The foundations of statistics concern the epistemological debate in statistics over how one should conduct inductive inference from data. Among the issues considered in statistical inference are the question of Bayesian inference versus frequentist inference, the distinction between Fisher's "significance testing" and Neyman–Pearson "hypothesis testing", and whether the likelihood principle should be followed. Some of these issues have been debated for up to 200 years without resolution. Bandyopadhyay & Forster describe four statistical paradigms: "(i) classical statistics or error statistics, (ii) Bayesian statistics, (iii) likelihood-based statistics, and (iv) the Akaikean-Information Criterion-based statistics". Leonard J. Savage's widely cited text Foundations of Statistics states: It is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis. (Wikipedia).
Welcome to my introductory series on Data Science! In this video, I explain how to talk about data in general, the difference between qualitative and quantitative data and finally, how to describe data succinctly by using summary statistics. Link to my notes on Introduction to Data Scien
From playlist Introduction to Data Science - Foundations
This branch of math can help you to organize and interpret information. It’s used in a variety of fields, and it has many applications in daily life. To learn more basic concepts in #statistics, check out the free tutorial on our website: https://edu.gcfglobal.org/en/statistics-basic-conce
From playlist Basic Statistics
The Scientific Method and the question of "Infinite Sets" | Sociology and Pure Maths| N J Wildberger
Let's get some kind of serious discussion going about the differences in methodology and philosophy between the sciences and mathematics, and how these differences manifest themselves in the attitude towards the logical foundations of mathematics. In particular we look at a bulwark notio
From playlist Sociology and Pure Mathematics
What is a number? | Arithmetic and Geometry Math Foundations 1 | N J Wildberger
The first of a series that will discuss foundations of mathematics. Contains a general introduction to the series, and then the beginnings of arithmetic with natural numbers. This series will methodically develop a lot of basic mathematics, starting with arithmetic, then geometry, then alg
From playlist Math Foundations
Introduction to a short course on foundations of statistics. If you've never taken a statistics class before (or even if you have), this course will walk you through what you need to know. The course will cover topics like sampling distributions, approximations, confidence intervals and Fr
From playlist Intro to Statistics
The essential dichotomy underlying mathematics | Data Structures Math Foundations 186
What lies at the very core of mathematics? What is mathematics ultimately about, once we strip away all the hoopla and complexity? In this video I give you my answer to this intriguing question. Surprisingly, it is not really the natural numbers: they are fundamental, but not the most fund
From playlist Math Foundations
What is the Fundamental theorem of Algebra, really? | Abstract Algebra Math Foundations 217
Here we give restatements of the Fundamental theorems of Algebra (I) and (II) that we critiqued in our last video, so that they are now at least meaningful and correct statements, at least to the best of our knowledge. The key is to abstain from any prior assumptions about our understandin
From playlist Math Foundations
The realm of natural numbers | Data structures in Mathematics Math Foundations 155
Here we look at a somewhat unfamiliar aspect of arithmetic with natural numbers, motivated by operations with multisets, and ultimately forming a main ingredient for that theory. We look at natural numbers, together with 0, under three operations: addition, union and intersection. We will
From playlist Math Foundations
Definitions, specification and interpretation | Arithmetic and Geometry Math Foundations 44
We discuss important meta-issues regarding definitions and specification in mathematics. We also introduce the idea that mathematical definitions, expressions, formulas or theorems may support a variety of possible interpretations. Examples use our previous definitions from elementary ge
From playlist Math Foundations
What Probability Theory Is — Topic 94 of Machine Learning Foundations
#MLFoundations #Probability #MachineLearning This video is a quick introduction to what Probability Theory is! There are eight subjects covered comprehensively in the ML Foundations series and this video is from the fifth subject, "Probability & Information Theory". More detail about th
From playlist Probability for Machine Learning
Why The Best Data Scientists have Mastered Algebra, Calculus and Probability
All the outstanding data scientist and ML engineers have one thing in common: They have a strong, working understanding of how ML's high-level software libraries work. Being able to look under the hood, and understand what's going in libraries such as scikit-learn, TensorFlow, and Keras,
From playlist Talks and Tutorials
Probability & Information Theory — Subject 5 of Machine Learning Foundations
#MLFoundations #Probability #MachineLearning Welcome to my course on Probability and Information Theory, which is part of my broader "Machine Learning Foundations" curriculum. This video is an orientation to the curriculum. There are eight subjects covered comprehensively in the ML Found
From playlist Probability for Machine Learning
Announcing the Machine Learning Foundations Tutorial Series
This Machine Learning Foundations series provides a comprehensive overview of all of the foundational subjects -- mathematics, statistics, and computer science -- that underlie contemporary machine learning approaches, including deep learning and other artificial intelligence techniques.
From playlist Talks and Tutorials
SDS 556: @Jon Krohn's Machine Learning Courses
#MachineLearning #DataScience #MachineLearningCourses Discover Jon’s extensive library of machine learning content and learn why Jon's Machine Learning House forms the knowledge structure of an outstanding data scientist or ML engineer. Additional materials: https://www.superdatascience.
From playlist Super Data Science Podcast
Math Needed for Mastering Data Science
In this video, I talk about the math concepts that you should master to find success in data science. Article by Tirthajyoti Sarkar: https://medium.com/s/story/essential-math-for-data-science-why-and-how-e88271367fbd 1) Statistics 2) Discrete Math 3) Linear Algebra 4) Calculus #DataS
From playlist Data Science Beginners
Favorite Stats Books: Seven Pillars of Statistical Wisdom
The Seven Pillars of Statistical Wisdom is a wonderful small book about seven foundational statistical ideas that were revolutionary for their time. These seven are heavily used in science, technology, and machine learning. Jay goes over the seven ideas and what makes this an accessible an
From playlist Book Reviews
Plug in Principle - Data Science
In this video, I explain the super important plugin principle! Using this principle, (and some assumptions) allows us to finally talk about topics like population. Here, I explain when to use the principle, what the tradeoffs are, and also go through some examples using it. Enjoy! Link to
From playlist Introduction to Data Science - Foundations
Sets and other data structures | Data Structures in Mathematics Math Foundations 151
In mathematics we often want to organize objects. Sets are not the only way of doing this: there are other data types that are also useful and that can be considered together with set theory. In particular when we group objects together, there are two fundamental questions that naturally a
From playlist Math Foundations