Dear Researchers,
I have a single point for my parameter as a prior information and 26 data points as current data-set.
How can I incorporate that point(/single point prior value) while doing Bayesian Analysis.
(Initially, I use to run a model with non-informative prior without considering the old info as it wasn't valid).
In this particular case, I want to know, Is there any way to include this old evidence (single prior point)? If yes, How can I? Which way should I select and why?
Best Regards,
Abhay
If I understand you correctly, you want to concentrate the density of your prior distribution about that parameter on a single point. In other words, the prior will be a point mass distribution. Then your posterior will also be a point mass distribution and concentrates all density on that point. I highly doubt that is what you really want, since your data will not influence the posterior at all. If you are really confident, put a informative prior on that parameter that will also allow some uncertainty.
You select your prior based on your knowledge and assumptions concerning the process of your data and information (distribution, uncertainty, limits). Does the information from your single data point inform you concerning the data? Is the single data point reliable? Will the single data point unduly affect the posterior? Explain and justify with transparency to allow criticism (especially your own criticism).
This is a good book, might help you:
https://www.amazon.com/Bayesian-Methods-Finance-Svetlozar-Rachev/dp/0471920835
If I understand you correctly, you want to concentrate the density of your prior distribution about that parameter on a single point. In other words, the prior will be a point mass distribution. Then your posterior will also be a point mass distribution and concentrates all density on that point. I highly doubt that is what you really want, since your data will not influence the posterior at all. If you are really confident, put a informative prior on that parameter that will also allow some uncertainty.
Identify the features of your parameters involved and try to grab those informations in the form of informative prior or at least less informative priors...
As what answerd above, and if I really undertood exactaly your question, you can use what we call "conjugate prior" , or as said @ Praveen Kumar : you use a non informative prior (Jefferys' type as exemple)...
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