Bayes Theorem Examples

The Beginner's Guide to Understanding Bayes Theorem and It's Applications

Author: Logan Styles

Publisher: Createspace Independent Publishing Platform

ISBN: 9781535194594


Page: 100

View: 3460

Discover how to use Bayes' Theorem for real world applications like weather prediction, criminal investigation, blackjack games, and countless others! Picture this... You've been feeling sick for a couple days. You have a job interview on Thursday. Today is Monday, and you want to make sure you're healthy by Thursday...but you can't afford the time or cost of seeing a doctor before then. What are the odds of being up and running by Thursday? Do they get better if you've just started a new health kick? Or do they stay the same? Or perhaps... notice your good ol' dog Spike walking clumsily and think he may be going blind. However you can't take him to a vet immediately...but you still want to know what the odds are that something's wrong with his eyes. So how do you determine this? These questions and countless others can be better answered when you apply Bayes' Theorem. To simplify it, Bayes' Theorem is the method by which you use to determine the probability of an event based on conditions that may be related to an event. So if you want to determine if your dog is sick and you know his breed is a golden retriever...well you could possibly use that information to assess the likely odds of him being sick! In this guide you'll see example after example of Bayes' Theorem being put into practice. You'll also see how each conclusion is arrived at with summation notation and basic equations. BUT...the purpose of this book isn't just to throw equations at you. It's to help you get an intuitive feel for the probability of an outcome without having to plug in all the numbers. I made sure this book wasn't filled with too much jargon or advanced notation. In fact, this book can be used if...1. You're just a lay person interested in learning how to "predict" the chances of events and gain deeper insight to the world around us2. You're a student who needs to learn about Bayes' Theorem quickly and easily3. You're a teacher or educator looking to advance or brush up on your existing knowledge of Bayes' Theorem I encourage you to download 'Bayes Theorem' so you can make more informed approximations of how events will play out. Plus, when you download "Bayes Theorem", you'll also discover: How to solve unobvious questions How to do your own genetic testing (find out if you're more prone to certain types of ailments) Why a smoker and non-smoker may have equal chances of developing chronic bronchitis How companies can use Bayes' Theorem to manipulate and spew propaganda What the chances are of someone becoming addicted to pills How to determine if a suspected criminal is more likely innocent or guilty The proper mathematical equations and notation to use-and guided explanations of each So download 'Bayes Theorem' today and enhance your statistical knowledge on the world and how things work
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Bayes Theorem Examples

Author: Scott Hartshorn

Publisher: Lulu Press, Inc

ISBN: 1329854128

Category: Education

Page: N.A

View: 2897

Bayes theorem describes the probability of an event based on other information that might be relevant. Essentially, you are estimating a probability, but then updating that estimate based on other things that you know. This book is designed to give you an intuitive understanding of how to use Bayes Theorem. It starts with the definition of what Bayes Theorem is, but the focus of the book is on providing examples that you can follow and duplicate. Most of the examples are calculated in Excel, which is useful for updating probability if you have dozens or hundreds of data points to roll in.
Posted in Education

Bayes Theorem Examples

Visual Book for Beginners

Author: Robert Collins

Publisher: Createspace Independent Publishing Platform

ISBN: 9781547270385


Page: 52

View: 4740

This book is a discussion about the Bayes' Theorem. The first part of the book helps you understand what Bayes' Theorem is and the areas in which it can be applied. The derivation of Bayes' Theorem is also discussed, so you will know the various steps it takes for you to derive Bayes' Theorem. Some basic examples are then given to help you understand how you can solve them by use of Bayes' Theorem. These examples have been picked from a wide range of areas, and they are all based on the concept of conditional probability. This is a situation in which you are given the evidence and you are expected to calculate or determine the probability of a certain event occurring, or in other words, if an event A has occurred, what is the probability that event B will occur. The application of Bayes' Theorem in drug and medical tests is then discussed in detail. You will learn how to determine the probability of individuals being users of a certain drug or non-users of that drug. You will also learn how to determine the probability of individuals having certain conditions. The book also discusses the application of Bayes' Theorem when you are rolling dice. You will learn how to apply this Theorem to determine the probability of getting Heads and Tails. The book also helps you in determining if a coin toss is fair or not based on the outcome after it has occurred. Here is a preview of what you'll learn: - What is Bayes Theorem? - Basic Examples - Drug and Medical Tests - Dice and Rolls - Is the Coin Fair?
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Neuronale Netze selbst programmieren

