Here are 13 books that An Introduction to Probability Theory and Its Applications, Vol. 1 fans have personally recommended if you like
An Introduction to Probability Theory and Its Applications, Vol. 1.
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When people ask me why I became a statistician, and what its attraction is, I simply tell them that, using statistics, I have been on voyages of discovery and travelled to worlds they didn’t know existed. Using data and statistical methods instead of light and optics, I have seen things others could not imagine. Like an explorer of old, I have joined adventures peeling back the mysteries of the world around us. In my books on statistics, data science, data mining, and artificial intelligence, I have tried to convey some of this excitement, and to show the reader how they too can take part in this wonderful modern adventure.
This is a deep and beautifully elegant overview of the ideas underlying statistical inference. It is the finest concise outline I know of the foundations, dealing with the key concepts and ideas in an accessible way. Written by one of the leading creators of modern statistics, without unnecessary mathematics or superfluous detail it includes a balanced description of the fundamentals of distinct schools of thought, such as Bayesian and frequentist schools. The book did not exist when I started learning statistics, but I am certain I would have understood the discipline’s subtleties much sooner if it had.
In this definitive book, D. R. Cox gives a comprehensive and balanced appraisal of statistical inference. He develops the key concepts, describing and comparing the main ideas and controversies over foundational issues that have been keenly argued for more than two-hundred years. Continuing a sixty-year career of major contributions to statistical thought, no one is better placed to give this much-needed account of the field. An appendix gives a more personal assessment of the merits of different ideas. The content ranges from the traditional to the contemporary. While specific applications are not treated, the book is strongly motivated by applications…
I was trained as a mathematician but have always been motivated by problem-solving challenges. Statistics and analytics combine mathematical models with statistical thinking. My career has always focused on this combination and, as a statistician, you can apply it in a wide range of domains. The advent of big data and machine learning algorithms has opened up new opportunities for applied statisticians. This perspective complements computer science views on how to address data science. The Real Work of Data Science, covers 18 areas (18 chapters) that need to be pushed forward in order to turning data into information, better decisions, and stronger organizations
The text covers classic statistical inference, early computer-age methods, and twenty-century topics. This puts a unique perspective on current analytic technologies labeled machine learning, artificial intelligence, and statical learning. The examples used provide a powerful description of the methods covered and the compare and contrast sections highlight the evolution of analytics. This book by Efron and Hastie is a natural follow-up source for readers interested in more details.
The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and influence. 'Data science' and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? How does it all fit together? Now in paperback and fortified with exercises, this book delivers a concentrated course in modern statistical thinking. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic…
I am a financial data scientist. I think it is important that data scientists are highly specialized if they want to be effective in their careers. I run a business called Conlan Scientific out of Charlotte, NC where me and my team of financial data scientists tackle complicated machine learning problems for our clients. Quant trading is a gladiator’s arena of financial data science. Anyone can try it, but few succeed at it. I am sharing my top five list of math books that are essential to success in this field. I hope you enjoy.
This book might as well be called Introduction to machine learning, and it is probably one of the only books truly deserving of the title. Did you know neural networks have been used for decades to scan checks at the bank? They are called Boltzman Machine. Have you ever heard of how decision trees were used in old-school data mining? You could only get them from proprietary software packages from the early 2000s.
In quant trading, you will constantly face compute power constraints, so it is invaluable to understand the mathematical foundations of the most old-school machine learning methods out there. Researchers 20 years ago used to do a lot of impressive work with a lot less computing power.
This book describes the important ideas in a variety of fields such as medicine, biology, finance, and marketing in a common conceptual framework. While the approach is statistical, the emphasis is on concepts rather than mathematics. Many examples are given, with a liberal use of colour graphics. It is a valuable resource for statisticians and anyone interested in data mining in science or industry. The book's coverage is broad, from supervised learning (prediction) to unsupervised learning. The many topics include neural networks, support vector machines, classification trees and boosting---the first comprehensive treatment of this topic in any book.
