Fisher Information: A Clinical Dissection of an Enigmatic Concept | by Sachin Date | Oct, 2024
Can you guess the true fraction of yellow M&Ms in the universe?
In his book A Brief History of Time, Stephen Hawking describes his struggle to explain relativistic physics without using a single equation.
His editor had warned him in literally these words: every equation you use will reduce your readership by half.
Faced with the vivid possibility of near-zero sales, Hawking published A Brief History of Time with exactly one equation: E = mc².
The book sold 25 million copies — a stunning achievement from any angle.
Had Professor Hawking, even for the most pressing of needs, included the formula for Fisher Information in his book, the sales figures might have been riveting for an altogether different reason.
For here lies, in its exquisitely inscrutable glory, the formula for Fisher Information:
Compare, if you will, the notational nightmare shown above with E=mc².
For bonus bewilderment, the above formula comes with the following chewy definition:
Given a random variable X with a probability distribution f(X | θ), the Fisher Information…
