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This book seeks to bridge the gap between statistics and computer science. It provides an overview of Monte Carlo methods, including Sequential Monte Carlo, Markov Chain Monte Carlo, Metropolis-Hastings, Gibbs Sampler, Cluster Sampling, Data Driven MCMC, Stochastic Gradient descent, Langevin Monte Carlo, Hamiltonian Monte Carlo, and energy landscape mapping. Due to its comprehensive nature, the book is suitable for developing and teaching graduate courses on Monte Carlo methods. To facilitate learning, each chapter includes several representative application examples from various fields. The book pursues two main goals: (1) It introduces researchers to applying Monte Carlo methods to broader problems in areas such as Computer Vision, Computer Graphics, Machine Learning, Robotics, Artificial Intelligence, etc.; and (2) it makes it easier for scientists and engineers working in these areas to employ Monte Carlo methods to enhance their research.

Computer mathematics. --- Mathematical statistics. --- Optical data processing. --- Statistics . --- Computational Mathematics and Numerical Analysis. --- Probability and Statistics in Computer Science. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Statistical Theory and Methods. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Computer mathematics --- Optical equipment --- Monte Carlo method. --- Computer science --- Mathematics. --- Artificial sampling --- Model sampling --- Monte Carlo simulation --- Monte Carlo simulation method --- Stochastic sampling --- Games of chance (Mathematics) --- Mathematical models --- Numerical analysis --- Numerical calculations --- Stochastic processes

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This book describes, as simply as possible, the mechanisms of scattering (both elastic and inelastic) of electrons with solid targets (electron–atom, electron–plasmon, and electron–phonon interactions). It also presents the main strategies of the Monte Carlo method, as well as numerous comparisons between simulation results and the experimental data available in the literature. Furthermore it provides readers with all the information they need in order to write their own Monte Carlo code and to compare the obtained results with the many numerical and experimental examples presented throughout the book. An extended and updated third edition of a work published in 2014 (first edition) and in 2017 (second edition) on the application of the Monte Carlo method to the transport of fast electrons in solids, this book includes, as novel topics, the theory of polarized electron beams (i.e. density matrix and spin polarization), the study of elastic scattering by molecules, a classical treatment of the Bethe-Bloch stopping power, a simple derivation of the f- and ps-sum rules, the Vicanek and Urbassek formula for the calculation of the backscattering coefficient, the Wolff theory describing the secondary electron spectra, and fundamental aspects of the interactions between electrons beams and solid targets. Further, it describes a completely analytical approach (the so-called multiple reflection method) for calculating the absorbed, backscattered, and transmitted fractions of electrons from unsupported and supported thin films. It also discusses recent applications of the Monte Carlo method.

Monte Carlo method. --- Artificial sampling --- Model sampling --- Monte Carlo simulation --- Monte Carlo simulation method --- Stochastic sampling --- Games of chance (Mathematics) --- Mathematical models --- Numerical analysis --- Numerical calculations --- Stochastic processes --- Solid state physics. --- Physics. --- Materials science. --- Applied mathematics. --- Engineering mathematics. --- Particle acceleration. --- Solid State Physics. --- Numerical and Computational Physics, Simulation. --- Characterization and Evaluation of Materials. --- Mathematical and Computational Engineering. --- Particle Acceleration and Detection, Beam Physics. --- Particles (Nuclear physics) --- Acceleration (Mechanics) --- Nuclear physics --- Engineering --- Engineering analysis --- Mathematical analysis --- Material science --- Physical sciences --- Natural philosophy --- Philosophy, Natural --- Dynamics --- Physics --- Solids --- Acceleration --- Mathematics --- Condensed matter. --- Mathematical physics. --- Materials --- Particle accelerators. --- Condensed Matter Physics. --- Theoretical, Mathematical and Computational Physics. --- Characterization and Analytical Technique. --- Mathematical and Computational Engineering Applications. --- Accelerator Physics. --- Analysis. --- Data processing. --- Accelerators, Particle --- Atom smashers --- Charged particle accelerators --- Accelerator mass spectrometry --- Physical mathematics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Instruments