The problem is coming up with a distribution for the task duration based on historical task durations (prior) as well as streaming live data on actual tasks that are being done. My approach is to fit the historical data to a gamma distribution to get

alpha_0, beta_0 and then as my data comes in (i.e. x_i ) i would then compute the posterior using the equation below. However, how do I get the alpha mentioned here ? Is that a guess where i can just set it to a larger value than my alpha_0 just to capture the concept that initially I have more uncertainty on what is my distribution like?