Recommended by Bill Gates

A thought-provoking and wide-ranging exploration of machine learning and the race to build computer intelligences as flexible as our own

In the world's top research labs and universities, the race is on to invent the ultimate learning algorithm: one capable of discovering any knowledge from data, and doing anything we want, before we even ask. In The Master Algorithm, Pedro Domingos lifts the veil to give us a peek inside the learning machines that power Google, Amazon, and your smartphone. He assembles a blueprint for the future universal learner--the Master Algorithm--and discusses what it will mean for business, science, and society. If data-ism is today's philosophy, this book is its bible.

Mathematical Statistics describes the mathematical underpinnings associated with the practice of statistics. The pre-requisite for this book is a calculus-based course in probability. Nearly 200 figures and dozens of Monte Carlo simulation experiments in R help develop the intuition behind the statistical methods. Real-world problems from a wide range of fields help the reader apply the statistical methods. Over 300 exercises are used to reinforce concepts and make this book appropriate for classroom use. The table of contents for this book is:

1. Random Sampling2. Point Estimation3. Interval Estimation4. Hypothesis Testing

30 Practical and applicable guidelines to think smarter, faster, and with expert insight (even if you aren't one).

Mental models are like giving a treasure map to someone lost in the woods. They provide instant understanding, context, and most importantly, a path to the end destination. Now imagine having such a map for all problems and decisions in your life.

Battle information overwhelm, focus on what really matters, and make complex decisions with speed and confidence.

Mental Models: 30 Thinking Tools sheds light on true intelligence: it's not about knowledge and knowing the capitals of all the countries in the world. It's about how you think, and each mental model is a specific framework on how to think smart and with insight. You can approach the world by trying to analyze each piece of information separately, or you can learn mental models that do the work for you.

Learn how billionaires/CEOs, Olympic athletes, and scientists think differently and avoid mistakes.

Peter Hollins has studied psychology and peak human performance for over a dozen years and is a bestselling author. He has worked with a multitude of individuals to unlock their potential and path towards success. His writing draws on his academic, coaching, and research experience.

The person with a hammer only sees nails. Become the person with a hammer, saw, sander, drill, screwdriver, and axe.

-How to balance information and action without sacrificing speed - MM #3 and #5.
-Understanding what data is really telling you - MM #8 and #10.
-Charles Darwin's secret to clear and honest thinking - MM #11.

Mental models for all walks of life: productivity, professional success, greater happiness, critical thinking, and decision-making.

-Understanding correlation, causation, root causation, and proximate causation - MM #15 and #16.
-Implementing anti-goals to find real priorities and focus - MM #19 and #23.
-Being able to predict the future with basic probabilistic thinking - MM #10 and #25.
-How to strategically allocate your time and resources for biggest impact - MM #27 and #30.

Fun guide to learning Bayesian statistics and probability through unusual and illustrative examples.

Probability and statistics are increasingly important in a huge range of professions. But many people use data in ways they don't even understand, meaning they aren't getting the most from it. Bayesian Statistics the Fun Way will change that.

This book will give you a complete understanding of Bayesian statistics through simple explanations and un-boring examples. Find out the probability of UFOs landing in your garden, how likely Han Solo is to survive a flight through an asteroid shower, how to win an argument about conspiracy theories, and whether a burglary really was a burglary, to name a few examples.

By using these off-the-beaten-track examples, the author actually makes learning statistics fun. And you'll learn real skills, like how to:

- How to measure your own level of uncertainty in a conclusion or belief
- Calculate Bayes theorem and understand what it's useful for
- Find the posterior, likelihood, and prior to check the accuracy of your conclusions
- Calculate distributions to see the range of your data
- Compare hypotheses and draw reliable conclusions from them

Next time you find yourself with a sheaf of survey results and no idea what to do with them, turn to Bayesian Statistics the Fun Way to get the most value from your data.

If you know how to program, you're ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical formulas, using discrete probability distributions rather than continuous mathematics. Once you get the math out of the way, the Bayesian fundamentals will become clearer and you'll begin to apply these techniques to real-world problems.

