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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?

Equation from Wiki on Conjugate Priors

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$\alpha_0$ and $\beta_0$ in the table are in the "Prior hyperparameters" column. Those are the parameters of your prior. You can choose the parameters after consulting the problem with domain experts, or choose them based on your prior knowledge, or intuition about the problem. Basically, given what you know about the problem, you need to choose the parameters in such a way that the prior Gamma distribution is a good a priori representation of the distribution of the parameter.

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  • $\begingroup$ Thanks Tim. How about the alpha parameter ? I know it says this is known shape alpha but in the context of this problem, how would i get this alpha parameter ? $\endgroup$
    – SriK
    Commented Sep 29, 2021 at 15:12
  • $\begingroup$ @SriK in case of this model $\alpha$ is just known, not assumed or guessed, but known. If you don’t know it, you can’t use such model. $\endgroup$
    – Tim
    Commented Sep 29, 2021 at 15:40
  • $\begingroup$ I guess that is the problem then. Im not sure which conjugate prior to use then. What is the practical way that alpha is known? I have raw data that describes my prior and data streaming in that will help compute the posterior. Is alpha basically an informed guess at what the streaming data would look like? $\endgroup$
    – SriK
    Commented Sep 29, 2021 at 21:05
  • $\begingroup$ @SriK if something is a guess, it’s a prior. For this formula $\alpha$ is known. Conjugate priors have many limitations like this to use them with real data, that is why for real problems you nearly always use MCMC or some other kind of approximate inference. $\endgroup$
    – Tim
    Commented Sep 29, 2021 at 21:22

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