based on the ideXlab platform.
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Riemann Sums for MCMC estimation and convergence monitoring
Statistics and Computing, 2001Co-Authors: Anne Philippe, Christian P. RobertAbstract:This paper develops an extension of the Riemann Sum techniques of Philippe (J. Statist. Comput. Simul. 59: 295–314) in the setup of MCMC algorithms. It shows that these techniques apply equally well to the output of these algorithms, with similar speeds of convergence which improve upon the regular estimator. The restriction on the dimension associated with Riemann Sums can furthermore be overcome by Rao–Blackwellization methods. This approach can also be used as a control variate technique in convergence assessment of MCMC algorithms, either by comparing the values of alternative versions of Riemann Sums, which estimate the same quantity, or by using genuine control variate, that is, functions with known expectations, which are available in full generality for constants and scores.
Basant K. Jha - One of the best experts on this subject based on the ideXlab platform.
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Unsteady Dean flow formation in an annulus with partial slippage: A Riemann-Sum approximation approach
Results in Engineering, 2020Co-Authors: Basant K. Jha, Yahaya Jibrin DanjumaAbstract:Abstract This paper investigates time-dependent Dean Flow of an incompressible fluid under homogeneous slip, non-homogeneous slip, and no-slip boundary conditions. The fluid flow is due to the sudden application of an azimuthal pressure gradient. The general solutions of the governing momentum equations are obtained using a two-step approach called Laplace transformation and Riemann-Sum approximation method of Laplace inversion. The velocity and skin friction are determined exactly in the Laplace domain and inverted back to time domain using a numerical approach known as Riemann-Sum approximation. The steady-state solutions for the velocity and the skin friction are obtained for the validation of the method employed. Graphs are plotted for analysis and numerical values are tabulated for comparison of the Riemann-Sum approximation and the exact solution at large values of time. From the analysis, it is observed that the velocity profile of the fluid is higher at the wall with the highest slip coefficients. Finally, the influence of the dimensionless time ( T ) and the slip coefficients is also discussed with the aid of graphical illustrations.
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Unsteady hydromagnetic-free convection flow with suction/injection
Taylor & Francis Group, 2019Co-Authors: Basant K. Jha, Luqman A. Azeez, Michael O. OniAbstract:This article analyses the unsteady hydromagnetic free convection flow near impulsive as well as accelerated motion of the infinite vertical porous plate. The governing momentum and energy partial differential equations exhibiting the physics of the flow formation are presented. Using suitable dimensionless parameters, the equations are transformed to their corresponding dimensionless form and solved exactly in the Laplace domain using the well-known Laplace transform technique. However, the Riemann-Sum approximation method is used to invert the solution from the Laplace domain to time domain due of the complexity of the solutions obtained in the Laplace domain. The effect of various pertinent parameters such as suction/injection, Hartmann number, Grashof number, and Prandtl number is discussed with the aid of line graphs
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Transient Dean flow in an annulus: a semi-analytical approach
Taylor & Francis Group, 2019Co-Authors: Basant K. Jha, Jibrin Danjuma YahayaAbstract:The mathematical model of a fully developed laminar transient flow formation between the gaps of two horizontally stationary concentric tubes forming concentric annulus due to the impact of sudden application of azimuthal pressure gradient is analysed. Analytical and numerical solutions of the momentum equations are obtained by the aid of two-step process. The first step is by solving the governing partial differential equation analytically by using Laplace transform technique in the Laplace domain. Using Riemann–Sum approximation of Laplace inversion, the velocity and skin friction are then inverted to time domain. Expressions for steady-state velocity and skin friction are obtained for the validations of the method employed. In the course of numerical computations, it is observed that increase in dimensionless time $ (T ) $ leads to increase in velocity as well as skin friction at the surfaces of tubes. It is also found that at large values of dimensionless time $ (T ) $ , the velocity and skin friction reach steady state
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Unsteady Hartmann Two-Phase Flow: The Riemann-Sum Approximation Approach
International Journal of Applied Mechanics and Engineering, 2016Co-Authors: Basant K. Jha, C. T. Babila, S. IsaAbstract:Abstract We consider the time dependent Hartmann flow of a conducting fluid in a channel formed by two horizontal parallel plates of infinite extent, there being a layer of a non-conducting fluid between the conducting fluid and the upper channel wall. The flow formation of conducting and non-conducting fluids is coupled by equating the velocity and shear stress at the interface. The unsteady flow formation inside the channel is caused by a sudden change in the pressure gradient. The relevant partial differential equations capturing the present physical situation are transformed into ordinary differential equations using the Laplace transform technique. The ordinary differential equations are then solved analytically and the Riemann-Sum approximation method is used to invert the Laplace domain into time domain. The solution obtained is validated by comparisons with the closed form solutions obtained for steady states which have been derived separately and also by the implicit finite difference method. The variation of velocity, mass flow rate and skin-friction on both plates for various physical parameters involved in the problem are reported and discussed with the help of line graphs. It was found that the effect of changes of the electric load parameter is to aid or oppose the flow as compared to the short-circuited case.
