Cereals play an important role in the human diet in India. However, the yield rate varies across the country. Rajasthan, which is a major contributor of the important cereal crops, i.e., Jowar, Bajara, Maize, Wheat, and Barley. The present paper has been an attempt to analyze the volatility, correlations, and regime shifts of crop yields from time series data from 1970-71 to 2023-24 on yields of Jowar, Bajara, Maize, Wheat, and Barley across the Rajasthan state of India. The Multivariate Analysis, Bayesian Principal Component Analysis (BPCA), Bayesian Multivariate GARCH, and Markov Switching Model (MSM) have been used to analyze and quantify yield correlations, identify shared volatility patterns, time-varying volatilities, and detect regime shifts. The data has been analyzed and production of graphs using the R software, which is a programming language specifically designed for statistical computing and graphics. The process of data collection was constrained by incomplete historical records and inconsistencies in yield reporting, which posed significant challenges for model convergence and the reliability of parameter estimation. Despite these issues, the findings reveal strong positive correlations between Jowar and Bajara, reflecting shared monsoon dependence. BPCA modeled standardized yields as a latent structure, estimating loadings for Jowar with 4 chains, 4000 iterations, and δ (0.95) to address convergence issues. Results also indicate that PC1 captures monsoon-driven volatility for coarse cereals. Bayes-MGARCH analyzed 52 log-returns with a constant-correlation model, outputting values suggesting persistent volatility and positive correlations. Applied to Jowar yields, MSM detected stable and volatile regimes, potentially linked to 1980s policy shifts, with probabilities.