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I'm a computer science student and is fairly familiar with basic probability (calculating the probability of a event occurring, pmfs and pdfs) but I find it very difficult to grasp the concepts of advanced probability like principles of data reduction (sufficiency, likelihood principle, etc), point and interval estimation, Hypothesis testing, etc. I think it is because I fail to see the intuition behind these concepts.

I tried reading books like Statistical Inference but most of the books don't give examples (may be with some pictures would help a lot) to explain the concepts well (they do give some examples to apply the theorem but not very helpful to understand the concepts). The online lectures I looked into didn't have Advanced Probability theory. :(

My question is what are some best resources online to understand these well or any books that you would recommend i.e. Books/links that has a pictorial representation of the theorems? By pictorial representation I mean something like this for example; easily understandable.

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Take a look at the this book. It begins with basic probability, sets, counting, then it moves on to statistical inference. This document is filled with examples and computer code in R, which you might like.

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I think you meant book by Michael W. Trosset. –  Sunil Mar 2 '12 at 16:35
    
@Sunil, you are right, someone incorrected edited my post. Since you are using Casella, have you tried looking for online notes based on that book? Also, there is a difference between probability and statistics. This book by Casella is more along the lines of statistics, this might help you in your search. –  Edison Mar 2 '12 at 17:33
    
Like I said, all the notes I've seen online doesn't give me a good understanding. The book you recommended is very good and I'm going through it now but I think a lot of it has to do with basic probability and lacks a bit on advanced probability like Sufficiency principle. I was more like looking for a same kind of book but for in-depth analysis of advanced probability. –  Sunil Mar 2 '12 at 19:33
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probability.net is a good online resource for measure-theoretic probability. I hope this helps. :)

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He wants statistics resources not probability. –  Apprentice Queue Mar 1 '12 at 18:50
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