Special: Statistical Models

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-rssdist 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