Ein verständlicher Einstieg mit Python

Author: Tariq Rashid

Publisher: O'Reilly

ISBN: 3960101031

Category: Computers

Page: 232

View: 8580

Neuronale Netze sind Schlüsselelemente des Deep Learning und der Künstlichen Intelligenz, die heute zu Erstaunlichem in der Lage sind. Sie sind Grundlage vieler Anwendungen im Alltag wie beispielsweise Spracherkennung, Gesichtserkennung auf Fotos oder die Umwandlung von Sprache in Text. Dennoch verstehen nur wenige, wie neuronale Netze tatsächlich funktionieren. Dieses Buch nimmt Sie mit auf eine unterhaltsame Reise, die mit ganz einfachen Ideen beginnt und Ihnen Schritt für Schritt zeigt, wie neuronale Netze arbeiten: - Zunächst lernen Sie die mathematischen Konzepte kennen, die den neuronalen Netzen zugrunde liegen. Dafür brauchen Sie keine tieferen Mathematikkenntnisse, denn alle mathematischen Ideen werden behutsam und mit vielen Illustrationen und Beispielen erläutert. Eine Kurzeinführung in die Analysis unterstützt Sie dabei. - Dann geht es in die Praxis: Nach einer Einführung in die populäre und leicht zu lernende Programmiersprache Python bauen Sie allmählich Ihr eigenes neuronales Netz mit Python auf. Sie bringen ihm bei, handgeschriebene Zahlen zu erkennen, bis es eine Performance wie ein professionell entwickeltes Netz erreicht. - Im nächsten Schritt tunen Sie die Leistung Ihres neuronalen Netzes so weit, dass es eine Zahlenerkennung von 98 % erreicht – nur mit einfachen Ideen und simplem Code. Sie testen das Netz mit Ihrer eigenen Handschrift und werfen noch einen Blick in das mysteriöse Innere eines neuronalen Netzes. - Zum Schluss lassen Sie das neuronale Netz auf einem Raspberry Pi Zero laufen. Tariq Rashid erklärt diese schwierige Materie außergewöhnlich klar und verständlich, dadurch werden neuronale Netze für jeden Interessierten zugänglich und praktisch nachvollziehbar.
Posted in Computers

Bayes Theorem

An Easy Guide with Visual Examples

Author: Jeffery Short

Publisher: Createspace Independent Publishing Platform

ISBN: 9781976231254


Page: 42

View: 4608

BAYES THEOREM An easy guide with visual examples Do you want to join the class of successful mathematicians who used this book to learn all about Bayes theorem? Then, all you need to do is download this book, the rest will be history. WHAT IS BAYES THEOREM? Bayes theorem describes the likelihood of an event occurring based on any additional information that is related to the event of interest. This theorem is simple, you first estimate the initial probability, and then you modify it using additional factors provided. You will actually enjoy learning more about this incredibly useful theorem. It is widely used in gambling, code breaking, medical field, email spam filters. Etc. WHAT IS IN THE BOOK? First if you have the enthusiasm to understand Bayes theorem then this is the book for you. Even if you are tackling this topic for the first time you will find it very easy to understand it here. This book starts with key definition to make it easier to understand the whole concept. You will then get the brief explanation of simple and conditional probabilities, which are very helpful in understanding the theorem. Then you will have the derivation of the Bayes formula, which is made easy for you to understand everything. Each and every area discussed has a worked-out example, and you can easily related these examples to their corresponding topics. This book is the real deal and you dearly need it to understand all about Bayes theorem once and for all.
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Probability for Risk Management

