My model contains five parameters. I want to make Bayesian estimation, but the Bayes estimates can not be obtained in closed form. So, I used Metropolis-Hastings to generate MCMC samples from conditional posterior density of each parameter. The trace and Auto-correlation plots were used to evaluate the generated sample. The trace plots for four parameters are random and the Auto-correlation plots are decreasing whereas for the fifth parameter(I will referred as alpha1), the trace plot is not random and the lags in Auto-correlation plot is not decreasing.
Discussion about alpha1
The acceptance rate is 0.99905 (It is too high) and the density plot is multimodal like the following graph
when I change the variance of the proposal density (absolute normal density) from 0.0005 to 0.5 the Acceptance rate becomes 0.1515 and the trace plot is horizontal line and the density function becomes uni-modal
I read MCMC for multimodal posterior and this chapter from this book Evaluating Markov Chain Monte Carlo (MCMC) Algorithms. I am beginner in MCMC, I would be appreciated if one can help me to detect the problem. Is it multi modal or the correlation between parameters are high.