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Due to climate change and resulting natural disasters, there has been a growing interest in measuring the value of social goods to our society, like environmental conservation. Traditionally, the stated preference, such as contingent valuation, captures an economics-perspective on the value of environmental goods through the willingness to pay (WTP) paradigm. Where the economics theory to estimate the WTP using machine learning is the random utility model. However, the estimation of WTP depends on rather simple preference assumptions based on a linear functional form. These models are therefore unable to capture the complex uncertainty in the human decision-making process. Further, contingent valuation only uses the mean or median estimation of WTP. Yet it has been recognized that other quantiles of the WTP would be valuable to ensure the provision of social goods. In this work, we propose to leverage the Bayesian Deep Learning (BDL) models to capture the uncertainty in stated preference estimation. We focus on the probability of paying for an environmental good and the conditional distribution of WTP. The Bayesian deep learning model connects with the economics theory of the random utility model through the stochastic component on the individual preferences. For testing our proposed model, we work with both synthetic and real-world data. The results on synthetic data suggest the BDL can capture the uncertainty consistently with different distribution of WTP. For the real-world data, a forest conservation contingent valuation survey, we observed a high variability in the distribution of the WTP, suggesting high uncertainty in the individual preferences for social goods. Our research can be used to inform environmental policy, including the preservation of natural resources and other social good.