Proof #555: "Posterior probability of the alternative model for the general contigency table" (ct-pp) #NewProof
statproofbook.github.io/P/ct-pp
statproofbook.github.io/P/ct-pp
Posterior probability of the alternative model for the general contigency table
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
October 7, 2026 at 8:45 AM
Proof #555: "Posterior probability of the alternative model for the general contigency table" (ct-pp) #NewProof
statproofbook.github.io/P/ct-pp
statproofbook.github.io/P/ct-pp
Proof #554: "Log Bayes factor for general contigency table models" (ct-lbf) #NewProof
statproofbook.github.io/P/ct-lbf
statproofbook.github.io/P/ct-lbf
Log Bayes factor for general contigency table models
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
October 6, 2026 at 2:11 PM
Proof #554: "Log Bayes factor for general contigency table models" (ct-lbf) #NewProof
statproofbook.github.io/P/ct-lbf
statproofbook.github.io/P/ct-lbf
Proof #545: "Posterior frequencies for random-effects Bayesian model selection using Dirichlet posterior distribution" (bmsrfx-freqpost) #NewProof
statproofbook.github.io/P/bmsrfx-fre...
statproofbook.github.io/P/bmsrfx-fre...
Posterior frequencies for random-effects Bayesian model selection using Dirichlet posterior distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
July 7, 2026 at 11:41 AM
Proof #545: "Posterior frequencies for random-effects Bayesian model selection using Dirichlet posterior distribution" (bmsrfx-freqpost) #NewProof
statproofbook.github.io/P/bmsrfx-fre...
statproofbook.github.io/P/bmsrfx-fre...
Proof #553: "Log model evidences for general contigency table models" (ct-lme) #NewProof
statproofbook.github.io/P/ct-lme
statproofbook.github.io/P/ct-lme
Log model evidences for general contigency table models
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
October 5, 2026 at 9:57 AM
Proof #553: "Log model evidences for general contigency table models" (ct-lme) #NewProof
statproofbook.github.io/P/ct-lme
statproofbook.github.io/P/ct-lme
Proof #485: "Marginal distributions of the multinomial distribution" (mult-marg) #NewProof
statproofbook.github.io/P/mult-marg
statproofbook.github.io/P/mult-marg
Marginal distributions of the multinomial distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
February 17, 2025 at 10:03 AM
Proof #485: "Marginal distributions of the multinomial distribution" (mult-marg) #NewProof
statproofbook.github.io/P/mult-marg
statproofbook.github.io/P/mult-marg
Proof #501: "Sampling from the matrix-normal distribution" (mvn-samp) #NewProof
statproofbook.github.io/P/mvn-samp
statproofbook.github.io/P/mvn-samp
Sampling from the matrix-normal distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
May 27, 2025 at 10:03 AM
Proof #501: "Sampling from the matrix-normal distribution" (mvn-samp) #NewProof
statproofbook.github.io/P/mvn-samp
statproofbook.github.io/P/mvn-samp
Proof #544: "Derivation of the group log Bayes factor" (glbf-der) #NewProof
statproofbook.github.io/P/glbf-der
statproofbook.github.io/P/glbf-der
Derivation of the group log Bayes factor
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
July 3, 2026 at 7:58 AM
Proof #544: "Derivation of the group log Bayes factor" (glbf-der) #NewProof
statproofbook.github.io/P/glbf-der
statproofbook.github.io/P/glbf-der
Proof #499: "Expectation of a quadratic form for the multivariate normal distribution" (mvn-meanqf) #NewProof
statproofbook.github.io/P/mvn-meanqf
statproofbook.github.io/P/mvn-meanqf
Expectation of a quadratic form for the multivariate normal distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
May 25, 2025 at 2:15 PM
Proof #499: "Expectation of a quadratic form for the multivariate normal distribution" (mvn-meanqf) #NewProof
statproofbook.github.io/P/mvn-meanqf
statproofbook.github.io/P/mvn-meanqf
Proof #507: "Distribution of the coefficient of determination under the null hypothesis" (rsq-dist) #NewProof
statproofbook.github.io/P/rsq-dist
statproofbook.github.io/P/rsq-dist
Distribution of the coefficient of determination under the null hypothesis
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
July 15, 2025 at 2:33 AM
Proof #507: "Distribution of the coefficient of determination under the null hypothesis" (rsq-dist) #NewProof
statproofbook.github.io/P/rsq-dist
statproofbook.github.io/P/rsq-dist
Proof #545: "Variational Bayesian estimation of random-effects Bayesian model selection using the mean-field approximation" (bmsrfx-vb) #NewProof
statproofbook.github.io/P/bmsrfx-vb
statproofbook.github.io/P/bmsrfx-vb
Variational Bayesian estimation of random-effects Bayesian model selection using the mean-field approximation
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
July 6, 2026 at 6:44 PM
Proof #545: "Variational Bayesian estimation of random-effects Bayesian model selection using the mean-field approximation" (bmsrfx-vb) #NewProof
statproofbook.github.io/P/bmsrfx-vb
statproofbook.github.io/P/bmsrfx-vb
Proof #552: "Posterior probability of the alternative model for the binary contigency table" (ct2x2-pp) #NewProof
statproofbook.github.io/P/ct2x2-pp
statproofbook.github.io/P/ct2x2-pp
Posterior probability of the alternative model for the binary contigency table
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
October 1, 2026 at 7:57 AM
Proof #552: "Posterior probability of the alternative model for the binary contigency table" (ct2x2-pp) #NewProof
statproofbook.github.io/P/ct2x2-pp
statproofbook.github.io/P/ct2x2-pp
Proof #551: "Log Bayes factor for binary contigency table models" (ct2x2-lbf) #NewProof