Bayesian statistical methods are becoming more common and more important, but there aren't many resources available to help beginners. Based on undergraduate classes taught by author Allen B. Downey, this book's computational approach helps you get a solid start.

• Use your programming skills to learn and understand Bayesian statistics
• Work with problems involving estimation, prediction, decision analysis, evidence, and Bayesian hypothesis testing
• Get started with simple examples, using coins, dice, and a bowl of cookies
• Learn computational methods for solving real-world problems

Bayesian analysis is today understood to be an extremely powerful method of statistical analysis, as well an approach to statistics that is particularly transparent and intuitive. It is thus being extensively and increasingly utilized in virtually every area of science and society that involves analysis of data.A widespread misconception is that Bayesian analysis is a more subjective theory of statistical inference than what is now called classical statistics. This is true neither historically nor in practice. Indeed, objective Bayesian analysis dominated the statistical landscape from roughly 1780 to 1930, long before 'classical' statistics or subjective Bayesian analysis were developed. It has been a subject of intense interest to a multitude of statisticians, mathematicians, philosophers, and scientists. The book, while primarily focusing on the latest and most prominent objective Bayesian methodology, does present much of this fascinating history.The book is written for four different audiences. First, it provides an introduction to objective Bayesian inference for non-statisticians; no previous exposure to Bayesian analysis is needed. Second, the book provides an overview of the development and current state of objective Bayesian analysis and its relationship to other statistical approaches, for those with interest in the philosophy of learning from data. Third, the book presents a careful development of the particular objective Bayesian approach that we recommend, the reference prior approach. Finally, the book presents as much practical objective Bayesian methodology as possible for statisticians and scientists primarily interested in practical applications.

This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well.
Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probability theory and stochastic processes, the author introduces and defines the problems of filtering, prediction, and smoothing. He presents the mathematical solutions to nonlinear filtering problems, and he specializes the nonlinear theory to linear problems. The final chapters deal with applications, addressing the development of approximate nonlinear filters, and presenting a critical analysis of their performance.

We live in the era of big data. However, small data sets are still common for ethical, financial, or practical reasons. Small sample sizes can cause researchers to seek out the most powerful methods to analyse their data, but they may also be wary that some methodologies and assumptions may not be appropriate when samples are small. The book offers advice on the statistical analysis of small data sets for various designs and levels of measurement, helping researchers to analyse such data sets, but also to evaluate and interpret others' analyses.

The book discusses the potential challenges associated with a small sample, as well as the ways in which these challenges can be mitigated. General topics with strong relevance to small sample sizes such as meta-analysis, sequential and adaptive designs, and multiple testing are introduced. While the focus is on hypothesis tests and confidence intervals, Bayesian analyses are also covered. Code written in the statistical software R is presented to carry out the proposed methods, many of which are not limited to use on small data sets, and the book also discusses approaches to computing the power or the necessary sample size, respectively.

What does a medical test tell us about the chances of having a particular disease? How can we tell if a spoken phrase is, 'four candles' or 'fork handles'? How do we a perceive a three-dimensional world from from the two-dimensional images on our retinas? The short answer is Bayes' rule, which transforms meaningless statistics and raw data into useful information. Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, intuitive visual representations of real-world examples are used to show how Bayes' rule is actually a form of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to gain an intuitive understanding of Bayesian analysis. As an aid to understanding, online computer code (in MatLab, Python and R) reproduces key numerical results and diagrams.

The Perfect Book for Beginners Wanting to Visually Learn About Bayes Theorem Through Real Examples

What if you could quickly and easily learn Bayesian data analysis without complex textbooks and statistics classes?

Imagine being able to apply your newly learned theory to real life situations

Multi-time best selling IT & mathematics author, Arthur Taff, presents the perfect guide for any beginner. Bayesian data analysis can be difficult to learn, especially through textbooks and statistic classes at school. This book aims to solve that issue by presenting the theories in an easy-to-understand and visually intuitive way. This book contains a number of visual examples to build a basic understanding of Bayesian data analysis and then works to teach at a deeper level without the complexities you'd see in other similar books. Additionally, every example in this book has been solved using Excel.