Author: Matthew J. Hassett,Donald Stewart

Publisher: ACTEX Publications

ISBN: 156698548X

Category: Probabilities

Page: 434

View: 1785

Posted in Probabilities

Wahrscheinlichkeitsrechnung für Dummies

Author: Deborah J. Rumsey

Publisher: John Wiley & Sons

ISBN: 3527805494

Category: Mathematics

Page: 374

View: 6854

Die Wahrscheinlichkeitsrechnung wird in der Schule oft nur beiläufig behandelt, dabei handelt es sich um ein besonders spannendes und alltagstaugliches Teilgebiet der Mathematik. Für alle, die über dieses Thema noch etwas mehr erfahren wollen oder müssen, erklärt Deborah Rumsey verständlich und mit Humor, was sie unbedingt wissen sollten. Egal ob Kontingenztabelle, zentraler Grenzwertsatz, Stichproben-, Binomial- oder Poissonverteilung, in diesem Buch lernen Sie, was es ist und wie Sie es anwenden. Zu jedem Kapitel finden Sie online eine Übungsaufgabe samt Lösung, um das Gelernte zu festigen. Auch Tipps zu praktischen Anwendungen - ob bei der Arbeit oder am Pokertisch - kommen nicht zu kurz. So finden Sie in diesem Buch alles, was Sie über Wahrscheinlichkeitsrechnung unbedingt wissen sollten.
Posted in Mathematics

Strategic Economic Decision-Making

Using Bayesian Belief Networks to Solve Complex Problems

Author: Jeff Grover

Publisher: Springer Science & Business Media

ISBN: 1461460409

Category: Mathematics

Page: 116

View: 2030

Strategic Economic Decision-Making: Using Bayesian Belief Networks to Solve Complex Problems is a quick primer on the topic that introduces readers to the basic complexities and nuances associated with learning Bayes’ theory and inverse probability for the first time. This brief is meant for non-statisticians who are unfamiliar with Bayes’ theorem, walking them through the theoretical phases of set and sample set selection, the axioms of probability, probability theory as it pertains to Bayes’ theorem, and posterior probabilities. All of these concepts are explained as they appear in the methodology of fitting a Bayes’ model, and upon completion of the text readers will be able to mathematically determine posterior probabilities of multiple independent nodes across any system available for study. Very little has been published in the area of discrete Bayes’ theory, and this brief will appeal to non-statisticians conducting research in the fields of engineering, computing, life sciences, and social sciences.
Posted in Mathematics

Bayes Theorem: Bayes Theorem Examples

Bayes Theorem Made Easy for Beginners with Step by Step Guidelines to Solve Any Problem

Author: K. A. Muhith

Publisher: Createspace Independent Publishing Platform

ISBN: 9781540675132


Page: 114

View: 574

Bayes Theorem: Bayes Theorem Examples: A Step by Step Guide For Beginners This book describes Bayes' Theorem in the simplest way possible in layman's language. This book does not contain complex formulas, jargon and hard-to-understand mathematical processes. Some unique examples like US presidential election (Trump vs Hilary!), picnic day, job interview, accident eyewitness reliability, breathalyzer test has been described and solved elaborately in step by step manner in this booklet. After going through this book, you will have a better understanding on what Bayes' Theorem is, when & where you can apply it and how it can help you deduce the most logical conclusions. From Amazon search results to dating, from spam filtering from email to search & rescue, from finding who might win the election to finding a missing plane - Bayes' has been used in real life scenario for many years. Bayes' Theorem is part of syllabus for science and business students. It is one the most basic theorems of statistics. But most teaching techniques of this theorem is too much analytical. Very little intuitive and visual aids is used to demonstrate this theorem in practice. This makes it very hard to grasp the core concept of Bayes' theorem and understand the applicability. This guide addresses this issue and introduces some visual examples and step by step guidelines to solve real life problems. There easy to follow steps will help you apply Bayes' theorem quickly in real life.
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Python Machine Learning By Example

