There's a lot of work done in statistics, while state-of-art in lossless data compression is apparently this: http://mattmahoney.net/dc/dce.html#Section_4
Please suggest good methods/models applicable for data compression.
To be specific:
1) How to estimate the probability of the next bit in a bit string?
2) How to integrate predictions of different models?
you should include a better description of what data you want to compress...
Why, I'm talking about universal compression obviously. For data with known structure its really not a mathematical problem, so there's no sense to discuss it here. In other words, the first question is: given a string of bits, what do we do to determine the probability of the next bit, as precisely as possible?
otherwise we will have 10 different answers trying to summarize different part of the huge theory of compression
I'd written quite a few statistical compressors, and I'm not interested in that. I'm asking how a statistician would approach this task, detect correlations in given data, and compute a probability estimation for the next bit.
In addition, the two point you give to be more specific are not detailed enough to be understood.
What's not detailed in there? I'm even talking about bits, not some vague "symbols". I'd note though, that I'm talking about "probability of a bit" because computing a probability of bit==0 or bit==1 is a matter of convenience.
Also, I'm obviously not talking about some "random data compression", or methods with infinite complexity, like "Kolmogorov compression". Again, I want to know how a good statistician would approach this problem, given a string of bits.
Here's an example, if you need one: hxxp://encode.ru/threads/482-Bit-guessing-game