In this book, you will get:

• A Basic Introduction to Bayes Theorem (with examples) - The initial introduction demonstrates how Bayesian data analysis works when you have a single new piece of data to update initial probabilities.
• Adding New Data & Updating Probabilities - Takes the above example and looks at what happens if we have multiple pieces of data instead of a single piece.
• Bayes Theorem Terminology - The formal names for the different parts of the Bayes Theorem equation, and how it all comes together for an easier overall understanding.
• How to Deal With Data Errors - In a real life situation, it is unlikely that your data will be error-free. This section shows you how to deal with those errors and still get accurate probability estimates.
• Arthur's personal email address for unlimited customer support if you have any questions
• And much, much more...

If you are a person that learns by example, especially visually, then this book is perfect for you It is a very important topic in a wide range of industries - so dive in to get a deep understanding

Well, what are you waiting for? Grab your copy today by clicking the BUY NOW button at the top of this page

Learn the fundamentals of Bayesian modeling using state-of-the-art Python libraries, such as PyMC, ArviZ, Bambi, and more, guided by an experienced Bayesian modeler who contributes to these libraries

Key Features

- Conduct Bayesian data analysis with step-by-step guidance

- Gain insight into a modern, practical, and computational approach to Bayesian statistical modeling

- Enhance your learning with best practices through sample problems and practice exercises

- Purchase of the print or Kindle book includes a free PDF eBook.

Book Description

The third edition of Bayesian Analysis with Python serves as an introduction to the main concepts of applied Bayesian modeling using PyMC, a state-of-the-art probabilistic programming library, and other libraries that support and facilitate modeling like ArviZ, for exploratory analysis of Bayesian models; Bambi, for flexible and easy hierarchical linear modeling; PreliZ, for prior elicitation; PyMC-BART, for flexible non-parametric regression; and Kulprit, for variable selection.

In this updated edition, a brief and conceptual introduction to probability theory enhances your learning journey by introducing new topics like Bayesian additive regression trees (BART), featuring updated examples. Refined explanations, informed by feedback and experience from previous editions, underscore the book's emphasis on Bayesian statistics. You will explore various models, including hierarchical models, generalized linear models for regression and classification, mixture models, Gaussian processes, and BART, using synthetic and real datasets.

By the end of this book, you will possess a functional understanding of probabilistic modeling, enabling you to design and implement Bayesian models for your data science challenges. You'll be well-prepared to delve into more advanced material or specialized statistical modeling if the need arises.

What you will learn

- Build probabilistic models using PyMC and Bambi

- Analyze and interpret probabilistic models with ArviZ

- Acquire the skills to sanity-check models and modify them if necessary

- Build better models with prior and posterior predictive checks

- Learn the advantages and caveats of hierarchical models

- Compare models and choose between alternative ones

- Interpret results and apply your knowledge to real-world problems

- Explore common models from a unified probabilistic perspective

- Apply the Bayesian framework's flexibility for probabilistic thinking

Who this book is for

If you are a student, data scientist, researcher, or developer looking to get started with Bayesian data analysis and probabilistic programming, this book is for you. The book is introductory, so no previous statistical knowledge is required, although some experience in using Python and scientific libraries like NumPy is expected.

Table of Contents

- Thinking Probabilistically

- Programming Probabilistically

- Hierarchical Models

- Modeling with Lines

- Comparing Models

- Modeling with Bambi

- Mixture Models

- Gaussian Processes

- Bayesian Additive Regression Trees

- Inference Engines

- Where to Go Next

Are you ready to unlock the mathematical secrets that power today's most advanced artificial intelligence systems? Essential Math for AI is an essential guide for anyone looking to understand the complex mathematical underpinnings of AI. Whether you're an AI enthusiast, a student, or a professional in the field, this book is tailored to enrich your knowledge and prepare you for the future of AI innovation.

