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I'm looking for a complete probability reference text, covering the majority of standard probability and stochastic process topics that can be covered without the use of measure theory.

I've already had a basic course in probability and in stochastic processes, so I'm looking for more of a desk reference type of book.

The three that have been recommended to me are

  1. Probability, Statistics, and Random Processes by Papoulis
  2. Probability for Statistics and Machine Learning by DasGupta
  3. Probability By Feller

I'm not too interested in Feller, since it seems that vol 2 has a fair bit of measure theory and vol 1 is only discrete. Any other recommendations?

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  • Ross: Introduction to Probability Models
  • Pitman: Probability

Both these books cover fundamental concepts in basic probability, all without measure theory. Ross covers Markov chains, Poisson processes, queuing theory, Brownian motion, while I think Pitman only mentions Poisson processes. Pitman has some nice prose when explaining Poisson processes/Poisson scatter and other concepts. As noted by V.V's answer, Ross's other book (A First Course in Probability) spends more time on the basics of probability without stochastic processes, so it may be similar to Pitman's book in that regard.

For Markov chains specifically, the first chapter of Norris's "Markov Chains" is a good reference.

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  • $\begingroup$ Why? How? Compared to what? And so on. $\endgroup$ – Did Jul 28 '17 at 8:36
  • $\begingroup$ @Did Sorry... I have added more comments $\endgroup$ – angryavian Jul 28 '17 at 17:37
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A First Course in Probability & Introduction to Probability Models by Sheldon. Ross. The first one is introduction to probability without stochastic processes, while the second one delves into probability models ("Stochastic models") after relatively short brief on basic probability notions, random variables, etc.

In my University, these two books are the standard references for the mandatory three undergraduate level courses in probability and stochastic processes. Absolutely no measure theory is required (or even mentioned in is these books).

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I will answer my own question for public documentation, but leave the discussion open for further recommendations.

I decided to use Probability for Statistics and Machine Learning By Anirban DasGupta as my non-measure theoretic reference text. The deciding factors were:

  1. The advantage of having to carry around only one physical copy, whereas with Ross/Feller there are two volumes
  2. Treats the standard first semester univariate probability material as a quick but self-contained review occupying only ~13% of the text. Great for those of us who are not learning the material for the first time.
  3. Large breadth of topics: Multivariate probability, stochastic processes, asymptotics, large deviations, simulation, statistics, and machine learning
  4. Extensive list of reference material
  5. Author is consistent about pointing out when certain definitions and propositions are poorly expressed due to the absence of measure theory.

Some downsides to the text:

  1. Poor index and glossary. I find myself again and again handwriting additional notes into the index and glossary. For example, the author spends a few pages discussing the Berry-Esseen theorem in great detail and yet omits it from the index.
  2. Some topics are covered too briefly and with little depth to be of much use as a reference (better served as short introductions to the topic), most notably the section on machine learning.
  3. It is in its first edition, and I have been unable to locate a list of errata, if it exists.
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  • $\begingroup$ Another downside: From the Amazon "look inside" feature, it seems Dasgupta's book doesn't have solutions to problems, nor are the solutions available online. $\endgroup$ – Nagdalf Feb 19 at 18:53
  • $\begingroup$ @Nagdalf That is certainly a downside worth pointing out. Although after 18 months I still haven't found a probability textbook (sans measure theory) that I prefer over this one. In fairness, I have littered my copy of DasGupta with thousands of scribbled notes in the margins where explanations were too weak and I had to consult other sources. Overall, from personal experience I still would not recommend anything else. $\endgroup$ – Ollie Feb 20 at 1:25

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