Proof #532: "Cross-validated log Bayes factor for multinomial observations" (mult-cvlbf) #NewProof
statproofbook.github.io/P/mult-cvlbf
Proof #531: "Cross-validated log Bayes factor for binomial observations" (bin-cvlbf) #NewProof
statproofbook.github.io/P/bin-cvlbf
Proof #530: "Partial correlation of random variables which are jointly multivariate normal distributed" (mvn-corrpart) #NewProof
statproofbook.github.io/P/mvn-corrpart
Proof #529: "Conditional correlation of random variables which are jointly multivariate normal distributed" (mvn-corrcond) #NewProof
statproofbook.github.io/P/mvn-corrcond
Proof #528: "The third standardized moment equals the skewness" (momstand-3rd) #NewProof
statproofbook.github.io/P/momstand-3rd
Proof #527: "The second standardized moment equals one" (momstand-2nd) #NewProof
statproofbook.github.io/P/momstand-2nd
Proof #526: "The first standardized moment equals zero" (momstand-1st) #NewProof
statproofbook.github.io/P/momstand-1st
Proof #525: "Marginal distributions of the multivariate t-distribution" (mvt-marg) #NewProof
statproofbook.github.io/P/mvt-marg
Proof #524: "Second-order expectations for the matrix-normal distribution" (matn-meanso) #NewProof
statproofbook.github.io/P/matn-meanso
Proof #523: "Expectation of quadratic forms for the matrix-normal distribution" (matn-meanqf) #NewProof
statproofbook.github.io/P/matn-meanqf
Proof #522: "Cross-covariance matrices of the matrix-normal distribution" (matn-ccm) #NewProof
statproofbook.github.io/P/matn-ccm
Proof #521: "Chi-squared distribution is a special case of gamma distribution" (chi2-gam2) #NewProof
statproofbook.github.io/P/chi2-gam2
Proof #520: "Mode of the beta distribution" (beta-mode) #NewProof
statproofbook.github.io/P/beta-mode
Proof #519: "Median of the beta distribution" (beta-med) #NewProof
statproofbook.github.io/P/beta-med
Proof #518: "Median of the gamma distribution" (gam-med) #NewProof
statproofbook.github.io/P/gam-med
Proof #517: "The variational free energy is a lower bound on the log model evidence" (fren-lme) #NewProof
statproofbook.github.io/P/fren-lme
Proof #516: "Decompositions of the variational free energy" (fren-dec) #NewProof
statproofbook.github.io/P/fren-dec
Proof #515: "Non-negativity of the Kullback-Leibler divergence" (kl-nonneg3) #NewProof
statproofbook.github.io/P/kl-nonneg3
Proof #514: "Jensen's inequality" (jens-ineq) #NewProof
statproofbook.github.io/P/jens-ineq
Proof #513: "Expectation of a bilinear form" (mean-blf) #NewProof
statproofbook.github.io/P/mean-blf
Proof #512: "Partition of a cross-covariance matrix into expected values" (covmatcross-mean) #NewProof
statproofbook.github.io/P/covmatcros...
Proof #510: "Prior predictive distribution is a marginal distribution of the joint likelihood" (priorpred-jl) #NewProof
statproofbook.github.io/P/priorpred-jl
Proof #509: "Variance of the coefficient of determination under the null hypothesis" (rsq-var) #NewProof
statproofbook.github.io/P/rsq-var
Proof #508: "Mean, mode and median of the coefficient of determination under the null hypothesis" (rsq-mmm) #NewProof
statproofbook.github.io/P/rsq-mmm
Proof #507: "Distribution of the coefficient of determination under the null hypothesis" (rsq-dist) #NewProof
statproofbook.github.io/P/rsq-dist
Proof #506: "Redundancy of parameters describing the matrix-normal distribution" (matn-red2) #NewProof
statproofbook.github.io/P/matn-red2
Proof #505: "Redundancy of parameters describing the matrix-normal distribution" (matn-red) #NewProof
statproofbook.github.io/P/matn-red
Proof #504: "Maximum likelihood estimation for multivariate normally distributed data" (mvn-mle) #NewProof
statproofbook.github.io/P/mvn-mle
Proof #503: "Maximum likelihood estimation for bivariate normally distributed data" (bvn-mle) #NewProof
statproofbook.github.io/P/bvn-mle
Proof #502: "Construction of a bivariate normal distribution from univariate standard normal random variables" (bvn-snorm) #NewProof
statproofbook.github.io/P/bvn-snorm