Here's what you'll discover inside:

• Linear Algebra: Dive into the core of machine learning with in-depth explorations of vectors, matrices, and data transformations.
• Probability and Statistics: Learn how to make sense of data and uncertainty, which is crucial for developing robust AI applications.
• Calculus: Optimize AI models using the power of derivatives, integrals, and multivariable optimization.
• Graph Theory: Model complex relationships and understand the algorithms that can navigate these structures in AI.
• Discrete Mathematics: Tackle combinatorial problems and optimize algorithmic efficiency, a cornerstone of AI development.
• Numerical Methods: Solve equations and approximate functions, enhancing the computational power of AI.
• Optimization Techniques: From gradient descent to swarm intelligence, master the methods that enhance AI performance.
• Game Theory: Analyze strategic decision-making and its profound implications in AI.
• Information Theory: Quantify and encode data, ensuring efficiency and integrity in AI systems.
• Topology and Geometry: Uncover hidden structures in data, paving the way for breakthroughs in AI research.

Essential Math for AI provides a comprehensive overview of the mathematical concepts propelling AI forward and offers a glimpse into the future of how these disciplines will continue to shape the AI landscape. With chapter summaries to consolidate your learning and a clear path charted for future exploration, this book is your roadmap to becoming well-versed in the mathematics of AI.

Take the next step in your AI journey. Embrace the mathematical challenges and opportunities with Essential Math for AI.

We live in the era of big data. However, small data sets are still common for ethical, financial, or practical reasons. Small sample sizes can cause researchers to seek out the most powerful methods to analyse their data, but they may also be wary that some methodologies and assumptions may not be appropriate when samples are small. The book offers advice on the statistical analysis of small data sets for various designs and levels of measurement, helping researchers to analyse such data sets, but also to evaluate and interpret others' analyses.

The book discusses the potential challenges associated with a small sample, as well as the ways in which these challenges can be mitigated. General topics with strong relevance to small sample sizes such as meta-analysis, sequential and adaptive designs, and multiple testing are introduced. While the focus is on hypothesis tests and confidence intervals, Bayesian analyses are also covered. Code written in the statistical software R is presented to carry out the proposed methods, many of which are not limited to use on small data sets, and the book also discusses approaches to computing the power or the necessary sample size, respectively.

Bayesian statistics is currently undergoing something of a renaissance. At its heart is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. It is an approach that is ideally suited to making initial assessments based on incomplete or imperfect information; as that information is gathered and disseminated, the Bayesian approach corrects or replaces the assumptions and alters its decision-making accordingly to generate a new set of probabilities. As new data/evidence becomes available the probability for a particular hypothesis can therefore be steadily refined and revised. It is very well-suited to the scientific method in general and is widely used across the social, biological, medical, and physical sciences. Key to this book's novel and informal perspective is its unique pedagogy, a question and answer approach that utilizes accessible language, humor, plentiful illustrations, and frequent reference to on-line resources.

Bayesian Statistics for Beginners is an introductory textbook suitable for senior undergraduate and graduate students, professional researchers, and practitioners seeking to improve their understanding of the Bayesian statistical techniques they routinely use for data analysis in the life and medical sciences, psychology, public health, business, and other fields.

A crisis is coming for everyone who uses math and science. For decades now, the classical model of probability (the indifference principle and the Gaussian distribution) has been breaking down and revealing its limitations in fields from economics to epidemiology. Now a new approach has revealed the underlying non-classical principle behind all these 'anomalous' laws:

- Pareto's law of elite incomes
- Zipf's law of word frequencies
- Lotka's law of scientific publications
- Kleiber's law of metabolic rates
- the Clausewitz-Dupuy law of combat friction
- Moore's law of computing costs
- the Wright-Henderson cost law
- Weibull's law of electronics failures
- the Flynn Effect in IQ scores
- Benford's law of digit frequencies
- Farr's law of epidemics
- Hubbell's neutral theory of biodiversity
- Rogers' law of innovation classes
- Wilson's law of island biogeography
- Smeed's law of traffic fatalities

