History of probability and statistics | Bayesian inference | Probability books
An Essay towards solving a Problem in the Doctrine of Chances is a work on the mathematical theory of probability by Thomas Bayes, published in 1763, two years after its author's death, and containing multiple amendments and additions due to his friend Richard Price. The title comes from the contemporary use of the phrase "doctrine of chances" to mean the theory of probability, which had been introduced via the title of a book by Abraham de Moivre. Contemporary reprints of the Essay carry a more specific and significant title: A Method of Calculating the Exact Probability of All Conclusions founded on Induction. The essay includes theorems of conditional probability which form the basis of what is now called Bayes's Theorem, together with a detailed treatment of the problem of setting a prior probability. Bayes supposed a sequence of independent experiments, each having as its outcome either success or failure, the probability of success being some number p between 0 and 1. But then he supposed p to be an uncertain quantity, whose probability of being in any interval between 0 and 1 is the length of the interval. In modern terms, p would be considered a random variable uniformly distributed between 0 and 1. Conditionally on the value of p, the trials resulting in success or failure are independent, but unconditionally (or "marginally") they are not. That is because if a large number of successes are observed, then p is more likely to be large, so that success on the next trial is more probable. The question Bayes addressed was: what is the conditional probability distribution of p, given the numbers of successes and failures so far observed. The answer is that its probability density function is (and ƒ(p) = 0 for p < 0 or p > 1) where k is the number of successes so far observed, and n is the number of trials so far observed. This is what today is called the Beta distribution with parameters k + 1 and n − k + 1. (Wikipedia).
Calculus: Optimization Problems
In this video, I discuss optimization problems. I give an outline for how to approach these kinds of problems and worth through a couple of examples.
From playlist Calculus
B06 Example problem calculating the error
B06 Example problem calculating the error
From playlist A Second Course in Differential Equations
Verifying Particular Solutions to Differential Equations Calculus 1 AB
I reintroduce Differential Equations including the definition of a differential equations, the order of differential equations, the difference between particular solutions and general solutions, and the number of arbitrary constants you can expect when solving these equations. I then work
From playlist Calculus
How to Solve a Formula Equation
TabletClass Math http://www.tabletclass.com complete courses in middle and high school math. Perfect for homeschoolers and those that want to learn math on their own. This video how to solve for a specific variable in a formula. Algebra students need to use the same steps to solve a linear
From playlist Pre-Algebra
B01 An introduction to numerical methods
Most differential equations cannot be solved by the analytical techniques that we have learned up until now. I these cases, we can approximate a solution by a set of points, by using a variety of numerical methods. The first of these is Euler's method.
From playlist A Second Course in Differential Equations
The Authoritative Weight of Non-Definitive Magisterial Teaching by Lawrence Jerome King (Part 3)
A guest reading by Riverrun. Text: https://cuislandora.wrlc.org/islandora/object/cuislandora%3A40891/datastream/PDF/view
From playlist Authentic Non-Infallible Magisterium
Theory of numbers:Introduction
This lecture is part of an online undergraduate course on the theory of numbers. This is the introductory lecture, which gives an informal survey of some of the topics to be covered in the course, such as Diophantine equations, quadratic reciprocity, and binary quadratic forms.
From playlist Theory of numbers
Solving Equations (Outlining the purpose of 'solving an equation')
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From playlist Formulae and Equations
5. Telling a Free Story: Fugitive Slaves and the Underground Railroad in Myth and Reality
The Civil War and Reconstruction (HIST 119) Professor Blight discusses the rise of abolitionism. Blight begins with an introduction to the genre of slave narratives, with particular attention to Frederick Douglass' 1845 narrative. The lecture then moves on to discuss the culture in whic
From playlist The Civil War and Reconstruction with David Blight
7. The Neoclassical Synthesis of Rights and Utility
Moral Foundations of Politics (PLSC 118) John Stuart Mill's synthesis rights and utility follows naturally in the vein of neoclassical utilitarianism, and it attempts to compensate for many of the shortcomings of Bentham's classical utilitarianism. In the end, it turns out to be a doctr
From playlist The Moral Foundations of Politics with Ian Shapiro
Disregarding Nonintervention: National Liberation and Imperial Paternalism
Michael W. Doyle, Harold Brown Professor of International Affairs, Law and Political Science at Columbia University, gave three public lectures where he examined the legal and ethical arguments supporting nonintervention, engaging in a dialogue with John Stuart Mill's famous remarks on the
From playlist Ethics, Politics and Economics
Solving Inequalities using Addition and Subtraction
This video is about Solving Inequalities using Addition and Subtraction
From playlist Equations and Inequalities
How to solve a word problem with systems of equations
👉Learn how to solve a system of linear equations from a word problem. A system of equations is a set of more than one equations which are to be solved simultaneously. A word problem is a real world simulation of a mathematical concept. The solution to a system of equation is the set of val
From playlist Solve a System Algebraically | Algebra 2
Spinoza & Leibniz - Bryan Magee & Anthony Quinton (1987)
Bryan Magee and Anthony Quinton discuss the 17th-18th century philosophers Spinoza and Leibniz. Both were rationalists who developed elaborate philosophical systems out of only a few basic principles of reason, but ended up with quite different views. Spinoza was a monist and pantheist. He
From playlist Bryan Magee Interviews - The Great Philosophers (1987)
Reflections: Science and Religion, Natural and Unnatural
Dwight H. Terry Lectureship October 26, 2006 Reflections: Science and Religion, Natural and Unnatural Barbara Herrnstein Smith is Braxton Craven Professor of Comparative Literature and English and director of the Center for Interdisciplinary Studies in Science and Cultural Theory at
From playlist Terry Lectures
Panel Discussion on “Containment: Rebuilding a Strategy Against Global Terror”
Panel Discussion on Ian Shapiro’s new book Containment: Rebuilding a Strategy Against Global Terror.
From playlist MacMillan Center Archives
Confucius (or, What to Do When Elites Break The Rules) | Philosophy Tube
Alternate Title - 'What to Do When Elites Break The Rules' https://www.patreon.com/PhilosophyTube Subscribe! http://tinyurl.com/pr99a46 Paypal.me/PhilosophyTube Wanna get me a gift for the show? http://amzn.eu/5JAYdOd Check out my other videos on: Who's Afraid of the Experts? https://
From playlist The Main Show
CGSR Seminar Series | Russian Nuclear Strategy and Conventional Inferiority
Abstract: Contemporary debates on Russian nuclear strategy focus on making sense of Russia’s nuclear capabilities, signaling and nuclear declarations. This article, recently awarded the Journal of Strategic Studies 2020 Amos Perlmutter Prize, argues that understanding how nuclear capabili
From playlist Center for Global Security Research
Solving Equations Using Multiplication or Division
This video is about Solving Equations with Multiplication and Division
From playlist Equations and Inequalities
10. J. D. Salinger, Franny and Zooey
The American Novel Since 1945 (ENGL 291) In this lecture on J. D. Salinger's Franny and Zooey, Professor Hungerford presents her argument about religion in the novel as an example to students of how to construct a sound literary critical paper using evidence from the text. Moving betwee
From playlist The American Novel Since 1945 with Amy Hungerford