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
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www.youtube.com/watch?v=ZMCH...
Proof #30: "Posterior distribution for binomial observations" (bin-post) #RandomProof
statproofbook.github.io/P/bin-post
statproofbook.github.io/P/bin-post
Posterior distribution 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
December 4, 2025 at 9:29 AM
Proof #30: "Posterior distribution for binomial observations" (bin-post) #RandomProof
statproofbook.github.io/P/bin-post
statproofbook.github.io/P/bin-post
Proof #388: "Posterior probability of the alternative model for multinomial observations" (mult-pp) #RandomProof
statproofbook.github.io/P/mult-pp
statproofbook.github.io/P/mult-pp
Posterior probability of the alternative model 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
December 3, 2025 at 11:38 AM
Proof #388: "Posterior probability of the alternative model for multinomial observations" (mult-pp) #RandomProof
statproofbook.github.io/P/mult-pp
statproofbook.github.io/P/mult-pp
Proof #438: "The log probability scoring rule is a strictly proper scoring rule" (lpsr-spsr) #RandomProof
statproofbook.github.io/P/lpsr-spsr
statproofbook.github.io/P/lpsr-spsr
The log probability scoring rule is a strictly proper scoring rule
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
December 2, 2025 at 10:10 AM
Proof #438: "The log probability scoring rule is a strictly proper scoring rule" (lpsr-spsr) #RandomProof
statproofbook.github.io/P/lpsr-spsr
statproofbook.github.io/P/lpsr-spsr
Proof #300: "Correlation always falls between -1 and +1" (corr-range) #RandomProof
statproofbook.github.io/P/corr-range
statproofbook.github.io/P/corr-range
Correlation always falls between -1 and +1
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
December 1, 2025 at 8:27 AM
Proof #300: "Correlation always falls between -1 and +1" (corr-range) #RandomProof
statproofbook.github.io/P/corr-range
statproofbook.github.io/P/corr-range
Proof #475: "Linear combination of bivariate normal random variables" (bvn-lincomb) #RandomProof
statproofbook.github.io/P/bvn-lincomb
statproofbook.github.io/P/bvn-lincomb
Linear combination of bivariate normal random variables
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 30, 2025 at 8:39 AM
Proof #475: "Linear combination of bivariate normal random variables" (bvn-lincomb) #RandomProof
statproofbook.github.io/P/bvn-lincomb
statproofbook.github.io/P/bvn-lincomb
Proof #168: "Moment-generating function of the Wald distribution" (wald-mgf) #RandomProof
statproofbook.github.io/P/wald-mgf
statproofbook.github.io/P/wald-mgf
Moment-generating function of the Wald distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 29, 2025 at 10:30 AM
Proof #168: "Moment-generating function of the Wald distribution" (wald-mgf) #RandomProof
statproofbook.github.io/P/wald-mgf
statproofbook.github.io/P/wald-mgf
Proof #37: "Probability density function of the continuous uniform distribution" (cuni-pdf) #RandomProof
statproofbook.github.io/P/cuni-pdf
statproofbook.github.io/P/cuni-pdf
Probability density function of the continuous uniform distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 28, 2025 at 10:43 AM
Proof #37: "Probability density function of the continuous uniform distribution" (cuni-pdf) #RandomProof
statproofbook.github.io/P/cuni-pdf
statproofbook.github.io/P/cuni-pdf
Proof #401: "Variance of the exponential distribution" (exp-var) #RandomProof
statproofbook.github.io/P/exp-var
statproofbook.github.io/P/exp-var
Variance of the exponential distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 27, 2025 at 9:32 AM
Proof #401: "Variance of the exponential distribution" (exp-var) #RandomProof
statproofbook.github.io/P/exp-var
statproofbook.github.io/P/exp-var
Proof #16: "Median of the normal distribution" (norm-med) #RandomProof
statproofbook.github.io/P/norm-med
statproofbook.github.io/P/norm-med
Median of the normal distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 26, 2025 at 8:02 AM
Proof #16: "Median of the normal distribution" (norm-med) #RandomProof
statproofbook.github.io/P/norm-med
statproofbook.github.io/P/norm-med
Proof #273: "Variance of parameter estimates for simple linear regression" (slr-olsvar) #RandomProof
statproofbook.github.io/P/slr-olsvar
statproofbook.github.io/P/slr-olsvar
Variance of parameter estimates for simple linear regression
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 25, 2025 at 6:44 AM