When people ask me why I became a statistician, and what its attraction is, I simply tell them that, using statistics, I have been on voyages of discovery and travelled to worlds they didn’t know existed. Using data and statistical methods instead of light and optics, I have seen things others could not imagine. Like an explorer of old, I have joined adventures peeling back the mysteries of the world around us. In my books on statistics, data science, data mining, and artificial intelligence, I have tried to convey some of this excitement, and to show the reader how they too can take part in this wonderful modern adventure.
This is a wonderful book because it says it all. Of course, that’s an exaggeration because no book could possibly encompass the vast breadth of modern statistics, but anyone who read through this multi-volume work would have an enviable knowledge of the discipline. It’s an unsurpassed general source of information about the foundational concepts and tools of statistics, and a reference source I regularly turn to when I need to remind myself of the theory underlying a concept or method.
My primary interest is in brain function. Because the principal job of
the brain is to process information, it is necessary to define exactly
what information is. For that, there is no substitute for Claude
Shannon’s theory of information. This theory is not only quite
remarkable in its own right, but it is essential for telecoms,
computers, machine learning (and understanding brain function).
I have written ten "tutorial introduction" books, on topics which vary
from quantum mechanics to AI.
In a parallel universe, I am still an Associate Professor at the
University of Sheffield, England.
This is a more comprehensive and mathematically rigorous book than Pierce’s book. For the novice, it should be read-only after first reading Pierce’s more informal text. Due to its vintage, the layout is fairly cramped, but the content is impeccable. At almost 500 pages, it covers a huge amount of material. This was my main reference book on information theory for many years, but it now sits alongside more recent texts, like MacKay’s book (see below). It is also published by Dover, so it is reasonably priced.
Written for an engineering audience, this book has a threefold purpose: (1) to present elements of modern probability theory — discrete, continuous, and stochastic; (2) to present elements of information theory with emphasis on its basic roots in probability theory; and (3) to present elements of coding theory. The emphasis throughout the book is on such basic concepts as sets, the probability measure associated with sets, sample space, random variables, information measure, and capacity. These concepts proceed from set theory to probability theory and then to information and coding theories. No formal prerequisites are required other than the usual undergraduate…
As Iago says in Shakespeare’s Othello, “I am nothing if not critical,” and regardless of what he meant, it applies to me - my intelligence works best at scrutinizing things for their significance. I studied science, worked in the financial sector, read fiction, watched cinema, and developed a sense of the interconnectedness of things. If the connections existed, I thought, there could be no one way of approaching anything; all intellectual paths were valid and the only criterion of value was that it must be intelligent. My book tries to stick to this since a writer may hold any opinions, but he or she must show intelligence.
JL Borges is, in my view, the greatest literary mind of the 20th Century.
This is a book of stories, philosophical essays and parables, but even when he is writing fiction, his favoured form is that of the mock critical essay about a non-existent book or writer.
What I especially love about him is his wit, subtle and easily missed since it often takes the shape of philosophical rumination when he is actually debunking something held very highly. My natural mode of expression is irony, and Borges’s irony is inimitable.
The groundbreaking trans-genre work of Argentinian writer Jorge Luis Borges (1899-1986) has been insinuating itself into the structure, stance, and very breath of world literature for well over half a century. Multi-layered, self-referential, elusive, and allusive writing is now frequently labeled Borgesian. Umberto Eco's international bestseller, The Name of the Rose, is, on one level, an elaborate improvisation on Borges' fiction "The Library," which American readers first encountered in the original 1962 New Directions publication of Labyrinths.
This new edition of Labyrinths, the classic representative selection of Borges' writing edited by Donald A. Yates and James E. Irby (in translations…
I’m a Harvard professor of psychology and a cognitive scientist who’s interested in all aspects of language, mind, and human nature. I grew up in Montreal, but have lived most of my adult life in the Boston area, bouncing back and forth between Harvard and MIT except for stints in California as a professor at Stanford and sabbatical visitor in Santa Barbara and now, Berkeley. I alternate between books on language (how it works, what it reveals about human nature, what makes for clear and stylish writing) and books on the human mind and human condition (how the mind works, why violence has declined, how progress can take place).
This is technically a textbook and isn’t marketed as a book you bring to the beach. But sometimes, it’s more satisfying to have the big ideas on a topic patiently explained to you in an orderly fashion than to try to pick them up from stories and arguments.
