পদ্ধতির তুলনা করুন

	মেট্রোপলিস-হেস্টিংস উইথ মেজারমেন্ট এরর	পরিমাপ ত্রুটিসহ হ্যামিলটোনিয়ান মন্টে কার্লো
ক্ষেত্র	বেইসীয়	বেইসীয়
পরিবার	Bayesian methods	Bayesian methods
উদ্ভবের বছর	1953 (base algorithm); 1990s (measurement-error application)	2006-2011
প্রবর্তক	Metropolis et al. (1953); measurement-error extension developed in the 1990s Bayesian literature	Neal (2011) for HMC; Carroll et al. (2006) for measurement error framework
ধরন	MCMC sampling algorithm	Bayesian sampling algorithm for latent-variable models
মৌলিক উৎস	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	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
অপর নাম	MH with measurement error, Metropolis-Hastings errors-in-variables, MCMC errors-in-variables, Bayesian errors-in-variables MCMC	HMC measurement error model, Bayesian errors-in-variables with HMC, HMC latent variable measurement error, Hamiltonian MCMC with covariate error
সম্পর্কিত	4	6
সারসংক্ষেপ	Metropolis-Hastings with measurement error is a Bayesian MCMC approach that jointly estimates model parameters and the true (unobserved) covariate values when predictors or outcomes are recorded with noise. By treating the latent true values as unknown parameters, it propagates measurement uncertainty fully into posterior inference rather than ignoring it or correcting for it post hoc.	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.