This textbook gives an overview of statistical methods that have been developed during the last years due to increasing computer use, including random number generators, Monte Carlo methods, Markov ...Chain Monte Carlo (MCMC) methods, Bootstrap, EM algorithms, SIMEX, variable selection, density estimators, kernel estimators, orthogonal and local polynomial estimators, wavelet estimators, splines, and model assessment. Computer Intensive Methods in Statistics is written for students at graduate level, but can also be used by practitioners.
Features
Presents the main ideas of computer-intensive statistical methods
Gives the algorithms for all the methods
Uses various plots and illustrations for explaining the main ideas
Features the theoretical backgrounds of the main methods.
Includes R codes for the methods and examples
Silvelyn Zwanzig is an Associate Professor for Mathematical Statistics at Uppsala University. She studied Mathematics at the Humboldt- University in Berlin. Before coming to Sweden, she was Assistant Professor at the University of Hamburg in Germany. She received her Ph.D. in Mathematics at the Academy of Sciences of the GDR. Since 1991, she has taught Statistics for undergraduate and graduate students. Her research interests have moved from theoretical statistics to computer intensive statistics.
Behrang Mahjani is a postdoctoral fellow with a Ph.D. in Scientific Computing with a focus on Computational Statistics, from Uppsala University, Sweden. He joined the Seaver Autism Center for Research and Treatment at the Icahn School of Medicine at Mount Sinai, New York, in September 2017 and was formerly a postdoctoral fellow at the Karolinska Institutet, Stockholm, Sweden. His research is focused on solving large-scale problems through statistical and computational methods.
Introduction
1. Randfom Variable Generation Basic Methods Congruential Generators The KISS Generator Beyond Uniform Distributions Transformation Methods Accept–Reject Methods Envelope Accept–Reject Methods Problems
2. Monte Carlo Methods Independent Monte Carlo Methods Importance Sampling The Rule of Thumb for Importance Sampling Markov Chain Monte Carlo - MCMC Metropolis-Hastings Algorithm Some Special Algorithms Adaptive MCMC Perfect Simulation The Gibbs Sampler Approximate Bayesian computation (ABC) methods Problems
3. Bootstrap General Principle Unified Bootstrap Framework Bootstrap and Monte Carlo Conditional and Unconditional Distribution Basic Bootstrap Plug–in Principle Why is Bootstrap Good? Example, where Bootstrap Fails Bootstrap Confidence Sets The Pivotal Method The Bootstrap Pivotal Methods Percentile Bootstrap Confidence Interval Basic Bootstrap Confidence Interval Studentized Bootstrap Confidence Interval Transformed Bootstrap Confidence Intervals Prepivoting Confidence Set BCa-Confidence Interval Bootstrap Hypothesis Tests Parametric Bootstrap Hypothesis Test Nonparametric Bootstrap Hypothesis Test Advanced Bootstrap Hypothesis Tests Bootstrap in Regression Model Based Bootstrap Parametric Bootstrap Regression Casewise Bootstrap In The Correlation Model Bootstrap For Time Series Problems
4. Simulation based Methods EM - Algorithm SIMEX Problems
5. Density Estimation Background Histogram Kernel Density Estimator Statistical Properties Bandwidth Selection in Practice Nearest Neighbor Estimator Orthogonal Series Estimators Minimax Convergence Rates Problems
6. Nonparametric Regression Background Kernel Regression Smoothing Local Regression Classes of Restricted Estimators Ridge Regression Lasso Spline Estimators Base Splines Smoothing Splines Wavelets Estimators Wavelet Base Wavelet Smoothing Choosing the Smoothing Parameter Bootstrap in Regression Problems
Silvelyn Zwanzig is an Associate Professor for Mathematical Statistics at Uppsala University. She studied Mathematics at the Humboldt- University in Berlin. Before coming to Sweden, she was Assistant Professor at the University of Hamburg in Germany. She received her Ph.D. in Mathematics at the Academy of Sciences of the GDR. Since 1991, she has taught Statistics for undergraduate and graduate students. Her research interests have moved from theoretical statistics to computer intensive statistics.
Behrang Mahjani is a postdoctoral fellow with a Ph.D. in Scientific Computing with a focus on Computational Statistics, from Uppsala University, Sweden. He joined the Seaver Autism Center for Research and Treatment at the Icahn School of Medicine at Mount Sinai, New York, in September 2017 and was formerly a postdoctoral fellow at the Karolinska Institutet, Stockholm, Sweden. His research is focused on solving large-scale problems through statistical and computational methods.
"...The book is rich in content, excellent in coverage, highly informative, extremely reader friendly in style, and full of cartoon illustrations. The reader will find this book as a collection of the most important ideas and tools that are used in computer intensive methods for statistical analysis and data analytic investigations...The book can be used by upper undergraduate and graduate students as well as researchers and practitioners in statistics, data science, and users of all disciplines. The good news is that it is available in paperback. - Subir Ghosh, Technometrics, Volume 62
Článek se zabývá simulací napájecího systému pro trolejbusy s využitím statistického modelování pomocí metody Monte Carlo. Ověření modelu bylo provedeno na základě výsledků měření napětí a proudů v ...trolejbusovém systému v městě Gdyni. V článku je prezentován případ studie využití metody Monte Carlo pro analýzu snížení požadavku na energii v trolejbusové dopravě s využitím superkapacitorových stanic nebo změnou konfigurace napájecího systému.
Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the ...theory and applications of Monte Carlo methods. It presents recent methods and algorithms, including the multilevel Monte Carlo method, the statistical Rom
The service life of railway wheels can differ significantly depending on their installed position, operating conditions, re-profiling characteristics, etc. This paper compares the wheels on two ...selected locomotives on the Iron Ore Line in northern Sweden to explore some of these differences. It proposes integrating reliability assessment data with both degradation data and re-profiling performance data. The following conclusions are drawn. First, by considering an exponential degradation path and given operation condition, the Weibull frailty model can be used to undertake reliability studies; second, among re-profiling work orders, rolling contact fatigue (RCF) is the principal reason; and third, by analysing re-profiling parameters, both the wear rate and the re-profiling loss can be monitored and investigated, a finding which could be applied in optimisation of maintenance activities.
Resurs kół pociągu może być znacząco różny w zależności od ich miejsca zamontowania, warunków pracy, charakterystyk związanych z reprofilacją, itp. W artykule, porównano koła dwóch wybranych lokomotyw kursujących na Linii Rud Żelaza w północnej Szwecji, aby zbadać niektóre ze wspomnianych różnic. Zaproponowano możliwość łączenia danych pochodzących z oceny niezawodności z danymi degradacyjnymi oraz danymi z reprofilacji. Przeprowadzone badania pozwalają wyciągnąć następujące wnioski. Po pierwsze, krzywa wykładnicza degradacji oraz zadane warunki pracy można wykorzystać w celu przeprowadzenia badań niezawodności z użyciem modelu Weibulla z efektami losowymi (tzw. "frailty model"); po drugie, główną przyczyną zlecania reprofilacji kół jest zmęczenie toczne (RCF); po trzecie, analiza parametrów reprofilacji pozwala na monitorowanie i badanie zarówno szybkości zużycia kół, jak i ubytku materiału podczas reprofilacji, co może mieć zastosowanie w optymalizacji czynności obsługowych.
PDF