This paperback, coauthored by one of my graduate school teachers (Hastie), explains the famous discoveries by Amos Tversky and Daniel Kahneman on biases in human reasoning, which Kahneman presented in his bestseller Thinking, Fast and Slow (too obvious for me to include on my list). It also explains lesser-known but still fascinating discoveries and has helpful appendices for those of us who forget some of the basics of probability theory.
In the Second Edition of Rational Choice in an Uncertain World the authors compare the basic principles of rationality with actual behaviour in making decisions. They describe theories and research findings from the field of judgment and decision making in a non-technical manner, using anecdotes as a teaching device. Intended as an introductory textbook for advanced undergraduate and graduate students, the material not only is of scholarly interest but is practical as well.
The Second Edition includes:
- more coverage on the role of emotions, happiness, and general well-being in decisions
My father, when he consented to talk about all the moments in his life when the odds against his survival were so small as to make them statistically non-existent, would say, ‘I was lucky.’ Trying to understand what he meant got me started on this book. As well as being a novelist, I’m a poker player. Luck is a subject that every poker player has a relationship to; more importantly it’s a subject that every person has a relationship to. The combination of family history and intellectual curiosity and the gambler’s desire to win drove me on this quest.
Sadly, Games, Gods, and Gambling by FN David is out of print.This is the next best thing. Lorraine Daston has the supreme gift of making the complicated idea seem straightforward. This is an account of the frenzy for measuring that happened in the 18th century, and how it made the world we live in today, when the gambler’s eye for odds has become the algorithm of taming chance that guides all our decisions.
What did it mean to be reasonable in the Age of Reason? Classical probabilists from Jakob Bernouli through Pierre Simon Laplace intended their theory as an answer to this question--as "nothing more at bottom than good sense reduced to a calculus," in Laplace's words. In terms that can be easily grasped by nonmathematicians, Lorraine Daston demonstrates how this view profoundly shaped the internal development of probability theory and defined its applications.
I am proud to be a human (social) scientist but think that we could collectively achieve a much more successful human science enterprise. And I believe that a better human science would translate into better public policy. Most human scientists focus on their own research, paying little attention to how the broader enterprise functions. I have written many works of a methodological nature over the years. I am pleased to point here to a handful of works with sound advice for enhancing the human science enterprise.
I really liked Williams’ writing style. He is very clear, provides good examples, and is very careful in his argumentation.
I very much liked – and indeed borrowed – his strategy of summarizing the main arguments of each chapter. This is especially important since his book addresses a wide range of challenges in social science. I especially liked his discussion of how the variables we measure are never perfect proxies for the phenomena that we hope to understand.
I also liked his careful discussion of how social scientists need to be more reflective in their work. And I found his discussion of the nature of causation in social science deeply insightful.
Realism and Complexity in Social Science is an argument for a new approach to investigating the social world, that of complex realism. Complex realism brings together a number of strands of thought, in scientific realism, complexity science, probability theory and social research methodology.
It proposes that the reality of the social world is that it is probabilistic, yet there exists enough invariance to make the discovery and explanation of social objects and causal mechanisms possible. This forms the basis for the development of a complex realist foundation for social research, that utilises a number of new and novel approaches to…
I believe that knowledge is power. Understanding how something works leads to practical applications. In markets, I believe you should develop your own ideas on how to invest rather than being told. After all, how can you profit if you’re doing what everyone else is doing? Markets are efficient enough to give an opportunity to everyone but advantage to no one, unless you do something different than the crowd. My list is designed to give you information to develop investment strategies based on chaos theory, complexity, and fractals. It is not designed to tell you how to invest.
While I’ve spent much of my career debunking the Random Walk Theory and the Efficient Market Hypothesis, I believe you need to understand where we’re coming from in order to develop new ideas.
Cootner’s anthology contains all of the important early writings that became Capital Market Theory. You will find Bachilier’s original paper from 1900 postulating using statistics to analyze markets. Mandelbrot’s original paper suggesting that markets are not a random walk is here, too.
It’s an important time capsule of the development of market theory. I’ve read it extensively because you can’t criticize widely held ideas unless you know them yourself.
