Here are 100 books that Probability fans have personally recommended if you like
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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.
While studying computer networks, Claude Shannon did something pretty impressive. He reformulated the majority of classical statistics from scratch using the language and concepts of computer science.
Statistical noise? There’s a new word for that; it’s called entropy. Also, it turns out it is a good thing, not a bad thing because entropy is equal to the information content or a data set. Tired of minimizing the squared error of everything? That’s fine, minimize the log of its likelihood instead. It does the same thing. This book challenges the assumptions of classical statistics in a way that fits neatly in the mind of a computer scientist. As a quant trader, this book will help you understand and measure the information content of data, which is critical to your success.
Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.
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.
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.
One of my favorite professors, Gretchen Martinet, used this to teach a course called “Mathematical Statistics” when I was at the University of Virginia. It is an extremely profound course full of dense but fundamental mathematical proofs in classical statistics.
You will learn why the formula for the normal distribution is the way it is, why the sum of squares appears everywhere in statistics, and how to fit a linear regression by hand. In the same way calculus elevates our understanding of rates of changes, the book elevates your understanding of samples, averages, and distributions. Quant trading requires an intuitive sense of how data, models, and aggregates work, making this content essential for your success.
Modern Mathematical Statistics with Applications, Second Edition strikes a balance between mathematical foundations and statistical practice. In keeping with the recommendation that every math student should study statistics and probability with an emphasis on data analysis, accomplished authors Jay Devore and Kenneth Berk make statistical concepts and methods clear and relevant through careful explanations and a broad range of applications involving real data.
The main focus of the book is on presenting and illustrating methods of inferential statistics that are useful in research. It begins with a chapter on descriptive statistics that immediately exposes the reader to real data. The…
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 is one of my favorite underappreciated statistics books of all time. Non-parametric statistics can be otherwise described as statistics without assumptions. The entire goal of this field of study is to prove X is greater than Y without making any assumptions about the underlying distributions of X or Y. The methods are different, and they require more data than other methods, but the learning journey is invaluable.
I personally believe that modern machine learning is simply the modeling section of the school of non-parametric statistics. Working through this book will give you a much deeper understanding of why tools like decision trees are so valuable. It will also to teach you to design rigorous numerical experiments on data sets that are beyond the help of classical statistics.
Guided by problems that frequently arise in actual practice, James Higgins' book presents a wide array of nonparametric methods of data analysis that researchers will find useful. It discusses a variety of nonparametric methods and, wherever possible, stresses the connection between methods. For instance, rank tests are introduced as special cases of permutation tests applied to ranks. The author provides coverage of topics not often found in nonparametric textbooks, including procedures for multivariate data, multiple regression, multi-factor analysis of variance, survival data, and curve smoothing. This truly modern approach teaches non-majors how to analyze and interpret data with nonparametric procedures…
Wealth Odyssey is a summary work based on a 12-hour adult education course I taught for 10 years. It’s important to me to educate people through my 29 years in the profession (1994-2023), my focus has always been on helping people first understand that retirement means you’re wealthy enough not to work anymore – working is optional. You don’t need to be rich. Wealth is scalable for any income level and comes from foundation income and investments to supplement that foundation to support your desired lifestyle’s Standard of Individual Living (SOIL) for as long as you live. Your focus should be on your plan and apply a few concepts grounded in well researched evidence.
When people think of financial planning, their first thought is investing. Their second thought is retirement.
Kaplans explain risk succinctly: “Everything is possible, yet only one thing happens.” People understand risk but don’t really understand how to apply it rationally to investing (market risks) or to retirement (longevity risk).
But first, having an understanding of what risk is and isn’t, and where it comes from is important before you can apply it to what fuels your plans – markets and longevity.
This book helped me formulate the basic planning concepts I use in my book since personal finance is all about taking risks – as are any other decisions and actions you take in life.
