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 Apr 3 comment How to learn Integral Transform? With some effort, I bought an used hard copy of Operational Mathematics from Amazon. I will read it. Mar 24 comment Is conditional probability also probability? Last night I had a good sleep. And this answer rings a bell to me this morning. So I am marking it as the answer. Hope it can last. Feb 22 comment How to learn Integral Transform? Thanks for your reply. I am very interested in the book Operational Mathematics. But in my country it is not easy to get a copy of this book. Do you know where I can get a PDF version? Feb 20 comment What does “Mathematics of Computation” mean? Thanks, I just try to summarize your examples into some kind of formal definition. Feb 20 comment What does “Mathematics of Computation” mean? So, computation is about the meaning/purpose/rational of some operation. mathematics is about the relation among operations. And mathematics of computation is about techniques to carry out such operations. Am I right? (I deliberately use the word operation 3 times here.) Mar 13 comment How to learn Integral Transform? Could you tell me the name of the book by K.Worf from Springer? Thanks. Mar 13 comment How to learn Integral Transform? @Karl You can star my question as your favorite. And you are welcome. ;) Feb 25 comment How could we know the Dirichlet allocation is describing the topic rather than something else? I don't have much reputation points. I will wait another day before I start a bounty. Feb 23 comment Conjugate priors make calculations easier but at what cost to the model? Thanks, it's more formal now. Feb 6 comment Is there any software package to calculate the entropy, information content, mutual information, etc? That looks awesome. Could you re-post your 2 comments as an answer so I can mark it? Feb 6 comment Is there any software package to calculate the entropy, information content, mutual information, etc? Thanks. If you change your comment to an answer, I will mark it. BTW, is there any Python option? Feb 4 comment What does the -log[P(X)] mean in the calculation of entropy? It does reveal something. Thanks. Actually, since the entropy/self-information is used to quantify/measure the uncertainty of a random variable, I did think about selecting a mathematical function according to a set of preferred properties. These properties are based on some common sense about the relation between uncertainty and information gain. It seems Shannon also took this approach. Feb 4 comment What does the -log[P(X)] mean in the calculation of entropy? From the perspective of probability, the entropy is just an expectation of -log[P(i)], so -log[P(i)] must have some solid meaning. So what is it? Feb 4 comment What does the -log[P(X)] mean in the calculation of entropy? It's an interesting/intuitive explanation when you mention "the surprise in n tosses is n×(surprise in one toss)" Feb 2 comment Is conditional probability also probability? Much appreciate your supplement. I will take some time to digest them. (BTW, is there any free download of Renyi's thesis?) Feb 2 comment Is conditional probability also probability? I haven't read Renyi's article yet. But indeed, I did considered that conditional probability should be more general. And probability is inherently a relative concept. Since it is human nature to consider things in a relative way. When we estimate the probability of something, we are actually (implicitly) compare the possibility of that thing to the possibility of something we are certain about. It is through such comparison that we get some feeling/estimation about the degree of possibility/belief. Feb 2 comment Is conditional probability also probability? When a deadend is encountered, we should look back to see if the start point is incorrect/too limited. This seems to be a promising answer. I will read that article when back home. Thanks! Feb 1 comment Is conditional probability also probability? Thanks. This is indeed an vivid/reasonable example. It could be seen as we changed to a new universe when considering the condition. But how could we use the value from the old universe in the new universe? Feb 1 comment Is conditional probability also probability? Yes, my doubt is about the quotient being of the same type as the divisor and divided. I can think ratio as the ultimate/subconscious origin of probability, but in some context, the ratio is not calculatable, such as the degree-of-belief scenario. But we just generalize our theory for all scenarios. Jan 31 comment Is conditional probability also probability? I just take a brief look at the Ch.9 of that book. It seems I need to read it from the start to comprehend it. It could take a while. Could you summarize a bit about the point?