Author: Yuxi (Hayden) Liu

Publisher: Packt Publishing Ltd

ISBN: 178355312X

Category: Computers

Page: 254

View: 4556

Take tiny steps to enter the big world of data science through this interesting guide About This Book Learn the fundamentals of machine learning and build your own intelligent applications Master the art of building your own machine learning systems with this example-based practical guide Work with important classification and regression algorithms and other machine learning techniques Who This Book Is For This book is for anyone interested in entering the data science stream with machine learning. Basic familiarity with Python is assumed. What You Will Learn Exploit the power of Python to handle data extraction, manipulation, and exploration techniques Use Python to visualize data spread across multiple dimensions and extract useful features Dive deep into the world of analytics to predict situations correctly Implement machine learning classification and regression algorithms from scratch in Python Be amazed to see the algorithms in action Evaluate the performance of a machine learning model and optimize it Solve interesting real-world problems using machine learning and Python as the journey unfolds In Detail Data science and machine learning are some of the top buzzwords in the technical world today. A resurging interest in machine learning is due to the same factors that have made data mining and Bayesian analysis more popular than ever. This book is your entry point to machine learning. This book starts with an introduction to machine learning and the Python language and shows you how to complete the setup. Moving ahead, you will learn all the important concepts such as, exploratory data analysis, data preprocessing, feature extraction, data visualization and clustering, classification, regression and model performance evaluation. With the help of various projects included, you will find it intriguing to acquire the mechanics of several important machine learning algorithms – they are no more obscure as they thought. Also, you will be guided step by step to build your own models from scratch. Toward the end, you will gather a broad picture of the machine learning ecosystem and best practices of applying machine learning techniques. Through this book, you will learn to tackle data-driven problems and implement your solutions with the powerful yet simple language, Python. Interesting and easy-to-follow examples, to name some, news topic classification, spam email detection, online ad click-through prediction, stock prices forecast, will keep you glued till you reach your goal. Style and approach This book is an enticing journey that starts from the very basics and gradually picks up pace as the story unfolds. Each concept is first succinctly defined in the larger context of things, followed by a detailed explanation of their application. Every concept is explained with the help of a project that solves a real-world problem, and involves hands-on work—giving you a deep insight into the world of machine learning. With simple yet rich language—Python—you will understand and be able to implement the examples with ease.
Posted in Computers

Die Berechnung der Zukunft

Warum die meisten Prognosen falsch sind und manche trotzdem zutreffen - Der New York Times Bestseller

Author: Nate Silver

Publisher: Heyne Verlag

ISBN: 3641112702

Category: Business & Economics

Page: 656

View: 3439

Zuverlässige Vorhersagen sind doch möglich! Nate Silver ist der heimliche Gewinner der amerikanischen Präsidentschaftswahlen 2012: ein begnadeter Statistiker, als »Prognose-Popstar« und »Wundernerd« weltberühmt geworden. Er hat die Wahlergebnisse aller 50 amerikanischen Bundesstaaten absolut exakt vorausgesagt – doch damit nicht genug: Jetzt zeigt Nate Silver, wie seine Prognosen in Zukunft Terroranschläge, Umweltkatastrophen und Finanzkrisen verhindern sollen. Gelingt ihm die Abschaffung des Zufalls? Warum werden Wettervorhersagen immer besser, während die Terrorattacken vom 11.09.2001 niemand kommen sah? Warum erkennen Ökonomen eine globale Finanzkrise nicht einmal dann, wenn diese bereits begonnen hat? Das Problem ist nicht der Mangel an Informationen, sondern dass wir die verfügbaren Daten nicht richtig deuten. Zuverlässige Prognosen aber würden uns helfen, Zufälle und Ungewissheiten abzuwehren und unser Schicksal selbst zu bestimmen. Nate Silver zeigt, dass und wie das geht. Erstmals wendet er seine Wahrscheinlichkeitsrechnung nicht nur auf Wahlprognosen an, sondern auf die großen Probleme unserer Zeit: die Finanzmärkte, Ratingagenturen, Epidemien, Erdbeben, den Klimawandel, den Terrorismus. In all diesen Fällen gibt es zahlreiche Prognosen von Experten, die er überprüft – und erklärt, warum sie meist falsch sind. Gleichzeitig schildert er, wie es gelingen kann, im Rauschen der Daten die wesentlichen Informationen herauszufiltern. Ein unterhaltsamer und spannender Augenöffner!
Posted in Business & Economics

