Thursday, May 19, 2011

Well to make myself feel better I think I will list all the concepts I've learned in the last two years and the stuff I need to learn hopefully over the summer.  This is just a partial list.  I will add to it as I think of things.

Still don't understand/have yet to try:
MCMC
Markov Chains
Priors and posteriors
Conjugate priors
Bayesian statistics
Network construction
Measure theory
Lebesgue integration
Bootstrapping
Jackknife
Ridge regression
Lasso

Learned/tried
LDU + SVD + Spectral + Cholesky Decompositions
Riemann sums/integrals
closed open sets
proof by induction/contradiction/contraposition
introductory topology
field axioms
limsup
liminf
metric spaces
compact 
complete
what a ring is
convergence of series
convergence of sets
uniform convergence
delta method
taylor series expansion and the remainder term
finding eigenvalues/eigenvectors
affine transformations
gradient/jacobian 
hessian
positive definite/negative definite
hermitian
lagrange multipliers
delta-epsilon proof method
lipschitz continuity

simple linear regression
ordinal logistic regression
ANOVA
ANCOVA
MANOVA
hazard functions 
survival function
Kaplan-Meier
dealing with left and right censored data
types of distributions
method of moments
characteristic functions
sufficient statistic
exponential family 
multilinearity
bootstrap
biased 
consistent estimators
UMVUE
BLUE
BLUP
pseudoinverse
oracle estimator
shrinkage


correlation structures
autoregressive correlation
longitudinal analysis
LME
GLM
GLMM
GAM
GEE
weighted least squares
iterative weighted least squares
newton-raphson
fisher scoring
principle components analysis
dose dependence curves
maximum likelihood
REML
quasi-likelihood
likelihood ratio
AIC 
BIC

fisher information
score equations
overdispersion
dose response 
link function
cross validation
classification
mixture models
asymptotic convergence
log parallel assays
smoothing 
cubic splines
kernel smoothing
local polynomial regression
wald test

non-parametric inference
semi-parametric inference
wilcoxon-rank sum test
factor analysis
mahalanobis distance
person, deviance, standardized, studentized residuals
deviance table
stepwise forward/backward/both model selection
hotelling's t2









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