statproofbook.github.io/P/ct2x2-lbf
statproofbook.github.io/P/ct2x2-lbf
Log Bayes factor for binary contigency table models
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
September 30, 2026 at 7:12 AM
Proof #551: "Log Bayes factor for binary contigency table models" (ct2x2-lbf) #NewProof
statproofbook.github.io/P/ct2x2-lbf
statproofbook.github.io/P/ct2x2-lbf
Proof #550: "Log model evidences for binary contigency table models" (ct2x2-lme) #NewProof
statproofbook.github.io/P/ct2x2-lme
statproofbook.github.io/P/ct2x2-lme
Log model evidences for binary contigency table models
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
September 29, 2026 at 6:07 PM
Proof #550: "Log model evidences for binary contigency table models" (ct2x2-lme) #NewProof
statproofbook.github.io/P/ct2x2-lme
statproofbook.github.io/P/ct2x2-lme
Proof #549: "Contrast-based t-test with null hypothesis parameter for multiple linear regression" (mlr-t0) #NewProof
statproofbook.github.io/P/mlr-t0
statproofbook.github.io/P/mlr-t0
Contrast-based t-test with null hypothesis parameter for multiple linear regression
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
September 2, 2026 at 5:43 AM
Proof #549: "Contrast-based t-test with null hypothesis parameter for multiple linear regression" (mlr-t0) #NewProof
statproofbook.github.io/P/mlr-t0
statproofbook.github.io/P/mlr-t0
Proof #548: "Joint distribution of marginally and conditionally multivariate normal random vectors" (mvn-jmc) #NewProof
statproofbook.github.io/P/mvn-jmc
statproofbook.github.io/P/mvn-jmc
Joint distribution of marginally and conditionally multivariate normal random vectors
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
September 1, 2026 at 9:07 AM
Proof #548: "Joint distribution of marginally and conditionally multivariate normal random vectors" (mvn-jmc) #NewProof
statproofbook.github.io/P/mvn-jmc
statproofbook.github.io/P/mvn-jmc
Proof #546: "Equivalence of conditional and partial correlation for the multivariate normal distribution" (mvn-ecpc) #NewProof
statproofbook.github.io/P/mvn-ecpc
statproofbook.github.io/P/mvn-ecpc
Equivalence of conditional and partial correlation for the multivariate normal distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
August 31, 2026 at 2:10 PM
Proof #546: "Equivalence of conditional and partial correlation for the multivariate normal distribution" (mvn-ecpc) #NewProof
statproofbook.github.io/P/mvn-ecpc
statproofbook.github.io/P/mvn-ecpc
Proof #543: "Derivation of the group Bayes factor" (gbf-der) #NewProof
statproofbook.github.io/P/gbf-der
statproofbook.github.io/P/gbf-der
Derivation of the group Bayes factor
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
July 2, 2026 at 5:42 AM
Proof #543: "Derivation of the group Bayes factor" (gbf-der) #NewProof
statproofbook.github.io/P/gbf-der
statproofbook.github.io/P/gbf-der
Proof #542: "Invariance of the sample correlation under linear transformation" (corrsamp-inv) #NewProof
statproofbook.github.io/P/corrsamp-inv
statproofbook.github.io/P/corrsamp-inv
Invariance of the sample correlation under linear transformation
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
June 5, 2026 at 8:43 AM
Proof #542: "Invariance of the sample correlation under linear transformation" (corrsamp-inv) #NewProof
statproofbook.github.io/P/corrsamp-inv
statproofbook.github.io/P/corrsamp-inv
Proof #541: "Invariance of the correlation under linear transformation" (corr-inv) #NewProof
statproofbook.github.io/P/corr-inv
statproofbook.github.io/P/corr-inv
Invariance of the correlation under linear transformation
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
June 4, 2026 at 5:48 AM
Proof #541: "Invariance of the correlation under linear transformation" (corr-inv) #NewProof
statproofbook.github.io/P/corr-inv
statproofbook.github.io/P/corr-inv
Proof #540: "Scaling of the covariance upon multiplication with constants" (cov-scal) #NewProof
statproofbook.github.io/P/cov-scal
statproofbook.github.io/P/cov-scal
Scaling of the covariance upon multiplication with constants
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
June 3, 2026 at 8:52 AM
Proof #540: "Scaling of the covariance upon multiplication with constants" (cov-scal) #NewProof
statproofbook.github.io/P/cov-scal
statproofbook.github.io/P/cov-scal
Proof #539: "Invariance of the covariance under addition of constants" (cov-inv) #NewProof
statproofbook.github.io/P/cov-inv
statproofbook.github.io/P/cov-inv
Invariance of the covariance under addition of constants
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
June 2, 2026 at 5:37 AM
Proof #539: "Invariance of the covariance under addition of constants" (cov-inv) #NewProof
statproofbook.github.io/P/cov-inv
statproofbook.github.io/P/cov-inv
Proof #538: "Linearity of the sample mean" (meansamp-lin) #NewProof
statproofbook.github.io/P/meansamp-lin
statproofbook.github.io/P/meansamp-lin
Linearity of the sample mean
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
June 1, 2026 at 8:56 AM
Proof #538: "Linearity of the sample mean" (meansamp-lin) #NewProof
statproofbook.github.io/P/meansamp-lin
statproofbook.github.io/P/meansamp-lin
Proof #537: "Maximum likelihood estimation for univariate von Mises data" (vm-mle) #NewProof
statproofbook.github.io/P/vm-mle
statproofbook.github.io/P/vm-mle
Maximum likelihood estimation for univariate von Mises data
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
May 1, 2026 at 2:06 PM
Proof #537: "Maximum likelihood estimation for univariate von Mises data" (vm-mle) #NewProof
statproofbook.github.io/P/vm-mle
statproofbook.github.io/P/vm-mle