Combines Monte Carlo Sampling Research Articles

Planning cost-effective operational forest inventories.

We address a Bayesian two-stage decision problem in operational forestry where the inner stage considers scheduling the harvesting to fulfill demand targets and the outer stage considers selecting the accuracy of pre-harvest inventories that are used to estimate the timber volumes of the forest tracts. The higher accuracy of the inventory enables better scheduling decisions but also implies higher costs. We focus on the outer stage, which we formulate as a maximization of the posterior value of the inventory decision under a budget constraint. The posterior value depends on the solution to the inner stage problem and its computation is analytically intractable, featuring an NP-hard binary optimization problem within a high-dimensional integral. In particular, the binary optimization problem is a special case of a generalized quadratic assignment problem. We present a practical method that solves the outer stage problem with an approximation which combines Monte Carlo sampling with a greedy, randomized method for the binary optimization problem. We derive inventory decisions for a dataset of 100 Swedish forest tracts across a range of inventory budgets and estimate the value of the information to be obtained.

Rogue waves and large deviations in deep sea

The appearance of rogue waves in deep sea is investigated by using the modified nonlinear Schrödinger (MNLS) equation in one spatial dimension with random initial conditions that are assumed to be normally distributed, with a spectrum approximating realistic conditions of a unidirectional sea state. It is shown that one can use the incomplete information contained in this spectrum as prior and supplement this information with the MNLS dynamics to reliably estimate the probability distribution of the sea surface elevation far in the tail at later times. Our results indicate that rogue waves occur when the system hits unlikely pockets of wave configurations that trigger large disturbances of the surface height. The rogue wave precursors in these pockets are wave patterns of regular height, but with a very specific shape that is identified explicitly, thereby allowing for early detection. The method proposed here combines Monte Carlo sampling with tools from large deviations theory that reduce the calculation of the most likely rogue wave precursors to an optimization problem that can be solved efficiently. This approach is transferable to other problems in which the system's governing equations contain random initial conditions and/or parameters.

Hybrid Sampling/Spectral Method for Solving Stochastic Coupled Problems

In this paper, we present a hybrid method that combines Monte Carlo sampling and spectral methods for solving stochastic coupled problems. After partitioning the stochastic coupled problem into subsidiary subproblems, the proposed hybrid method entails iterating between these subproblems in a way that enables the use of the Monte Carlo sampling method for subproblems that depend on a very large number of uncertain parameters and the use of spectral methods for subproblems that depend on only a small or moderate number of uncertain parameters. To facilitate communication between the subproblems, the proposed hybrid method shares between the subproblems a reference representation of all the solution random variables in the form of an ensemble of samples; for each subproblem solved by a spectral method, it uses a dimension-reduction technique to transform this reference representation into a subproblem-specific reduced-dimensional representation to facilitate a computationally efficient solution in a reduced...

Combined Monte Carlo sampling and penalty method for Stochastic nonlinear complementarity problems

In this paper, we consider a new formulation with recourse for a class of stochastic nonlinear complementarity problems. We show that the new formulation is equivalent to a smooth semi-infinite program that no longer contains recourse variables. We then propose a combined Monte Carlo sampling and penalty method for solving the problem in which the underlying sample space is assumed to be compact. Furthermore, we suggest a compact approximation approach for the case where the sample space is unbounded. Two preliminary numerical examples are included as well.

Blind sequential detection for Rayleigh fading channels using hybrid Monte Carlo-recursive identification algorithms

Detection of data transmitted over a Rayleigh fading channel, where the channel is unknown, has been a problem of interest for many researchers. In this paper, we present a new algorithm for joint detection and channel estimation for Rayleigh fading channels. Our algorithm combines Monte Carlo sampling with classical recursive identification methods. The channel is modeled as an autoregressive process, which allows for representation of the communication system by a dynamic state space model. A more accurate modeling of the channel, especially in fast fading along with exploitation of time diversity in the received signal, is also considered. Simulation results illustrating the effectiveness of this algorithm are presented.

Trajectory study of atomic recombination reactions. VIII. The energy transfer mechanism

The energy transfer (ET) mechanism of atomic recombination reactions, X+X=X2*, X2*+M→X2+M, where X2* is a classically unstable orbiting quasidimer consisting of two X atoms and M is a third body, has been commonly used for the past forty years. Presently it is studied in some detail using the 3-D trajectory calculation technique and the Monte Carlo method of sampling. Since this mechanism approximates a pure three body problem by considering two independent and consecutive two body collisions, it introduces an error in trajectory calculations. In order to improve upon this approximation, a more reasonable modified method of trajectory sampling is made. It is found that even in one of the most favorable cases where the ET mechanism is predominant, i.e., for the 2I+He=I2+He reaction, the error introduced by the ET mechanism is of the order of two in the rate constant. It is concluded, in light of the present findings, that earlier as well as present trajectory studies for halogen atom recombination in helium are consistent with experimental data. The existing discrepancy between computed and experimental results can be accounted for by the approximations used in trajectory calculations. On the other hand, the combined Monte Carlo sampling and experimental errors cannot account for the existing discrepancies.