in Bayesian inference we can model prior knowledge using prior distribution. There is a lot of information available on how to construct flat or weakly informative priors, but I cannot find good examples of how to construct a prior from historical data.
How, would I, for example, deal with the following situations:
1) A manager has to decide on whether to stop or pursuit the redesign of a website. A pilot study is inconclusive about the expected revenue. But, the manager has had five projects in the past, with a recorded revenue increase of factor 1.1, 1.2, 1.1, 1.3, 1. How can one add the managers optimism as a prior to the data from the pilot study.
2) An experiment (N = 20) is conducted where response time is measured in two conditions, A and B. The same experiment has been done in dozens of studies before, and all studies have reported their sample size, the average response time and standard deviation of A and B. Again: How to put that into priors?
I would be very thankful for any pointers to accessible material on the issue.
--Martin
I believe that the paper
@article(KarBodGuyKraNedRug:14,
title = {Fully Probabilistic Knowledge Expression and Incorporation},
author = {M. K{\'{a}}rn{\'{y}} and A. Bodini and T.V. Guy and J. Krac{\'{\i}}k and P. Nedoma and F. Ruggeri},
journal = {Statistics and Its Interface},
volume = 7,
number = 4,
year = {2014},
pages = {503--515})
could be good starting point to solution of your problem.
Best regards Miroslav Karny
Here's our paper on this topic:
https://www.researchgate.net/publication/282136270_A_joint_Bayesian_forecasting_model_of_judgment_and_observed_data?ev=prf_pub
Feel free to ask if you have any questions about how to apply the methodology proposed in the paper to your practical tasks.
Technical Report A joint Bayesian forecasting model of judgment and observed data
Straight foreward: use the old data and some reasonable "flat" prior and calculate the posterior for that data. This will be the prior for your new data.
Applying a flat prior to the old set of data and using the posterior as a prior to the new set of data is totally the same as applying the flat prior to the whole set of data. Both methods will result in the same posterior.
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