The Book of Statistical Proofs
@statproofbook.bsky.social
– a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences. #StatProofBook #RandomProof
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How to submit a new theorem to The Book of Statistical Proofs
YouTube video by Joram Soch
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How to submit a new theorem to The Book of Statistical Proofs
www.youtube.com/watch?v=ZMCH...
www.youtube.com/watch?v=ZMCH...
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 #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 #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 #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 #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 #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 #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
Proof #536: "Relationship between bivariate normal distribution and von Mises distribution" (vm-bvn) #NewProof
statproofbook.github.io/P/vm-bvn
statproofbook.github.io/P/vm-bvn
Relationship between bivariate normal distribution and von Mises distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
April 30, 2026 at 7:10 AM
Proof #536: "Relationship between bivariate normal distribution and von Mises distribution" (vm-bvn) #NewProof
statproofbook.github.io/P/vm-bvn
statproofbook.github.io/P/vm-bvn
Proof #535: "Full width at half maximum for the von Mises distribution" (vm-fwhm) #NewProof
statproofbook.github.io/P/vm-fwhm
statproofbook.github.io/P/vm-fwhm
Full width at half maximum for the von Mises distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
April 29, 2026 at 7:56 AM
Proof #535: "Full width at half maximum for the von Mises distribution" (vm-fwhm) #NewProof
statproofbook.github.io/P/vm-fwhm
statproofbook.github.io/P/vm-fwhm
Proof #534: "Probability density function of the von Mises distribution" (vm-pdf) #NewProof
statproofbook.github.io/P/vm-pdf
statproofbook.github.io/P/vm-pdf
Probability density function of the von Mises distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
April 28, 2026 at 5:58 AM
Proof #534: "Probability density function of the von Mises distribution" (vm-pdf) #NewProof
statproofbook.github.io/P/vm-pdf
statproofbook.github.io/P/vm-pdf
Proof #532: "Cross-validated log Bayes factor for multinomial observations" (mult-cvlbf) #NewProof
statproofbook.github.io/P/mult-cvlbf
statproofbook.github.io/P/mult-cvlbf
Cross-validated log Bayes factor for multinomial observations
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
April 2, 2026 at 4:56 AM
Proof #532: "Cross-validated log Bayes factor for multinomial observations" (mult-cvlbf) #NewProof
statproofbook.github.io/P/mult-cvlbf
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
statproofbook.github.io/P/bin-cvlbf
Cross-validated log Bayes factor for binomial observations
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
April 1, 2026 at 7:32 AM
Proof #531: "Cross-validated log Bayes factor for binomial observations" (bin-cvlbf) #NewProof
statproofbook.github.io/P/bin-cvlbf
statproofbook.github.io/P/bin-cvlbf