Articles by "Bayesian Method"

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Jianye Ching ... 188 pages - Language: ‎English - Publisher: CRC Press; (August, 2024).

Bayesian data analysis and modelling linked with machine learning offers a new tool for handling geotechnical data. This book presents recent advancements made by the author in the area of probabilistic geotechnical site characterization.

Two types of correlation play central roles in geotechnical site characterization: cross-correlation among soil properties and spatial-correlation in the underground space. The book starts with the introduction of Bayesian notion of probability “degree of belief”, showing that well-known probability axioms can be obtained by Boolean logic and the definition of plausibility function without the use of the notion “relative frequency”. It then reviews probability theories and useful probability models for cross-correlation and spatial correlation. Methods for Bayesian parameter estimation and prediction are also presented, and the use of these methods demonstrated with geotechnical site characterization examples.

Bayesian Machine Learning in Geotechnical Site Characterization suits consulting engineers and graduate students in the area.

David Kaplan ... 250 pages - Language: English - Publisher: ‎The Guilford Press; 2nd edition (November, 2023) - ISBN-10:‎ 1462553540 - ISBN-13: ‎978-1462553549.


The second edition of this practical book equips social science researchers to apply the latest Bayesian methodologies to their data analysis problems. It includes new chapters on model uncertainty, Bayesian variable selection and sparsity, and Bayesian workflow for statistical modeling. Clearly explaining frequentist and epistemic probability and prior distributions, the second edition emphasizes use of the open-source RStan software package. The text covers Hamiltonian Monte Carlo, Bayesian linear regression and generalized linear models, model evaluation and comparison, multilevel modeling, models for continuous and categorical latent variables, missing data, and more. Concepts are fully illustrated with worked-through examples from large-scale educational and social science databases, such as the Program for International Student Assessment and the Early Childhood Longitudinal Study. Annotated RStan code appears in screened boxes; the companion website (www.guilford.com/kaplan-materials) provides data sets and code for the book's examples.

New to This Edition: • Utilizes the R interface to Stan—faster and more stable than previously available Bayesian software—for most of the applications discussed. • Coverage of Hamiltonian MC; Cromwell’s rule; Jeffreys' prior; the LKJ prior for correlation matrices; model evaluation and model comparison, with a critique of the Bayesian information criterion; variational Bayes as an alternative to Markov chain Monte Carlo (MCMC) sampling; and other new topics. • Chapters on Bayesian variable selection and sparsity, model uncertainty and model averaging, and Bayesian workflow for statistical modeling.

Cameron Davidson-Pilon  ... 256 pages - Publisher: ‎Addison-Wesley Professional; (October, 2015) - Language: English -  ISBN-10: 0133902838 - ISBN-13: 978-0133902839.

Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention.

Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples and intuitive explanations that have been refined after extensive user feedback. You’ll learn how to use the Markov Chain Monte Carlo algorithm, choose appropriate sample sizes and priors, work with loss functions, and apply Bayesian inference in domains ranging from finance to marketing. Once you’ve mastered these techniques, you’ll constantly turn to this guide for the working PyMC code you need to jumpstart future projects.

Coverage includes: • Learning the Bayesian “state of mind” and its practical implications • Understanding how computers perform Bayesian inference • Using the PyMC Python library to program Bayesian analyses • Building and debugging models with PyMC • Testing your model’s “goodness of fit” • Opening the “black box” of the Markov Chain Monte Carlo algorithm to see how and why it works • Leveraging the power of the “Law of Large Numbers” • Mastering key concepts, such as clustering, convergence, autocorrelation, and thinning • Using loss functions to measure an estimate’s weaknesses based on your goals and desired outcomes • Selecting appropriate priors and understanding how their influence changes with dataset size • Overcoming the “exploration versus exploitation” dilemma: deciding when “pretty good” is good enough • Using Bayesian inference to improve A/B testing • Solving data science problems when only small amounts of data are available.

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