The Problem of the Monte Carlo Method
. The problem with Monte Carlo sampling is that if the probability of failure is a small value, a large number of samples are needed in order to predict this accurately, causing a sharp increase in required cost and time.
When direct computation is too complicated, resource or time consuming, too approximate, or simply not feasible, we make use of Monte Carlo methods
. These are based on computer simulations involving random numbers.
The furnished rooms with surfaces that have different optical properties, with the advantage of the stochlastic (probability) luminosity calculation, are often referred to as the Monte Carlo method
. Generally, these methods used a large number of random light beams or posted particles of bearing energy.
This theoretical work was performed within frame of Monte Carlo method
which describes the transport of light.
Many new Monte Carlo methods
have been developed and applied in nuclear medicine since the first edition was published in 1998, so radiologists, medical physicists, and related professionals update their account while keeping the focus on diagnostic imaging applications.
ERIC Descriptors: Educational Improvement; Federal Programs; Academic Achievement; Educational Indicators; Bayesian Statistics; Federal Legislation; Accountability; Generalizability Theory; Sample Size; Intervals; Monte Carlo Methods
They first give readers background on distribution related to the normal distribution, quadratic forms and estimation, then cover model fitting, exponential family and generalized linear models, estimation (including maximum livelihood estimation and the Poisson regression example), inference, normal linear models, binary variables and logistic regression, nominal and ordinal logistic regression, Poisson regression and log-linear models, survival analysis, clustered and longitudinal data, and the aforesaid chapters on Bayesian analysis, including a chapter on Markov Chain Monte Carlo methods
and another of examples.
Among the topics are multi-level Monte Carlo methods
for applications in finance, asymptotic and non-asymptotic approximations for option valuation, discretization of backward stochastic Volterra integral equations, derivative-free weak approximation methods for stochastic differential equations, randomized multi-level quasi-Monte Carlo path simulation, applying simplest random walk algorithms for pricing barrier options, and dimension-wide decompositions and their efficient parallelization.
He focuses on one of the most important classes of simulation techniques, mesh-free particle-based methods, in particular the molecular dynamics and the Monte Carlo methods
ERIC Descriptors: Evidence; Effect Size; Research Methodology; Intervention; Evaluation; Regression (Statistics); Statistical Analysis; Models; Comparative Analysis; Meta Analysis; Markov Processes; Intervals; Monte Carlo Methods
; Hypothesis Testing
His topics include what robust design is, design-of-experiments for robust design, noise and control factors, smaller-the-better and larger-the-better, regression for robust design, the mathematics of robust design, the design and analysis of computer experiments, Monte Carlo methods
for robust design, and Taguchi and his ideas on robust design.