Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book ...explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometrics, and applied mathematics, this is both an entry-level text and a valuable reference.
This book covers adaptive mesh generation and moving mesh methods for solving time-dependent PDEs. It gives a general description of the components of moving mesh methods as well as examples of their ...application for a number of nontrivial physical problems.
Due to the complexity of modeling the radiative transfer inside the accretion columns of neutron star binaries, their X-ray spectra are still commonly described with phenomenological models, e.g., a ...cut off power law. While the behavior of these models is well understood and they allow for a comparison of different sources and studying source behavior, the extent to which the underlying physics can be derived from the model parameters is very limited. During recent years, several physically motivated spectral models have been developed to overcome these limitations. Their application, however, is generally computationally much more expensive and they require a high number of parameters which are difficult to constrain. In particular, Becker & Wolff(2007) presented an analytical solution to the radiative transfer equation inside the accretion column assuming a velocity profile that is linear in the optical depth. An implementation of this model that is both fast and accurate enough to be fitted to observed spectra is available in XSPEC. The main difficulty of this implementation is that some solutions violate energy conservation and therefore have to be rejected by the user. We propose a novel fitting strategy that ensures energy conservation during theχ2-minimization which simplifies the application of the model considerably. We demonstrate this approach as well as a study of possible parameter degeneracies with a comprehensive Markov-Chain Monte Carlo analysis of the complete parameter space for a combined NuSTAR and Swift/XRT data-set of Cen X-3.The derived accretion-flow structure features a small column radius of∼63 m and a spectrum dominated by bulk-Comptonization of bremsstrahlung seed photons, in agreement with previous studies
In magnetic Cataclysmic Variables (mCVs), X-ray radiation originates from the shock heated multi-temperature plasma in the post-shock region near the white dwarf surface. These X-rays are modified by ...a complex distribution of absorbers in the pre-shock region. The presence of photo-ionized lines and warm absorber features in the soft X-ray spectra of these mCVs suggests that these absorbers are ionized. We developed the ionized complex absorber model zxipab, which is represented by a power-law distribution of ionized absorbers in the pre-shock ow. Using the ionized absorber model zxipab along with a cooling ow model and a reflection component, we model the broadband Chandra/HETG and NuSTAR spectra of two IPs: NY Lup and V1223 Sgr. We nd that this model describes well many of the H and He like emission lines from medium Z elements, which arises from the collisionally excited plasma. However the model fails to account for some of the He like triplets from medium Z elements, which points towards its photo-ionization origin. We do not find a compelling evidence for a blackbody component to model the soft excess seen in the residuals of the Chandra/HETG spectra, which could be due to the uncertainties in estimation of the interstellar absorption of these sources using Chandra/HETG data and/or excess fluxes seen in some photo-ionized emission lines which are not accounted by the cooling ow model. We describe the implications of this model with respect to the geometry of the pre-shock region in these two IPs
Numerical Methods Lindfield, George; Penny, John
2012, 2012-09-01
eBook
Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB for a graphical interpretation to help ...researchers analyze a particular outcome. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science across the board.
Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB, to help researchers analyze a particular outcome. Many worked examples are given, together with exercises and solutions, to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science. Over 500 numerical algorithms, their fundamental principles, and applicationsGraphs are used extensively to clarify the complexity of problemsIncludes coded genetic algorithmsIncludes the Lagrange multiplier methodUser-friendly and written in a conversational style
This book aims to present meshfree methods in a friendly and straightforward manner, so that beginners can very easily understand, comprehend, program, implement, apply and extend these methods. It ...provides first the fundamentals of numerical analysis that are particularly important to meshfree methods. Typical meshfree methods, such as EFG, RPIM, MLPG, LRPIM, MWS and collocation methods are then introduced systematically detailing the formulation, numerical implementation and programming. Many well-tested computer source codes developed by the authors are attached with useful descriptions. The application of the codes can be readily performed using the examples with input and output files given in table form. These codes consist of most of the basic meshfree techniques, and can be easily extended to other variations of more complex procedures of meshfree methods. Readers can easily practice with the codes provided to effective learn and comprehend the basics of meshfree methods.
Due to the fast developments of information technology and sensor technology, drivers get a precise estimate of real-time traffic conditions in the next moment. According to the situation, drivers ...can change their driving behavior while using their skills in advance with the help of prior information and they change their path through the turning point on road. To explore this phenomenon, a two-dimensional (2D) lattice model by incorporating the prior information (predictive effect) with the junction on road is proposed. At the junction of the road, traffic can enter into various downstream lanes from the upstream. The intensity of traffic at downstream may vary depending on the proportion of traffic. To analyze the proposed model, the stability condition is obtained without and with the control signal through the control method which shows that the stable region increases when the control signal is considered into account. The theoretical findings indicate that the predictive effect could affect the stability of diverging traffic. Numerical simulation verifies the theoretical findings which shows the results for the traffic flow stability with the consideration of the predictive effect and junction on road in 2D lattice model.
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