The effects of climate change on hydro-meteorological events have been causing significant damage to human lives and the built environment. Therefore, it is imperative to analyze the change in the annual maximum rainfall, otherwise, the consequent impacts would continue to lead to several other problems. While conventional methods are available to statistically characterize the rainfall behavior, mostly they assume the data to be stationarity. However, extreme weather events would tend to introduce more non-stationarity in the annual maximum rainfall series. This paper proposes to use a stochastic Bayesian inference parameter estimation technique for modeling the non-stationary of the different duration annual maximum rainfall series. To demonstrate the potential of the proposed modeling approach and compare it with conventional methods, the gridded rainfall data collected for nine coastal cities spread across the Arabian and Bay of Bengal sea stretches of India were used. The main reason for choosing the coastal cities for this study are i) they experience more frequent flooding due to the depressions and currents from the oceans and seas and ii) the growth rate is comparatively faster due to better connectivity to the other places. Consequently, the damages and losses in coastal cities are significant when compared to other cities. It was found from the results that short-duration rainfall (i.e., hourly rainfall) has shown significant non-stationary behavior in most cities. However, for a longer duration of rainfall, the stationary models were found to be a better choice. The model results for the future climate projected data revealed that there is a growing trend in maximum rainfall over time in most cities with an obvious increase in the nonstationary. Further, the rainfall intensity of a 100-year return period for one-hour and one-day annual maximum rainfall under RCP 4.5 showed a maximum rise of 72.3 and 93.3 % respectively. However, under RCP 8.5 for a 100-year return period, a maximum increment of 142.5% was noted for the 1-hour duration but it reduced to 67 % for 1-day annual maximum rainfall. These results further confirm that modeling the non-stationarity for short-duration rainfall is extremely important for effectively monitoring extreme hydrological events.