For this reason, Nathan, Weinmann and Hill (2003) proposed a Monte Carlo technique
based on critical duration concept (further details in Nathan and Weinmann 2004, 2013).
The [PD.sub.new] values were stored in specific files, as well as the values calculated by the Monte Carlo techniques
, which were previously normalized with respect to the dose percent maximum located at the 3.25 cm depth below the water surface inside the phantom and over the radiation beam symmetry.
The Monte Carlo technique
is an area of physics, which became important during the Manhattan Project in the Second World War which led to the development of the atomic bomb.
Quasi Monte Carlo techniques
, such as those in Li (2000) and Siegl and Tichy (2000), overcome the problems of the random number generator by using well-spaced grids of points, which are particularly effective at mapping the boundary of the problem even with a relatively small batch size.
Monte Carlo techniques
were used to test the appropriateness of statistical procedures when the underlying assumptions of these procedures are violated.
Methods for improved calculation of these effects are under development by Monte Carlo techniques
or direct solution of the drift kinetic equation.
Among specific topics are the decomposition of the optical polarization components of the Crab pulsar and its nebula, the analysis of single pulses from radio pulsars at high observing frequencies, the population synthesis of normal radio and gamma-ray pulsars using Markov chain Monte Carlo techniques
, symmetry energy effects in the neutron star properties, and radio timing observations of four gamma-ray pulsars at Nanshan.
Continuing to focus on analytic strategies for regression problems for practical situations in which predictors are measured with error, this edition includes developments across the last decade, including greatly expanded discussion and applications of Bayesian computation through chain Monte Carlo techniques
, a new chapter on longitudinal data and mixed models, and new material on nonparametric regression, density estimation, survival analysis, and score functions, with unique data sets available online.
He has published more than 100 archival papers concerned with developments of EPMA instrumentation, improvements in microanalysis techniques, metallurgical and geological applications (including lunar samples and asbestos), characterization of microanalysis standards, uncertainties in quantitative EPMA and correction procedures, bibliographies of EPMA publications, tables of mass absorption coefficients and x-ray lines, development of matrix correction procedures, the early use of color in wavelength dispersive x-ray dot mapping, energy dispe rsive qualitative and quantitative analysis, and the use of Monte Carlo techniques
in quantitative EPMA.
Case studies illustrate the use of GMRFs in complex hierarchical models in which statistical inference is only possible using Markov chain Monte Carlo techniques
. Emphasis is on the connection between GMRFs and numerical methods for sparse matrices.