... techniques in MonteCarlo simulation, such as antithetic and common random numbers, control random variables, conditional Monte Carlo, stratified sampling, and importance sampling The last is the most ... enabling the flow of information and understanding necessary to meet their needs and fulfill their aspirations Today, bold new technologies are changing the way we live and learn Wiley will be there, ... analysis and optimization of both static and dynamic models We introduce the celebrated score function method for sensitivity analysis, and two alternative methods for MonteCarlo optimization, the...
... 1.15.1 Lagrangian MethodThe main components of the Lagrangian method are the Lagrange multipliers andthe Lagrange function, Themethod was developed by Lagrange in 1797 for the optimization ... the limiting distribution j T = (1 - r )(1,r, r ,r , ) for this Markov chain, and all the states are therefore j positive recurrent On the other hand, when p q, C n is either or infinite, and ... (X,Y ) and fx and fy are the (marginal) pdfs of X and Y, respectively In other words, the mutual information can be viewed as the CE that measures 32 PRELIMINARIES the distance between the joint...
... generate X from the cdf Gi 2.3.4 Acceptance-Rejection MethodThe inverse-transform and composition methods are direct methods in the sense that they deal directly with the cdf of the random variable ... from the pdf (2.20) and then assign to X a random sign The validity of this procedure follows from the symmetry of the standard normal distribution about zero 60 RANDOM NUMBER RANDOM VARIABLE, AND ... one-dimensional random variables from a prescribed distribution We consider the inverse-transform method, the alias method, the composition method, andthe acceptance-rejection method 2.3.1 Inverse-Transform...
... approximation to the real system and incorporate most of the important aspects of the real system On the other hand, the model must not be so complex as to preclude its understanding and manipulation There ... namely, the simulation clock andthe event list Finally, in Section 3.3 we further explain the ideas behind discrete-event simulation via a number of worked examples Simulation andtheMonteCarlo Method, ... Programming, and Analysis SpringerVerlag, New York, 2001 J M Hammersley and D C Handscomb MonteCarlo Methods John Wiley & Sons, New York, 1964 M H Kalos and P A Whitlock MonteCarlo Methods, Volume...
... Sample paths for the two inventory processes Let D , and A, be the size of the i-th demand andthe length of the i-th interdemand time, respectively We assume that both { D,} and { A , } are iid ... of the standard deviation of H , that is, the square root of ’ (4.29) In the percentile method, the upper and lower bounds of the (1- a ) 100%confidence interval fore are given by the - a / and ... further reduce the variance 5.5 STRATIFIED SAMPLING Stratified sampling is closely related to both the composition method of Section 2.3.3 andthe conditional MonteCarlomethod discussed in the...
... multiplying and dividing the integrand by f(x;w) We now replace the expected value in (5.57)by its sample (stochastic) counterpart and then take the optimal solution of the associated MonteCarlo program ... on a and H ( X ) is ignored In the special case of equal weights ( p , = l / m and N, = N / m ) , the estimator (5.34) reduces to (5.38) andthemethod is known as the systematic sampling method ... represents the original values u, andthe reference values vi obtained by using (5.65) The numbers 1-32 correspond to the generators andthe numbers 33-70 correspond to the lines Note that the data...
... adaptively, as with the CE and TLR methods THE HIT -AND- RUN SAMPLER 173 6.3 THE HIT -AND- RUN SAMPLER The hit -and- run sampler, pioneered by Robert Smith [24], is among the first MCMC samplers in the category ... independent nearest neighbor random walks in 9thatstart at X t andend when they step out o f One random walk is called the forward walk andthe other is called the backward walk The bidirectional walk ... sense, the C E and VM methods are similar, because the C E method minimizes the Kullback-Leibler distance between g* and g 5.16 Repeat Problem 5.2 using importance sampling, where the lengths of the...
... Hessians, etc.) of the response function ! u) ( with respect to parameter vector u, and it is based on the score function andthe Fisher inforSimulation andtheMonteCarlo Method, Second Edition ... iterations Plot the histograms of j ( p x) and f ( 2I x) and find the sample means of these posteriors Compare them with the classical estimates d) Show that the true posterior pdf of p given the data ... SENSITIVITY ANALYSIS ANDMONTE CARL0 OPTIMIZATION and then solve the latter by standard mathematical programming techniques The resultant optimal solution provides an estimator of the corresponding...
... of the CE method to several such problems, such as the max-cut problem andthe TSP, and provide supportive numerical results on the performance of the algorithm Simulation andtheMonteCarloMethod ... in 1990 and independently in 1989 by Reiman and Weiss [ 121, who called it the likelihoodratio method Since then, both the IPA and S F methods have evolved over the past decade or so and have ... solve the optimization problem (PN)by standard methods of mathematical programming The resultant optimal function value andthe optimal decision vector of the program (PN)provide estimators of the...
... several applications of the CE method to combinatorial optimization, namely the max-cut, the bipartition andthe TSP We demonstrate numerically the efficiency of the C E methodand its fast convergence ... ,n} and a set of edges E between the nodes, partition the nodes of the graph into two arbitrary subsets V1 and V such that the sum of 254 THE CROSS-ENTROPY METHODthe weights (costs) ctI of the ... i } and {oi }the means and standard deviations of the components, the updating formulas are (see Problem 8.17) (8.46) and (8.47) where Xki is the i-th component of Xk and X I , , X, is a random...