A compelling journey through history, mathematics, and philosophy, charting humanity’s struggle against randomness
Our lives are played out in the arena of chance. However little we recognize it in our day-to-day existence, we are always riding the odds, seeking out certainty but settling—reluctantly—for likelihood, building our beliefs on the shadowy props of probability. Chances Are is the story of man’s millennia-long search for the tools to manage the recurrent but unpredictable—to help us prevent, or at least mitigate, the seemingly random blows of disaster, disease, and injustice. In these pages, we meet the brilliant individuals who developed the first abstract…
I started my career in neuroscience. I wanted to understand brains. That is still proving difficult, and somewhere along the way, I realized my real motivation was to build things, and I wound up working in AI. I love the elegance of mathematical models of the world. Even the simplest machine learning model has complex implications, and exploring them is a joy.
My knees tremble and my heart quakes when I think of how much work must have gone into these two companion volumes. Collectively, they are more than four times the length of my book, covering the whole of machine learning.
It is an essential encyclopedic resource that should be on the desk of anyone serious about machine learning.
A detailed and up-to-date introduction to machine learning, presented through the unifying lens of probabilistic modeling and Bayesian decision theory.
This book offers a detailed and up-to-date introduction to machine learning (including deep learning) through the unifying lens of probabilistic modeling and Bayesian decision theory. The book covers mathematical background (including linear algebra and optimization), basic supervised learning (including linear and logistic regression and deep neural networks), as well as more advanced topics (including transfer learning and unsupervised learning). End-of-chapter exercises allow students to apply what they have learned, and an appendix covers notation.
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…
I’ve wanted to be a philosopher since I read Plato’s Phaedo when I was 17, a new immigrant in Canada. Since then, I’ve been fascinated with time, space, and quantum mechanics and involved in the great debates about their mysteries. I saw probability coming into play more and more in curious roles both in the sciences and in practical life. These five books led me on an exciting journey into the history of probability, the meaning of risk, and the use of probability to assess the possibility of harm. I was gripped, entertained, illuminated, and often amazed at what I was discovering.
I found a copy of this book in the sixties. That copy, much loved, was lost in moves and mayhem. Now, I only have a Dover reprint (water-logged during yet another move), but I have never been without and would search high and low if I were.
This is also a history of probability but with a very different focus. Ms. David was a statistician able to explain the calculations intuitively (good to assign to my students). But she was also thoroughly interested in the personalities involved. What was Galileo like? What happened to Pascal at Port-Royal?
I felt personally drawn into the historical narrative that often reads like a novel.
The development of gambling techniques led to the beginning of modern statistics, and this absorbing history illustrates the science's rise with vignettes from the lives of Galileo, Fermat, Pascal, and others. Fascinating allusions to the classics, archaeology, biography, poetry, and fiction endow this volume with universal appeal. 1962 edition.
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’ve wanted to be a philosopher since I read Plato’s Phaedo when I was 17, a new immigrant in Canada. Since then, I’ve been fascinated with time, space, and quantum mechanics and involved in the great debates about their mysteries. I saw probability coming into play more and more in curious roles both in the sciences and in practical life. These five books led me on an exciting journey into the history of probability, the meaning of risk, and the use of probability to assess the possibility of harm. I was gripped, entertained, illuminated, and often amazed at what I was discovering.
One day, in conversation with Ian Hacking, he announced a new passion: Archaeology of ideas. The concept we now have of probability was new, he said; it was born in the 17th century and was different from anything before!
I love this book because it is, first of all, a philosopher’s take on history. Hacking confronts the conceptual puzzles that defeated some of the best mathematical minds, raises controversial questions about what it all meant, and gives us a new vision of the history of concepts.
Historical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. Ian Hacking presents a philosophical critique of early ideas about probability, induction, and statistical inference and the growth of this new family of ideas in the fifteenth, sixteenth, and seventeenth centuries. Hacking invokes a wide intellectual framework involving the growth of science, economics, and the theology of the period. He argues that the transformations that made it possible for probability concepts to emerge have constrained all subsequent development of probability theory and…
