Bayesian Deep Learning & Estimating Uncertainty

I am using weather data (publicly available under CC0 license), measured over a period of 10 years, from 2006 to 2016. For simplicity, I will be using only the Temperature and Humidity values and our goal would be to find how humidity varies as a function of temperature and build a model that not only predicts the behaviour but also gives us model (& data) uncertainty information. As we can see, measurements are taken every hour over a period of 10 years, resulting in over 95,000 data points. For further simplification, we re-sample the dataframe to decrease the frequency of the input data, and instead of a 1-hour interval, I chose 3 days interval, resulting in 1340 data points. We see that humidity (relative) varies between 0.4 to 1 and temperature varies between -10 to 30 degrees (Celsius) and seems like there's an inverse linear relationship.