Some statistical inferences of parameter in MCMC approach and the application in uncertainty analysis of hydrological simulation

•Parameter σ2 in MCMC approach is interpreted and estimated through statistical inference and theoretical analysis.•A new label called Confidence Level of Model (CLM) is developed to guide the estimation of parameter σ2.•The natural logarithm of posterior probability distribution for NSCE is a first-order linear equation associated with CLM.•The MCMC method based on CLM performs well in generating posterior distributions and confidence intervals.