Index: The Book of Statistical Proofs ▷ Statistical Models

Proofs and Definitions on Statistical Models in the StatProofBook, as of 2023-12-23.

Model Definition Estimation Maximum
likelihood
estimation
Conjugate
prior
Posterior
distribution
Log
model
evidence
Other
Univariate
normal data

Univariate Gaussian ug   ug-mle ug-prior ug-post ug-lme
ug-anc
ug-ttest1
ug-ttest2
ug-ttestp
Univariate Gaussian with known variance ugkv   ugkv-mle ugkv-prior ugkv-post ugkv-lme
ugkv-anc
ugkv-cvlme
ugkv-ztest1
ugkv-ztest2
ugkv-ztestp
ugkv-lbf
ugkv-lbfmean
ugkv-cvlbf
ugkv-cvlbfmean
One-way analysis of variance anova1 anova1-ols         anova1-pss
anova1-f
anova1-fols
anova1-repara
Two-way analysis of variance anova2 anova2-ols         anova2-pss
anova2-cochran
anova2-fme
anova2-fia
anova2-fgm
anova2-fols
Simple linear regression slr slr-ols
slr-olsmean
slr-olsvar
slr-olsdist
slr-olscorr
slr-wls
slr-mle       slr-mlr
slr-meancent
slr-comp
slr-proj
slr-sss
slr-mat
slr-ressum
slr-rescorr
slr-resvar
slr-corr
slr-rsq
Multiple linear regression mlr mlr-olstr
mlr-ols
mlr-wls
mlr-olsdist
mlr-wlsdist
mlr-ind
mlr-mle
mlr-mll
mlr-dev
mlr-glm
mlr-pss
mlr-mat
mlr-idem
mlr-symm
mlr-t
mlr-f
mlr-aic
mlr-aicc
mlr-bic
Bayesian linear regression       blr-prior blr-post blr-lme blr-pp
blr-pcr
blr-dic
Multivariate
normal data

General linear model glm glm-ols
glm-wls
glm-mle
Transformed general linear model tglm           tglm-dist
tglm-para
Inverse general linear model iglm
cfm
iglm-dist
iglm-blue
cfm-para
cfm-exist
Multivariate Bayesian linear regression       mblr-prior mblr-post mblr-lme
Poisson data
Poisson-distributed data poiss   poiss-mle poiss-prior poiss-post poiss-lme
Poisson distribution with exposure values poissexp   poissexp-mle poissexp-prior poissexp-post poissexp-lme
Probability data
Beta-distributed data beta beta-mome
Dirichlet-distributed data dir   dir-mle
Beta-binomial data betabin-data betabin-mome
Categorical data
Binomial observations bin   bin-mle
bin-mll
bin-prior bin-post
bin-map
bin-lme bin-test
bin-lbf
bin-pp
Multinomial observations mult   mult-mle
mult-mll
mult-prior mult-post
mult-map
mult-lme mult-test
mult-lbf
mult-pp
Logistic regression logreg           logreg-pnlo
logreg-lonp