方法对比

	Hamiltonian Monte Carlo with Measurement Error	带测量误差的变分推断
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	2006-2011	2000s–2010s
提出者	Neal (2011) for HMC; Carroll et al. (2006) for measurement error framework	Building on Blei et al. (2017) for VI and Carroll et al. (2006) for measurement error frameworks
类型	Bayesian sampling algorithm for latent-variable models	Approximate Bayesian inference
开创性文献	Carroll, R. J., Ruppert, D., Stefanski, L. A., & Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Models: A Modern Perspective (2nd ed.). Chapman and Hall/CRC. ISBN: 978-1584886334	Blei, D. M., Kucukelbir, A., & McAuliffe, J. D. (2017). Variational inference: A review for statisticians. Journal of the American Statistical Association, 112(518), 859–877.
别名	HMC measurement error model, Bayesian errors-in-variables with HMC, HMC latent variable measurement error, Hamiltonian MCMC with covariate error	VI with measurement error, variational Bayes measurement error model, VBEM with errors-in-variables, approximate Bayesian inference under measurement error
相关	6	4
摘要	Hamiltonian Monte Carlo (HMC) with measurement error is a Bayesian computational strategy for fitting models where one or more covariates are observed with noise. HMC samples jointly from the posterior over model parameters and the unobserved true covariate values, using gradient-based proposals that explore the high-dimensional posterior efficiently and avoid the slow random-walk behaviour of standard Metropolis sampling.	Variational inference with measurement error is a scalable Bayesian approach that simultaneously estimates model parameters and latent true covariates when observed variables are contaminated by noise. Rather than sampling the posterior via MCMC, it finds the closest tractable distribution to the true posterior by maximising the evidence lower bound (ELBO), making it applicable to large datasets where full MCMC is too costly.