Abstract <p>Applications of Bayesian methods and Markov chain Monte Carlo (MCMC) methods for statistical inference in complex non-Gaussian models are considered. Key applications are identified, including generalized linear models, survival analysis, hierarchical and space–time models, and current challenges in mechanics and hydrodynamics. Significant Russian research contributions are noted. Particular attention is paid to the integration of these approaches with fuzzy logic in the case of qualitative indeterminacy. Their importance as a computational tool in the absence of analytical solutions and large data sets is emphasized.</p>