Linganisha mbinu

	Uchambuzi Imara wa Bayesian	Uchanganuzi wa Mfumo wa Markov wa Monte Carlo (MCMC)
Nyanja	Mbinu za Bayes	Uigaji
Familia	Bayesian methods	Process / pipeline
Mwaka wa asili	1984–1990	1953 (Metropolis-Hastings); 1984 (Gibbs)
Mwanzilishi	James O. Berger	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)
Aina	Bayesian sensitivity / robustness framework	Simulation-based Bayesian inference / numerical integration
Chanzo asilia	Berger, J. O. (1990). Robust Bayesian analysis: sensitivity to the prior. Journal of Statistical Planning and Inference, 25(3), 303–328.	Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. & Rubin, D.B. (2013). Bayesian Data Analysis (3rd ed.). Chapman & Hall/CRC.
Majina mbadala	Bayesian sensitivity analysis, prior robustness, epsilon-contamination Bayesian analysis, robust Bayes	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)
Zinazohusiana	6	5
Muhtasari	Robust Bayesian inference extends standard Bayesian analysis by replacing a single prior distribution with a class of plausible priors and examining how much the posterior conclusions change across that class. Instead of committing to one prior, the analyst bounds the posterior quantity of interest, revealing whether findings are stable or critically dependent on prior assumptions.	Markov Chain Monte Carlo (MCMC) is a family of simulation algorithms that constructs a Markov chain whose stationary distribution is the target posterior, enabling Bayesian inference and high-dimensional integral computation that would otherwise be analytically intractable. Pioneered by Metropolis and colleagues in 1953 and extended by Hastings in 1970, MCMC underpins modern Bayesian statistics. The two most widely used variants are Metropolis-Hastings, which proposes moves from a general proposal distribution, and Gibbs sampling, which draws each parameter in turn from its full conditional distribution.