The general law behind all these particular laws (and countless others) is the decline effect. As a system ages or grows in size, the rules of probability subtly change. Entropy increases, rare items become rarer, and average performance measures decline. The human meaning of a decline may be positive (decreasing costs, falling epidemic mortality) or negative (lower customer loyalty, decreasing efficiency), but the mathematical pattern is always the same. The implications are enormous, as these examples show:

All epidemic diseases decline in infectiousness and in lethality. HIV-AIDS went from a highly infectious, 95-percent fatal disease, to a survivable condition with a latency of decades. COVID-19 went from a death rate of 7 percent in early 2020, to under 2 percent in 2022.

Hereditary dynasties around the world declined smoothly in lifespan, from hundreds of years to tens of years. When democracies replaced monarchies, the decline (in spans of party control) continued.

Bayesian Analysis of Probability Distributions by Kawsar Fatima is an essential reference guide for statisticians, data analysts, and researchers. The book provides a comprehensive overview of Bayesian analysis methods for probability distributions, including advanced modeling techniques and the latest developments in computational algorithms. It covers a range of topics, from basic concepts and principles of Bayesian inference to advanced Bayesian hierarchical modeling and model selection.

The book provides numerous examples and case studies to illustrate the use of Bayesian analysis in practical applications. It covers a wide range of probability distributions, including univariate, multivariate, continuous, and discrete distributions. The author also discusses the use of Bayesian analysis in fields such as finance, engineering, medicine, and social sciences.

Overall, Bayesian Analysis of Probability Distributions is an excellent resource for anyone looking to learn or expand their knowledge of Bayesian analysis. With its comprehensive coverage of probability distributions and advanced modeling techniques, this book is an indispensable tool for researchers and practitioners in many fields.

A crisis is coming for everyone who uses math and science. For decades now, the classical model of probability (the indifference principle and the Gaussian distribution) has been breaking down and revealing its limitations in fields from economics to epidemiology. Now a new approach has revealed the underlying non-classical principle behind all these 'anomalous' laws:

- Pareto's law of elite incomes
- Zipf's law of word frequencies
- Lotka's law of scientific publications
- Kleiber's law of metabolic rates
- the Clausewitz-Dupuy law of combat friction
- Moore's law of computing costs
- the Wright-Henderson cost law
- Weibull's law of electronics failures
- the Flynn Effect in IQ scores
- Benford's law of digit frequencies
- Farr's law of epidemics
- Hubbell's neutral theory of biodiversity
- Rogers' law of innovation classes
- Wilson's law of island biogeography
- Smeed's law of traffic fatalities

The general law behind all these particular laws (and countless others) is the decline effect. As a system ages or grows in size, the rules of probability subtly change. Entropy increases, rare items become rarer, and average performance measures decline. The human meaning of a decline may be positive (decreasing costs, falling epidemic mortality) or negative (lower customer loyalty, decreasing efficiency), but the mathematical pattern is always the same. The implications are enormous, as these examples show:

All epidemic diseases decline in infectiousness and in lethality. HIV-AIDS went from a highly infectious, 95-percent fatal disease, to a survivable condition with a latency of decades. COVID-19 went from a death rate of 7 percent in early 2020, to under 2 percent in 2022.

Hereditary dynasties around the world declined smoothly in lifespan, from hundreds of years to tens of years. When democracies replaced monarchies, the decline (in spans of party control) continued.

Handbook of Price Impact Modeling provides practitioners and students with a mathematical framework grounded in academic references to apply price impact models to quantitative trading and portfolio management. Automated trading is now the dominant form of trading across all frequencies. Furthermore, trading algorithm rise introduces new questions professionals must answer, for instance:

• How do stock prices react to a trading strategy?
• How to scale a portfolio considering its trading costs and liquidity risk?
• How to measure and improve trading algorithms while avoiding biases?