... them are the standard CE, exponential change of measure (ECM), andthe celebrated MinxEnt method [ 171 Here we shall us a particular modification of the MinxEnt method called the PME methodand ... with the values l,-l, and in the clause matrix A , which indicates if the literal corresponds to the variable, its negation, or that neither appears in the clause If, for example, z3 = and at3 ... 0,1,0,1) is the only other assignment that renders all the clauses true The problem of deciding whether there exists a valid assignment, and indeed providing such a vector, is called the SAT-assignment...
... some known p,o and Co, one determines 111 and 51,then j k and C1, and so on Notice and that 2, Ct not depend on the observations y1, y2, and can therefore be determined of-line The Kalman filter ... Simulation andtheMonteCarlo Method, Second Edition By R.Y Rubinstein and D P Kroese Copyright @ 2007 John Wiley & Sons, Inc 315 316 APPENDIX Generally, the bij can be found from the recursive ... C,) distributed The objective is to obtain the filtering pdf f(xt ~ : and thepredictive pdf f(zt1 y1:t-1) ~ ) must be Gaussian, since these random vectors and YITt Observe that the joint pdf of...
... that all uses of theMonteCarlo are for the purposes of understanding physical phenomena There are others uses of theMonteCarlomethod for purely mathematical reasons, such as the determination ... Neumann and Ulam during the initial development of thermonuclear weapons6 Ulam and von Neumann coined the phrase MonteCarloand were pioneers in the development of theMonteCarlo technique and ... MONTECARLO Basic understanding Figure 1.2: The role of MonteCarlo methods in basic science possible, as in the example of Figure 1.1 where two people can not occupy the same seat, a Monte Carlo...
... techniques in MonteCarlo simulation, such as antithetic and common random numbers, control random variables, conditional Monte Carlo, stratified sampling, and importance sampling The last is the most ... enabling the flow of information and understanding necessary to meet their needs and fulfill their aspirations Today, bold new technologies are changing the way we live and learn Wiley will be there, ... analysis and optimization of both static and dynamic models We introduce the celebrated score function method for sensitivity analysis, and two alternative methods for MonteCarlo optimization, the...
... 3.2.2 The crude MonteCarlomethod 57 3.2.3 TheMonteCarlo method: Some first applications 60 3.3 Improving the speed of convergence of theMonteCarlo method: Variance reduction methods ... 51 52 53 53 53 TheMonteCarlo Method: Basic Principles 55 3.1 Introduction 55 3.2 The strong law of large numbers andtheMonteCarlomethod 56 3.2.1 The strong law ... MonteCarlo Methods and Models in Finance and Insurance CHAPMAN & HALL/CRC Financial Mathematics Series Aims and scope: The field of financial mathematics forms an ever-expanding slice of the...
... between the CDF of both the real and imaginary part of the OFDM signal andthe CDF of a Gaussian random variable with zero mean and variance 1/2 The summand in (B.3) is the product of the likelihood ... approximation for the multicarrier signal increases with both the number of subcarriers andthe size of the constellation Moreover, the approximation accuracy for the real and imaginary part of the multicarrier ... accuracy as a function of the SNR The performance of the proposed estimator is compared to the PCRB For βT = 10−3 , it performs close to the PCRB The gap between the PCRB andthe JSCPE-MPF increases...
... target aspect and motion and review the observation and clutter models focusing on the GMRf representation of the background andthe derivation of the associated likelihood function for the observed ... ]T , that collects the positions, xn and yn , and ˙ ˙ the velocities, xn and yn , of the target’s centroid in a system of 2D Cartesian coordinates (x, y) On the other hand, the target’s aspect ... I, andthe initial probabilities Pr({z0 = i}), i ∈ I where ζ and ζ are the spatial resolutions of the image, respectively, in the directions x and y The parameter pa in (2) denotes in turn the...
... the spins toward the [100] andthe [010] directions grow and form one big DW at around B=0.85 Then the DW was fixed andthe spins in the two domains gradually rotate toward the [110] direction, ... E2A, E2B Then E2 = E2 A + E2 B ; • (7) the difference of the energies before and after the exchange of the points A and B is ΔE = E2 − E1 ; • (6) (8) if ∆E ≤ 0, the exchange of the sites A and B ... and (b) The susceptibility of (a) diverges around temperature kBT=1.0 andthe magnetic property shows ferro-magnetism The direction of the 546 Applications of MonteCarloMethod in Science and Engineering...
... Stubos and Theodore A Steriotis Chapter 27 Effect of the Repulsive Interactions on the Nucleation and Island Growth: Kinetic MonteCarlo Simulations 677 Hu Juanmei and Wu Fengmin Chapter 28 MonteCarlo ... detector The task itself demands a certain image quality which depends also on the X-ray spectrum, the examination geometry and furthermore on the size of the X-ray source’s focal spot andthe resolution ... between the cathode (the electron emitter) andthe anode (the X-ray target) When the electrons hit the target, they are decelerated hard by collisions with electrons of the target material or in the...