Risk Assessment and Decision Analysis with Bayesian Networks

Author: Norman Fenton,Martin Neil

Publisher: CRC Press

ISBN: 1439809100

Category: Business & Economics

Page: 524

View: 897

Although many Bayesian Network (BN) applications are now in everyday use, BNs have not yet achieved mainstream penetration. Focusing on practical real-world problem solving and model building, as opposed to algorithms and theory, Risk Assessment and Decision Analysis with Bayesian Networks explains how to incorporate knowledge with data to develop and use (Bayesian) causal models of risk that provide powerful insights and better decision making. Provides all tools necessary to build and run realistic Bayesian network models Supplies extensive example models based on real risk assessment problems in a wide range of application domains provided; for example, finance, safety, systems reliability, law, and more Introduces all necessary mathematics, probability, and statistics as needed The book first establishes the basics of probability, risk, and building and using BN models, then goes into the detailed applications. The underlying BN algorithms appear in appendices rather than the main text since there is no need to understand them to build and use BN models. Keeping the body of the text free of intimidating mathematics, the book provides pragmatic advice about model building to ensure models are built efficiently. A dedicated website,, contains executable versions of all of the models described, exercises and worked solutions for all chapters, PowerPoint slides, numerous other resources, and a free downloadable copy of the AgenaRisk software.
Posted in Business & Economics

Statistics for Business and Financial Economics

Author: Cheng F. Lee,John C. Lee,Alice C. Lee

Publisher: World Scientific

ISBN: 9789810234850

Category: Business & Economics

Page: 1077

View: 9221

This text integrates various statistical techniques with concepts from business, economics and finance, and demonstrates the power of statistical methods in the real world of business. This edition places more emphasis on finance, economics and accounting concepts with updated sample data.
Posted in Business & Economics

Statistik-Workshop für Programmierer

Author: Allen B. Downey

Publisher: O'Reilly Germany

ISBN: 3868993436

Category: Computers

Page: 160

View: 2089

Wenn Sie programmieren können, beherrschen Sie bereits Techniken, um aus Daten Wissen zu extrahieren. Diese kompakte Einführung in die Statistik zeigt Ihnen, wie Sie rechnergestützt, anstatt auf mathematischem Weg Datenanalysen mit Python durchführen können. Praktischer Programmier-Workshop statt grauer Theorie: Das Buch führt Sie anhand eines durchgängigen Fallbeispiels durch eine vollständige Datenanalyse -- von der Datensammlung über die Berechnung statistischer Kennwerte und Identifikation von Mustern bis hin zum Testen statistischer Hypothesen. Gleichzeitig werden Sie mit statistischen Verteilungen, den Regeln der Wahrscheinlichkeitsrechnung, Visualisierungsmöglichkeiten und vielen anderen Arbeitstechniken und Konzepten vertraut gemacht. Statistik-Konzepte zum Ausprobieren: Entwickeln Sie über das Schreiben und Testen von Code ein Verständnis für die Grundlagen von Wahrscheinlichkeitsrechnung und Statistik: Überprüfen Sie das Verhalten statistischer Merkmale durch Zufallsexperimente, zum Beispiel indem Sie Stichproben aus unterschiedlichen Verteilungen ziehen. Nutzen Sie Simulationen, um Konzepte zu verstehen, die auf mathematischem Weg nur schwer zugänglich sind. Lernen Sie etwas über Themen, die in Einführungen üblicherweise nicht vermittelt werden, beispielsweise über die Bayessche Schätzung. Nutzen Sie Python zur Bereinigung und Aufbereitung von Rohdaten aus nahezu beliebigen Quellen. Beantworten Sie mit den Mitteln der Inferenzstatistik Fragestellungen zu realen Daten.
Posted in Computers