Price impact models answer these novel questions at the forefront of quantitative finance. Hence, practitioners and students can use this Handbook as a comprehensive, modern view of systematic trading.

For financial institutions, the Handbook's framework aims to minimize the firm's price impact, measure market liquidity risk, and provide a unified, succinct view of the firm's trading activity to the C-suite via analytics and tactical research.

The Handbook's focus on applications and everyday skillsets makes it an ideal textbook for a master's in finance class and students joining quantitative trading desks. Using price impact models, the reader learns how to:

• Build a market simulator to back test trading algorithms
• Implement closed-form strategies that optimize trading signals
• Measure liquidity risk and stress test portfolios for fire sales
• Analyze algorithm performance controlling for common trading biases
• Estimate price impact models using public trading tape

Finally, the reader finds a primer on the database kdb+ and its programming language q, which are standard tools for analyzing high-frequency trading data at banks and hedge funds.

Authored by a finance professional, this book is a valuable resource for quantitative researchers and traders.

In response to unanswered difficulties in the generalized case of conditional expectation and to treat the topic in a well-deservedly thorough manner, M.M. Rao gave us the highly successful first edition of Conditional Measures and Applications. Until this groundbreaking work, conditional probability was relegated to scattered journal articles and mere chapters in larger works on probability. This second edition continues to offer a thorough treatment of conditioning while adding substantial new information on developments and applications that have emerged over the past decade. Conditional Measures and Applications, Second Edition clearly elucidates the subject, from fundamental principles to abstract analysis. The author illustrates the computational difficulties in evaluating conditional probabilities in nondiscrete cases with numerous examples, demonstrates applications to Markov processes, martingales, potential theory, and Reynolds operators as well as sufficiency in statistics, and clarifies ideas in modern noncommutative probability structures through conditioning in general structures, including parts of operator algebras and free random variables. He also discusses existence and construction problems from the Bishop-Brouwer constructive analysis point of view. With open problems in every chapter and links to other areas of mathematics, this invaluable second edition offers complete coverage of conditional probability and expectation and their structural analysis, from simple to advanced abstract levels, for both novices and seasoned mathematicians.

Applied sciences, both physical and social, such as atmospheric, biological, climate, demographic, economic, ecological, environmental, oceanic and political, routinely gather large volumes of spatial and spatio-temporal data in order to make wide ranging inference and prediction. Ideally such inferential tasks should be approached through modelling, which aids in estimation of uncertainties in all conclusions drawn from such data. Unified Bayesian modelling, implemented through user friendly software packages, provides a crucial key to unlocking the full power of these methods for solving challenging practical problems.

Key features of the book:

- Accessible detailed discussion of a majority of all aspects of Bayesian methods and computations with worked examples, numerical illustrations and exercises

- A spatial statistics jargon buster chapter that enables the reader to build up a vocabulary without getting clouded in modeling and technicalities

- Computation and modeling illustrations are provided with the help of the dedicated R package bmstdr, allowing the reader to use well-known packages and platforms, such as rstan, INLA, spBayes, spTimer, spTDyn, CARBayes, CARBayesST, etc

- Included are R code notes detailing the algorithms used to produce all the tables and figures, with data and code available via an online supplement

- Two dedicated chapters discuss practical examples of spatio-temporal modeling of point referenced and areal unit data

- Throughout, the emphasis has been on validating models by splitting data into test and training sets following on the philosophy of machine learning and data science

This book is designed to make spatio-temporal modeling and analysis accessible and understandable to a wide audience of students and researchers, from mathematicians and statisticians to practitioners in the applied sciences. It presents most of the modeling with the help of R commands written in a purposefully developed R package to facilitate spatio-temporal modeling. It does not compromise on rigour, as it presents the underlying theories of Bayesian inference and computation in standalone chapters, which would be appeal those interested in the theoretical details. By avoiding hard core mathematics and calculus, this book aims to be a bridge that removes the statistical knowledge gap from among the applied scientists.