Statistical proof is the rational demonstration of degree of certainty for a proposition, hypothesis or theory that is used to convince others subsequent to a statistical test of the supporting evidence and the types of inferences that can be drawn from the test scores. Statistical methods are used to increase the understanding of the facts and the proof demonstrates the validity and logic of inference with explicit reference to a hypothesis, the experimental data, the facts, the test, and the odds. Proof has two essential aims: the first is to convince and the second is to explain the proposition through peer and public review. The burden of proof rests on the demonstrable application of the statistical method, the disclosure of the assumptions, and the relevance that the test has with respect to a genuine understanding of the data relative to the external world. There are adherents to several different statistical philosophies of inference, such as Bayes theorem versus the likelihood function, or positivism versus critical rationalism. These methods of reason have direct bearing on statistical proof and its interpretations in the broader philosophy of science. A common demarcation between science and non-science is the hypothetico-deductive proof of falsification developed by Karl Popper, which is a well-established practice in the tradition of statistics. Other modes of inference, however, may include the inductive and abductive modes of proof. Scientists do not use statistical proof as a means to attain certainty, but to falsify claims and explain theory. Science cannot achieve absolute certainty nor is it a continuous march toward an objective truth as the vernacular as opposed to the scientific meaning of the term "proof" might imply. Statistical proof offers a kind of proof of a theory's falsity and the means to learn heuristically through repeated statistical trials and experimental error. Statistical proof also has applications in legal matters with implications for the legal burden of proof. (Wikipedia).
Proof: What is it, and how does it work?
From playlist The Nature of Proof
Introduction to Direct Proofs: If n is even, then n squared is even
This video introduces the mathematical proof method of direct proof provides an example of a direct proof. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Proof: a³ - a is always divisible by 6 (2 of 2: Proof by exhaustion)
More resources available at www.misterwootube.com
From playlist The Nature of Proof
Introduction to Common Mathematical Proof Methods
This video introduces the common methods of mathematical proofs and provides a basic example of a direct proof. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Every Subset of a Linearly Independent Set is also Linearly Independent Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A proof that every subset of a linearly independent set is also linearly independent.
From playlist Proofs
How does a statistical PROOF work?
Statistical hypothesis testing may appear to be an arcane procedure from a faraway galaxy… but what do we really do when we perform a hypothesis test? What does all its jargon mean? And once we perform this procedure, how much can we trust in its outcomes? Statistics is an integral part
From playlist Summer of Math Exposition Youtube Videos
High dimensional estimation via Sum-of-Squares Proofs – D. Steurer & P. Raghavendra – ICM2018
Mathematical Aspects of Computer Science Invited Lecture 14.6 High dimensional estimation via Sum-of-Squares Proofs David Steurer & Prasad Raghavendra Abstract: Estimation is the computational task of recovering a ‘hidden parameter’ x associated with a distribution 𝒟_x, given a ‘measurem
From playlist Mathematical Aspects of Computer Science
All the Math Classes that Math Majors Take
In this video I go over all of the classes that most math majors take. These are the ones I took which were, all of the most common ones and the recommended ones for a pure math degree. Hopefully this gives you an idea of what kind of things you will study if you decide to major in math. I
From playlist Book Reviews
How to Prepare for a Masters in Mathematics
In this video I answer an email I received from a viewer. She has been accepted into Masters Degree program for mathematics and wants to prepare. Do you have any advice? If so, please leave a comment below. Great Proof Writing Book: https://amzn.to/3ZUSYQ0 Statistics Book by Wackerly: htt
From playlist Inspiration and Advice
How to Prove a Function is Injective(one-to-one) Using the Definition
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to prove a function is injective. Injective functions are also called one-to-one functions. This is a short video focusing on the proof.
From playlist Proofs
In this video I answer a question I received from a viewer. They want to know about mathematics for quantitative finance. They are specifically concerned with math for real analysis and probability. Do you have any advice or opinions? If so, please leave a comment. Quantative Finance Bo
From playlist Inspiration and Advice
Introduction to Proof by Counter Example
This video provides an introduction to the proof method of proof by counter example. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Learn Mathematics from START to FINISH (2nd Edition)
In this video I will show you how to learn mathematics from start to finish. I will give you three different ways to get started with mathematics. I hope this video helps someone. Here are the books Elementary Algebra https://amzn.to/3S7yG0Y Pre-Algebra https://amzn.to/3TpW8HK Discrete Ma
From playlist Book Reviews
Spectral Statistics of Lévy Matrices - Patrick Lopatto
Analysis Seminar Topic: Spectral Statistics of Lévy Matrices Speaker: Patrick Lopatto Affiliation: Member, School of Mathematics Date: October 19, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
A Brief Introduction to Proofs
This video serves as an introduction to proofs.
From playlist Summer of Math Exposition Youtube Videos
Getting Started With Mathematical Statistics
In this video I answer a question I received from a viewer. The topic is mathematical statistics. Do you have advice for this person? If so, please leave a comment below. This is the book I mention in the video: https://amzn.to/3i3RD54 (Note the above link is my affiliate link) If you en
From playlist Inspiration and Advice
A Math Book For Every Person In The World
Here are the math books and who they are for. I hope this helps you decide which one is best for you. How to Prove It: https://amzn.to/3VnYS9Q (learn to write proofs with this with almost no background) All The Math You Missed (overview of tons of math, knowing some math is helpful befor
From playlist Math Sorcerer Live Streams
Spectral statistics of random matrices and random graphs - Horng-Tzer Yau
Marston Morse Lectures Topic: Spectral statistics of random matrices and random graphs Speaker: Horng-Tzer Yau Affiliation: Harvard University Date: March 14, 2022
From playlist Mathematics