Bayes Theorem

The Ultimate Beginner's Guide to Bayes Theorem

Author: Arthur Taff

Publisher: Createspace Independent Publishing Platform

ISBN: 9781984178947


Page: 84

View: 1740

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!
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Author: Rob DeSalle,Jeffrey A. Rosenfeld

Publisher: Garland Science

ISBN: 1135038716

Category: Science

Page: 352

View: 3180

Phylogenomics: A Primer is for advanced undergraduate and graduate biology students studying molecular biology, comparative biology, evolution, genomics, and biodiversity. It explores the origins of organic life on the planet, examines the use of scientific databases to understand the function of proteins within organisms, and provides insight into the interpretation of linear sequence information in the context of organismal change. This book explains the essential concepts underlying the storage and manipulation of genomics level data, construction of phylogenetic trees, population genetics, natural selection, the tree of life, DNA barcoding, and metagenomics. The inclusion of problem-solving exercises in each chapter provides students with a solid grasp of the important molecular and evolutionary questions facing modern biologists as well as the tools needed to answer them. Online exercises are also available to assist students in working with the programs and dabases used to analyze phylogenomic data.
Posted in Science

Der Zahlensinn oder Warum wir rechnen können

Author: Stanislas Dehaene

Publisher: Springer-Verlag

ISBN: 3034878257

Category: Science

Page: 311

View: 6326

Wir sind umgeben von Zahlen. Ob auf Kreditkarten gestanzt oder auf Münzen geprägt, ob auf Schecks gedruckt oder in den Spalten computerisierter Tabellen aufgelistet, überall beherrschen Zahlen unser Leben. Sie sind auch der Kern unserer Technologie. Ohne Zahlen könnten wir weder Raketen starten, die das Sonnensystem erkunden, noch Brücken bauen, Güter austauschen oder Rech nungen bezahlen. In gewissem Sinn sind Zahlen also kulturelle Erfindungen, die sich ihrer Bedeutung nach nur mit der Landwirtschaft oder mit dem Rad vergleichen lassen. Aber sie könnten sogar noch tiefere Wurzeln haben. Tausende von Jahren vor Christus benutzten babylonische Wissenschaftler Zahlzeichen, um erstaun lich genaueastronomische Tabellen zu berechnen. Zehntausende von Jahren zuvor hatten Menschen der Steinzeit die ersten geschriebenen Zahlenreihen geschaffen, indem sie Knochen einkerbten oder Punkte auf Höhlenwände malten. Und, wie ich später überzeugend darzustellen hoffe, schon vor weiteren Millionen von Jahren, lange bevor es Menschen gab, nahmen Tiere aller Arten Zahlen zur Kenntnis und stellten mit ihnen einfache Kopfrechnungen an. Sind Zahlen also fast so alt wie das Leben selbst? Sind sie in der Struktur unseres Gehirns verankert? Besitzen wir einen Zahlensinn, eine spezielle Intuition, die uns hilft, Zahlen und Mathematik mit Sinn zu erfüllen? Ich wurde vor fünfzehn Jahren, während meiner Ausbildung zum Mathema tiker, fasziniert von den abstrakten Objekten, mit denen ich umzugehen lernte, vor allem von den einfachsten von ihnen- den Zahlen.
Posted in Science


Author: A. W. F. Edwards

Publisher: CUP Archive

ISBN: 9780521318716

Category: Mathematics

Page: 235

View: 9919

Dr Edwards' stimulating and provocative book advances the thesis that the appropriate axiomatic basis for inductive inference is not that of probability, with its addition axiom, but rather likelihood - the concept introduced by Fisher as a measure of relative support amongst different hypotheses. Starting from the simplest considerations and assuming no more than a modest acquaintance with probability theory, the author sets out to reconstruct nothing less than a consistent theory of statistical inference in science.
Posted in Mathematics