A First Course in Probability Models and Statistical Inference


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Why It Matters: Linking Probability to Statistical Inference

This is version 0. This is intended to be a gentle introduction to the practice of analyzing data and answering questions using data the way data scientists, statisticians, data journalists, and other researchers would. We present a map of your upcoming journey in Figure 0. What do we mean by data stories? We mean any analysis involving data that engages the reader in answering questions with careful visuals and thoughtful discussion.

In particular, this book will lean heavily on data visualization. We will explore what makes a good graphic and what the standard ways are used to convey relationships within data. To impart the statistical lessons of this book, we have intentionally minimized the number of mathematical formulas used. We hope this is a more intuitive experience than the way statistics has traditionally been taught in the past and how it is commonly perceived.

Hal Abelson coined the phrase that we will follow throughout this book:. We understand that there may be challenging moments as you learn to program. Both of us continue to struggle and find ourselves often using web searches to find answers and reach out to colleagues for help.

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A First Course in Probability Models and Statistical Inference

In the long run though, we all can solve problems faster and more elegantly via programming. We wrote this book as our way to help you get started and you should know that there is a huge community of R users that are always happy to help everyone along as well. This community exists in particular on the internet on various forums and websites such as stackoverflow. You may think of statistics as just being a bunch of numbers. Statistics in particular, data analysis , in addition to describing numbers like with baseball batting averages, plays a vital role in all of the sciences.

Inside data analysis are many sub-fields that we will discuss throughout this book though not necessarily in this order :. We will begin by digging into the gray Understand portion of the cycle with data visualization, then with a discussion on what is meant by tidy data and data wrangling, and then conclude by talking about interpreting and discussing the results of our models via Communication.

These steps are vital to any statistical analysis. But why should you care about statistics? Scientific knowledge grows through an understanding of statistical significance and data analysis. Another goal of this book is to help readers understand the importance of reproducible analyses.

The hope is to get readers into the habit of making their analyses reproducible from the very beginning. This will take practice and be difficult at times. Copying and pasting results from one program into a word processor is not the way that efficient and effective scientific research is conducted. This is error prone and a frustrating use of time. Reproducibility means a lot of things in terms of different scientific fields. Are experiments conducted in a way that another researcher could follow the steps and get similar results?

To qualify as a probability, the assignment of values must satisfy the requirement that if you look at a collection of mutually exclusive events events with no common results, e. See Complementary event for a more complete treatment. If two events, A and B are independent then the joint probability is. If either event A or event B but never both occurs on a single performance of an experiment, then they are called mutually exclusive events.

Conditional probability is the probability of some event A , given the occurrence of some other event B. It is defined by [32]. In this form it goes back to Laplace and to Cournot ; see Fienberg See Inverse probability and Bayes' rule. In a deterministic universe, based on Newtonian concepts, there would be no probability if all conditions were known Laplace's demon , but there are situations in which sensitivity to initial conditions exceeds our ability to measure them, i.

In the case of a roulette wheel, if the force of the hand and the period of that force are known, the number on which the ball will stop would be a certainty though as a practical matter, this would likely be true only of a roulette wheel that had not been exactly levelled — as Thomas A.

Statistics and Probability | Khan Academy

Bass' Newtonian Casino revealed. This also assumes knowledge of inertia and friction of the wheel, weight, smoothness and roundness of the ball, variations in hand speed during the turning and so forth. A probabilistic description can thus be more useful than Newtonian mechanics for analyzing the pattern of outcomes of repeated rolls of a roulette wheel. Physicists face the same situation in kinetic theory of gases, where the system, while deterministic in principle , is so complex with the number of molecules typically the order of magnitude of the Avogadro constant 6.

Probability theory is required to describe quantum phenomena. The objective wave function evolves deterministically but, according to the Copenhagen interpretation , it deals with probabilities of observing, the outcome being explained by a wave function collapse when an observation is made. However, the loss of determinism for the sake of instrumentalism did not meet with universal approval. Albert Einstein famously remarked in a letter to Max Born : "I am convinced that God does not play dice".

From Wikipedia, the free encyclopedia. For the mathematical field of probability specifically rather than a general discussion, see Probability theory. For other uses, see Probability disambiguation. Not to be confused with Probably. Main article: Probability interpretations. Further information: Likelihood. Main article: History of probability.

Further information: History of statistics. Main article: Probability theory. See also: Probability axioms.

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Main article: Randomness. This section needs expansion. You can help by adding to it. April Mathematics portal Philosophy portal. Main article: Outline of probability. This is an important distinction when the sample space is infinite. For example, for the continuous uniform distribution on the real interval [5, 10], there are an infinite number of possible outcomes, and the probability of any given outcome being observed — for instance, exactly 7 — is 0. This means that when we make an observation, it will almost surely not be exactly 7.

However, it does not mean that exactly 7 is impossible. Ultimately some specific outcome with probability 0 will be observed, and one possibility for that specific outcome is exactly 7. Webster's Revised Unabridged Dictionary.


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The Logic of Statistical Inference. Cambridge University Press. Acta Psychologica. Edward N. Zalta ed. The Stanford Encyclopedia of Philosophy Winter ed. Retrieved 22 April Introduction to Mathematical Statistics 6th ed. Upper Saddle River: Pearson. There is something here for everyone.

All of Statistics

The greatest strength of this book is as a first point of reference for a wide range of statistical methods. Langdon, Journal of Applied Statistics, Vol. Draper, Short Book Reviews, Vol. It is full of theorems and proofs …. Presuming no previous background in statistics … this certainly would be my choice of textbook if I was required to learn mathematical statistics again for a couple of semesters.

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Ziegel, Technometrics, Vol. It introduces many modern topics …. Adequate references are provided at the end of each chapter which the instructor will be able to use profitably …. The worked examples are complemented with numerous theoretical and practical exercises …. Library copies would also see plenty of use. Email Address.


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    A First Course in Probability Models and Statistical Inference A First Course in Probability Models and Statistical Inference
    A First Course in Probability Models and Statistical Inference A First Course in Probability Models and Statistical Inference
    A First Course in Probability Models and Statistical Inference A First Course in Probability Models and Statistical Inference
    A First Course in Probability Models and Statistical Inference A First Course in Probability Models and Statistical Inference
    A First Course in Probability Models and Statistical Inference A First Course in Probability Models and Statistical Inference
    A First Course in Probability Models and Statistical Inference A First Course in Probability Models and Statistical Inference
    A First Course in Probability Models and Statistical Inference A First Course in Probability Models and Statistical Inference
    A First Course in Probability Models and Statistical Inference

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