{"product_id":"understanding-computational-bayesian-statistics-9780470046098","title":"Understanding Computational Bayesian Statistics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA hands-on introduction to computational statistics   from a Bayesian point of view  Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective,  Understanding Computational Bayesian Statistics  successfully guides readers through this new, cutting-edge approach.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Understanding computational Bayesian statistics is an excellent book for courses on computational statistics at the advanced undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who use computer programs to conduct statistical analyses of data and solve problems in their everyday work.\" (Mathematical Reviews, 2011)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction to Bayesian Statistics I\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 The Frequentist Approach to Statistics 1\u003c\/p\u003e \u003cp\u003e1.2 The Bayesian Approach to Statistics 3\u003c\/p\u003e \u003cp\u003e1.3 Comparing Likelihood and Bayesian Approaches to Statistics 6\u003c\/p\u003e \u003cp\u003e1.4 Computational Bayesian Statistics 19\u003c\/p\u003e \u003cp\u003e1.5 Purpose and Organization of This Book 20\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Monte Carlo Sampling from the Posterior 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Acceptance-Rejection-Sampling 27\u003c\/p\u003e \u003cp\u003e2.2 Sampling-Importance-Resampling 33\u003c\/p\u003e \u003cp\u003e2.3 Adaptive-Rejection-Sampling from a Log-Concave Distribution 35\u003c\/p\u003e \u003cp\u003e2.4 Why Direct Methods Are Inefficient for High-Dimension Parameter Space 42\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Bayesian Inference 47\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Bayesian Inference from the Numerical Posterior 47\u003c\/p\u003e \u003cp\u003e3.2 Bayesian Inference from Posterior Random Sample 54\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Bayesian Statistics Using Conjugate Priors 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 One-Dimensional Exponential Family of Densities 61\u003c\/p\u003e \u003cp\u003e4.2 Distributions for Count Data 62\u003c\/p\u003e \u003cp\u003e4.3 Distributions for Waiting Times 69\u003c\/p\u003e \u003cp\u003e4.4 Normally Distributed Observations with Known Variance 75\u003c\/p\u003e \u003cp\u003e4.5 Normally Distributed Observations with Known Mean 78\u003c\/p\u003e \u003cp\u003e4.6 Normally Distributed Observations with Unknown Mean and Variance 80\u003c\/p\u003e \u003cp\u003e4.7 Multivariate Normal Observations with Known Covariance Matrix 85\u003c\/p\u003e \u003cp\u003e4.8 Observations from Normal Linear Regression Model 87\u003c\/p\u003e \u003cp\u003eAppendix: Proof of Poisson Process Theorem 97\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Markov Chains 101\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Stochastic Processes 102\u003c\/p\u003e \u003cp\u003e5.2 Markov Chains 103\u003c\/p\u003e \u003cp\u003e5.3 Time-Invariant Markov Chains with Finite State Space 104\u003c\/p\u003e \u003cp\u003e5.4 Classification of States of a Markov Chain 109\u003c\/p\u003e \u003cp\u003e5.5 Sampling from a Markov Chain 114\u003c\/p\u003e \u003cp\u003e5.6 Time-Reversible Markov Chains and Detailed Balance 117\u003c\/p\u003e \u003cp\u003e5.7 Markov Chains with Continuous State Space 120\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Markov Chain Monte Carlo Sampling from Posterior 127\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Metropolis-Hastings Algorithm for a Single Parameter 130\u003c\/p\u003e \u003cp\u003e6.2 Metropolis-Hastings Algorithm for Multiple Parameters 137\u003c\/p\u003e \u003cp\u003e6.3 Blockwise Metropolis-Hastings Algorithm 144\u003c\/p\u003e \u003cp\u003e6.4 Gibbs Sampling 149\u003c\/p\u003e \u003cp\u003e6.5 Summary 150\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Statistical Inference from a Markov Chain Monte Carlo Sample 159\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Mixing Properties of the Chain 160\u003c\/p\u003e \u003cp\u003e7.2 Finding a Heavy-Tailed Matched Curvature Candidate Density 162\u003c\/p\u003e \u003cp\u003e7.3 Obtaining An Approximate Random Sample For Inference 168\u003c\/p\u003e \u003cp\u003eAppendix: Procedure for Finding the Matched\u003c\/p\u003e \u003cp\u003eCurvature Candidate Density for a Multivariate Parameter 176\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Logistic Regression 179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Logistic Regression Model 180\u003c\/p\u003e \u003cp\u003e8.2 Computational Bayesian Approach to the Logistic Regression Model 184\u003c\/p\u003e \u003cp\u003e8.3 Modelling with the Multiple Logistic Regression Model 192\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Poisson Regression and Proportional Hazards Model 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Poisson Regression Model 204\u003c\/p\u003e \u003cp\u003e9.2 Computational Approach to Poisson Regression Model 207\u003c\/p\u003e \u003cp\u003e9.3 The Proportional Hazards Model 214\u003c\/p\u003e \u003cp\u003e9.4 Computational Bayesian Approach to Proportional Hazards Model 218\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Gibbs Sampling and Hierarchical Models 235\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Gibbs Sampling Procedure 236\u003c\/p\u003e \u003cp\u003e10.2 The Gibbs Sampler for the Normal Distribution 237\u003c\/p\u003e \u003cp\u003e10.3 Hierarchical Models and Gibbs Sampling 242\u003c\/p\u003e \u003cp\u003e10.4 Modelling Related Populations with Hierarchical Models 244\u003c\/p\u003e \u003cp\u003eAppendix: Proof That Improper Jeffrey's Prior Distribution for the Hypervariance Can Lead to an\u003cbr\u003eImproper Postenor 261\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Going Forward with Markov Chain Monte Carlo 265\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA Using the Included Minitab Macros 271\u003c\/p\u003e \u003cp\u003eB Using the Included R Functions 289\u003c\/p\u003e \u003cp\u003eReferences 307\u003c\/p\u003e \u003cp\u003eTopic Index 313\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":53515413619031,"sku":"9780470046098","price":115.16,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/understanding-computational-bayesian-statistics-9780470046098","provider":"Book Curl","version":"1.0","type":"link"}