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Bayesian Analysis of Time Series1889Skickas inom 10-15 vardagar.
Fri frakt inom Sverige för privatpersoner.In many branches of science relevant observations are taken sequentially over time. Bayesian Analysis of Time Series discusses how to use models that explain the probabilistic characteristics of these time series and then utilizes the Bayesian approach to make inferences about their parameters. This is done by taking the prior information and via Bayes theorem implementing Bayesian inferences of estimation, testing hypotheses, and prediction. The methods are demonstrated using both R and WinBUGS. The R package is primarily used to generate observations from a given time series model, while the WinBUGS packages allows one to perform a posterior analysis that provides a way to determine the characteristic of the posterior distribution of the unknown parameters. Features Presents a comprehensive introduction to the Bayesian analysis of time series. Gives many examples over a wide variety of fields including biology, agriculture, business, economics, sociology, and astronomy. Contains numerous exercises at the end of each chapter many of which use R and WinBUGS. Can be used in graduate courses in statistics and biostatistics, but is also appropriate for researchers, practitioners and consulting statisticians. About the author Lyle D. Broemeling, Ph.D., is Director of Broemeling and Associates Inc., and is a consulting biostatistician. He has been involved with academic health science centers for about 20 years and has taught and been a consultant at the University of Texas Medical Branch in Galveston, The University of Texas MD Anderson Cancer Center and the University of Texas School of Public Health. His main interest is in developing Bayesian methods for use in medical and biological problems and in authoring textbooks in statistics. His previous books for Chapman & Hall/CRC include Bayesian Biostatistics and Diagnostic Medicine, and Bayesian Methods for Agreement.
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"...(This book) by Lyle D. Broemeling is an excellent source to learn time series concepts, methods, expressions, and interpretations from the Bayesian viewpoint using R code and WinBugs code...The book is suitable for usage to teach in a graduate-level Bayesian time series course...The references are exhaustive and well selected for the readers. The exercises are challenging." - Ramalingam Shanmugam, JSCS, Aug 2020
Lyle D. Broemeling, Ph.D., is Director of Broemeling and Associates Inc., and is a consulting biostatistician. He has been involved with academic health science centers for about 20 years and has taught and been a consultant at the University of Texas Medical Branch in Galveston, The University of Texas MD Anderson Cancer Center and the University of Texas School of Public Health. His main interest is in developing Bayesian methods for use in medical and biological problems and in authoring textbooks in statistics. His previous books for Chapman & Hall/CRC include Bayesian Biostatistics and Diagnostic Medicine, and Bayesian Methods for Agreement.
Table of Contents 1. Introduction to the Bayesian Analysis of Time Series Introduction Bayesian Analysis Fundamentals of Time Series Analysis Basic Random Models Time Series and Regression Time Series and Stationarity Time Series and Spectral Analysis Dynamic Linear Model The Shift Point Problem Residuals and Diagnostic Tests References 2. Bayesian Analysis Introduction Bayes' Theorem Prior Information The Binomial Distribution The Normal Distribution Posterior Information The Binomial Distribution The Normal Distribution The Poisson Distribution Inference Introduction Estimation Testing Hypotheses Predictive Inference Introduction The Binomial Population Forecasting from a Normal Population Checking Model Assumptions Introduction Forecasting from an Exponential, but Assuming a Normal Population A Poisson Population The Wiener Process Testing the Multinomial Assumption Computing Introduction Monte Carlo Markov Chains Introduction The Metropolis Algorithm Gibbs Sampling The Common Mean of Normal Populations An Example Comments and Conclusions Exercises References 3. Preliminary Considerations for Time Series Time Series Airline Passenger Bookings Sunspot Data Los Angeles Annual Rainfall Graphical Techniques Plot of Air Passenger Bookings Sunspot Data Graph of Los Angeles Rainfall Data Trends, Seasonality, and Trajectories Decomposition Decompose Air Passenger Bookings Average Monthly Temperatures for Debuque, Iowa Graph of Los Angeles Rainfall Data Mean, Variance, Correlation and General Sample Characteristic of a Time Series Other Fundamental Considerations Summary and Conclusions Exercises References 4. Basic Random Models Introduction White Noise A Random Walk Another Example Goodness of Fit Predictive Distributions Comments and Conclusions Exercises References 5. Time Series and Regression Introduction Linear Models Linear Regression with Seasonal Effects and Autoregressive Models Bayesian Inference for a Non-Linear Trend in Time Series Nonlinear Trend with Seasonal Effects Regression with AR(2) Errors Simple Linear Regression Model Nonlinear Regression with Seasonal Effects Comments and Conclusions Exercises References 6. Time Series and Stationarity Moving Average Models Regression Models with Moving Average Errors Regression Model with MA Errors and Seasonal Effects Autoregressive Moving Average Models Another Approach for the Bayesian analysis of MA Processes Second Order Moving Average Process Quadratic Regression With MA(2) Residuals Regression Model With MA(2) Errors and Seasonal Effects Forecasting with Moving Average Processes Another Example Testing Hypotheses Forecasting with a Moving Average Time Series Exercises References 7. Time Series and Spectral Analysis Introduction The Fundamentals Unit of Measurement of Frequency The Spectrum Examples Bayesian Spectral Analysis of Autoregressive Moving Average Series MA(1) Process MA(2) Series The AR(1) Time Series AR(2) ARMA(1,1) Time Series Sunspot Cycle Comments and Conclusions Exercises References 8. Dynamic Linear Models Introduction Discrete Time Linear Dynamic Systems Estimation of the States Filtering Smoothing Prediction The Control problem Example The Kalman Filter The Control Problem Adaptive Estimation An Example of Adaptive Estimation Testing Hypotheses Summary Exercises References 9. The Shift Point Problem in Time Series Introduction A Shifting Normal Sequence Structural Change in an Autoregressive Time Series One Shift in a MA(1) Time Series Changing Models in Econometrics Regression Model with Autocorrelated Errors Another Example of Structural Change Testing Hypotheses Analyzing Threshold Autoregression with the Bayesian Approach A Numerical Example of Threshold Autoregression Comments and Conclusions Exercises References 10. Residuals and Diagnostic Tests Introduction Diagnostic Checks for Autoregressive Models Residuals for Model of Color Data Residuals and Diagnostic Checks for Regression Models with AR(1) Errors Diagnostic T