probability spaces

conditional probability

independence

conditional probability

independence

definitions

discrete

continuous

conditional

functions

generation

proofs

discrete

continuous

conditional

functions

generation

proofs

discrete

continuous

joint distributions

independence

functions

generation

rejection sampling

continuous

joint distributions

independence

functions

generation

rejection sampling

operators

mean & variance

covariance

conditional

proofs

mean & variance

covariance

conditional

proofs

definitions

mean & autocovariance

independent indentically-distributed sequences

gaussians

poissons

random walks

proofs

mean & autocovariance

independent indentically-distributed sequences

gaussians

poissons

random walks

proofs

types

law of large numbers

central limit theorem

monte carlo

law of large numbers

central limit theorem

monte carlo

time-homogeneous, discrete-time

recurrences

periodicity

convergence

markov-chain monte carlo

recurrences

periodicity

convergence

markov-chain monte carlo

histograms

sample mean & variance

sample order

sample covariance

sample covariance matrix

sample mean & variance

sample order

sample covariance

sample covariance matrix

IID (independent, identically-distributed) sampling

MSE (mean square error)

consistency

confidence intervals

model estimation (non-parametric)

model estimation (parametric)

proofs

MSE (mean square error)

consistency

confidence intervals

model estimation (non-parametric)

model estimation (parametric)

proofs

parametric models

conjugate priors

estimators

conjugate priors

estimators

framework

parametric testing

non-parametric (permutations) testing

multiple testing

parametric testing

non-parametric (permutations) testing

multiple testing

linear models

least squares estimation

overfit

global warming

proofs

least squares estimation

overfit

global warming

proofs

definitions

operations

operations

vector spaces

inner products & norms

orthogonality

projections

matrices

eigendecomposition

eigendecomposition - symmetric matrices

proofs

inner products & norms

orthogonality

projections

matrices

eigendecomposition

eigendecomposition - symmetric matrices

proofs