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Role of Induced Magnetic Field on Transient Natural Convection Flow in a Vertical Channel: The Riemann Sum Approximation Approach
International Journal of Applied Mechanics and Engineering, 2015Co-Authors: Basant K. Jha, I. SaniAbstract:Abstract This paper investigates the role of induced magnetic field on a transient natural convection flow of an electrically conducting, incompressible and viscous fluid in a vertical channel formed by two infinite vertical parallel plates. The transient flow formation inside the channel is due to sudden asymmetric heating of channel walls. The time dependent momentum, energy and magnetic induction equations are solved semi-analytically using the Laplace transform technique along with the Riemann-Sum approximation method. The solutions obtained are validated by comparisons with the closed form solutions obtained for the steady states which have been derived separately and also by the implicit finite difference method. Graphical results for the temperature, velocity, induced magnetic field, current density, and skin-friction based on the semi-analytical solutions are presented and discussed.
Matthias Patzold - One of the best experts on this subject based on the ideXlab platform.
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the Riemann Sum method for the design of Sum of cisoids simulators for rayleigh fading channels in non isotropic scattering environments
International Conference on Ultra Modern Telecommunications, 2009Co-Authors: Carlos A Gutierrez, Matthias PatzoldAbstract:In this paper, we introduce the Riemann Sum method (RSM) as an effective tool for the design of Sum-of-cisoids (SOC) simulators for narrowband mobile Rayleigh fading channels under non-isotropic scattering conditions. We show that the RSM results in an excellent approximation of the channel's autocorrelation function (ACF). Furthermore, we compare the performance of the RSM with that of the generalized method of equal areas (GMEA) and L p -norm method (LPNM), which were until now the only methods available for the design of SOC simulators for non-isotropic scattering channels. The obtained results indicate that the RSM is better suited than the GMEA and the LPNM to approximate the channel's ACF, whereas the latter two methods provide better results regarding the emulation of the envelope distribution. Owing to its simplicity and good performance, the RSM can be used to design flexible simulation platforms for the analysis of mobile communication systems operating in non-isotropic scattering environments.
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ICUMT - The Riemann Sum method for the design of Sum-of-cisoids simulators for Rayleigh fading channels in non-isotropic scattering environments
2009 International Conference on Ultra Modern Telecommunications & Workshops, 2009Co-Authors: Carlos A Gutierrez, Matthias PatzoldAbstract:In this paper, we introduce the Riemann Sum method (RSM) as an effective tool for the design of Sum-of-cisoids (SOC) simulators for narrowband mobile Rayleigh fading channels under non-isotropic scattering conditions. We show that the RSM results in an excellent approximation of the channel's autocorrelation function (ACF). Furthermore, we compare the performance of the RSM with that of the generalized method of equal areas (GMEA) and L p -norm method (LPNM), which were until now the only methods available for the design of SOC simulators for non-isotropic scattering channels. The obtained results indicate that the RSM is better suited than the GMEA and the LPNM to approximate the channel's ACF, whereas the latter two methods provide better results regarding the emulation of the envelope distribution. Owing to its simplicity and good performance, the RSM can be used to design flexible simulation platforms for the analysis of mobile communication systems operating in non-isotropic scattering environments.
Victor Hernandez - One of the best experts on this subject based on the ideXlab platform.
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random Riemann Sum estimator versus monte carlo
Computational Statistics & Data Analysis, 2007Co-Authors: Henar Urmeneta, Victor HernandezAbstract:Two estimators of the expectation of a function, the classical based in Monte Carlo sampling method and one based in Random Riemann Sums, are compared. It presents the differences on bias, variance, convergence and mainly convergence rates. Two ways of sampling to obtain a Random Riemann Sum estimator are given. The first one provides a sequence of estimations whose terms are independent, this fact produces a loss of order one in the convergence rate for the strong law compared with Monte Carlo sampling method. The second one is considered in order to improve these results.
