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DanielLC comments on Frugality and working from finite data - Less Wrong
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Alternative solution: package all the cosmic observations into a big database. Given an astrophysical theory, instantiate it as a specialized compression program, and invoke it on the database. To select between rival theories, measure the sum of encoded file size plus length of compressor; smaller is better.
I think it would be easier to figure out how much data it would take. For example, I can easily work out that the data in something happening 1,001,000 times out of 2,000,000 when that's how often it should happen is 1,999,998.56 bits. Actually making the compression isn't so easy.