Data Analysis and Machine Learning: Elements of Probability Theory and Statistical Data Analysis
Contents
Things to add
Domains and probabilities
Tossing a dice
Stochastic variables
Stochastic variables and the main concepts, the discrete case
Stochastic variables and the main concepts, the continuous case
The cumulative probability
Properties of PDFs
Important distributions, the uniform distribution
Gaussian distribution
Exponential distribution
Expectation values
Stochastic variables and the main concepts, mean values
Stochastic variables and the main concepts, central moments, the variance
Probability Distribution Functions
Probability Distribution Functions
The three famous Probability Distribution Functions
Probability Distribution Functions, the normal distribution
Probability Distribution Functions, the normal distribution
Probability Distribution Functions, the cumulative distribution
Probability Distribution Functions, other important distribution
Probability Distribution Functions, the binomial distribution
Probability Distribution Functions, Poisson's distribution
Probability Distribution Functions, Poisson's distribution
Additions to make
Meet the covariance!
Meet the covariance in matrix disguise
Covariance
Meet the covariance, uncorrelated events
Numerical experiments and the covariance
Numerical experiments and the covariance
Numerical experiments and the covariance, actual situations
Numerical experiments and the covariance, our observables
Numerical experiments and the covariance, the sample variance
Numerical experiments and the covariance, central limit theorem
Definition of Correlation Functions and Standard Deviation
Definition of Correlation Functions and Standard Deviation
Definition of Correlation Functions and Standard Deviation
Definition of Correlation Functions and Standard Deviation
Definition of Correlation Functions and Standard Deviation, sample variance
Definition of Correlation Functions and Standard Deviation
Code to compute the Covariance matrix and the Covariance
Random Numbers
Random Numbers, better name: pseudo random numbers
Random number generator RNG
Random number generator RNG and periodic outputs
Random number generator RNG and its period
Random number generator RNG, other examples
Random number generator RNG, other examples
Random number generator RNG, RAN0
Random number generator RNG, RAN0
Random number generator RNG, RAN0
Random number generator RNG, RAN0
Random number generator RNG, RAN0 code
Properties of Selected Random Number Generators
Properties of Selected Random Number Generators
Properties of Selected Random Number Generators
Simple demonstration of RNGs using python
Properties of Selected Random Number Generators
Autocorrelation function
Correlation function and which random number generators should I use
Which RNG should I use?
How to use the Mersenne generator
Why blocking?
Why blocking?
Code to demonstrate the calculation of the autocorrelation function
What is blocking?
What is blocking?
What is blocking?
Implementation
Actual implementation with code, main function
The Bootstrap method
Bootstrapping
Bootstrapping, recipe
Bootstrapping, "code":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/Programs/Sampling/analysis.py"
Jackknife, "code":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/Programs/Sampling/analysis.py"
Additions to make
discuss more sample mean and variance
sample covariance and Bessel's theorem on 1/(n-1) versus 1/n
add more text to covariance matrix and results of codes
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