SKU/Artículo: AMZ-B0G1XZPH52
Modern Bayesian Computation: Theorems, Proofs, and Python Implementations (Computational Mathematics Library)
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Paperback
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En stock
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0.95 kg
0.95 kg
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Nuevo
Nuevo
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Amazon
Amazon
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USA
USA
Sobre este producto
- From measure-theoretic Bayes to state-of-the-art samplers and variational methods, this rigorous text unifies theory and practice in modern posterior computation. Build the machinery of posterior integration with Radon-Nikodym derivatives and disintegration, then develop Markov chains with invariant measures, detailed balance, and ergodicity. Explore Metropolis-Hastings with Peskun ordering and optimal scaling, Gibbs with blocking and collapsing, Langevin methods, and Hamiltonian Monte Carlo with symplectic integrators, shadow Hamiltonians, and NUTS. Go deeper with Riemannian manifolds and constrained reparameterizations, adaptive MCMC with diminishing adaptation and containment, pseudo-marginal and noisy MCMC, importance sampling and population Monte Carlo. Sequential Monte Carlo is treated via the Feynman-Kac formalism, resampling theory, particle filtering and smoothing, particle MCMC, and annealed SMC for static targets. Variational inference covers the ELBO, coordinate ascent in conjugate models, stochastic gradients with reparameterization and control variates, expressive families with normalizing flows, natural gradients, and Riemannian geometry. Evidence estimation is developed through bridge sampling, path sampling, thermodynamic integration, and annealed importance sampling.Designed for graduate students and researchers in statistics, machine learning, econometrics, and the computational sciences, every chapter states precise assumptions and proves core results on stationarity, spectral gap, conductance, drift-minorization, central limit theorems, and complexity scaling, with connections to coupling and regenerative simulation for error quantification. Each chapter has proofs and end of chapter python demonstrations that implement MH, Gibbs, MALA, HMC, NUTS, Riemannian HMC, SMC samplers, particle filters, PMMH and Particle Gibbs, black-box and amortized VI with flows, and evidence estimators, complete with reproducible diagnostics for ESS, split R-hat, and energy-based checks.
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AR$330.933
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AR$169.713
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