Proof #273: "Variance of parameter estimates for simple linear regression" (slr-olsvar) #RandomProof
statproofbook.github.io/P/slr-olsvar
statproofbook.github.io/P/slr-olsvar
Proof #368: "Derivation of the family evidence" (fe-der) #RandomProof
statproofbook.github.io/P/fe-der
statproofbook.github.io/P/fe-der
Derivation of the family evidence
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 23, 2025 at 9:12 AM
Proof #368: "Derivation of the family evidence" (fe-der) #RandomProof
statproofbook.github.io/P/fe-der
statproofbook.github.io/P/fe-der
Proof #106: "Ordinary least squares for the general linear model" (glm-ols) #RandomProof
statproofbook.github.io/P/glm-ols
statproofbook.github.io/P/glm-ols
Ordinary least squares for the general linear model
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 22, 2025 at 8:42 AM
Proof #106: "Ordinary least squares for the general linear model" (glm-ols) #RandomProof
statproofbook.github.io/P/glm-ols
statproofbook.github.io/P/glm-ols
Proof #230: "Variance of the Poisson distribution" (poiss-var) #RandomProof
statproofbook.github.io/P/poiss-var
statproofbook.github.io/P/poiss-var
Variance of the Poisson distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 21, 2025 at 7:31 AM
Proof #230: "Variance of the Poisson distribution" (poiss-var) #RandomProof
statproofbook.github.io/P/poiss-var
statproofbook.github.io/P/poiss-var
Proof #64: "Log Bayes factor in terms of log model evidences" (lbf-lme) #RandomProof
statproofbook.github.io/P/lbf-lme
statproofbook.github.io/P/lbf-lme
Log Bayes factor in terms of log model evidences
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 20, 2025 at 8:35 AM
Proof #64: "Log Bayes factor in terms of log model evidences" (lbf-lme) #RandomProof
statproofbook.github.io/P/lbf-lme
statproofbook.github.io/P/lbf-lme
Proof #422: "Kullback-Leibler divergence for the continuous uniform distribution" (cuni-kl) #RandomProof
statproofbook.github.io/P/cuni-kl
statproofbook.github.io/P/cuni-kl
Kullback-Leibler divergence for the continuous uniform distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 19, 2025 at 9:24 AM
Proof #422: "Kullback-Leibler divergence for the continuous uniform distribution" (cuni-kl) #RandomProof
statproofbook.github.io/P/cuni-kl
statproofbook.github.io/P/cuni-kl
Proof #35: "Marginal distributions of the multivariate normal distribution" (mvn-marg) #RandomProof
statproofbook.github.io/P/mvn-marg
statproofbook.github.io/P/mvn-marg
Marginal distributions of 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
November 18, 2025 at 9:03 AM
Proof #35: "Marginal distributions of the multivariate normal distribution" (mvn-marg) #RandomProof
statproofbook.github.io/P/mvn-marg
statproofbook.github.io/P/mvn-marg
Proof #70: "Probability density function of the matrix-normal distribution" (matn-pdf) #RandomProof
statproofbook.github.io/P/matn-pdf
statproofbook.github.io/P/matn-pdf
Probability density function of 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
November 17, 2025 at 8:13 AM
Proof #70: "Probability density function of the matrix-normal distribution" (matn-pdf) #RandomProof
statproofbook.github.io/P/matn-pdf
statproofbook.github.io/P/matn-pdf
Proof #197: "Probability density function of the chi-squared distribution" (chi2-pdf) #RandomProof
statproofbook.github.io/P/chi2-pdf
statproofbook.github.io/P/chi2-pdf
Probability density function of the chi-squared distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 16, 2025 at 8:46 AM
Proof #197: "Probability density function of the chi-squared distribution" (chi2-pdf) #RandomProof
statproofbook.github.io/P/chi2-pdf
statproofbook.github.io/P/chi2-pdf
Proof #383: "Log Bayes factor for binomial observations" (bin-lbf) #RandomProof
statproofbook.github.io/P/bin-lbf
statproofbook.github.io/P/bin-lbf
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
November 15, 2025 at 8:31 AM
Proof #383: "Log Bayes factor for binomial observations" (bin-lbf) #RandomProof
statproofbook.github.io/P/bin-lbf
statproofbook.github.io/P/bin-lbf
Proof #361: "Value of the probability-generating function for argument zero" (pgf-zero) #RandomProof
statproofbook.github.io/P/pgf-zero
statproofbook.github.io/P/pgf-zero
Value of the probability-generating function for argument zero
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 13, 2025 at 3:31 PM
Proof #361: "Value of the probability-generating function for argument zero" (pgf-zero) #RandomProof
statproofbook.github.io/P/pgf-zero
statproofbook.github.io/P/pgf-zero
Proof #39: "Quantile function of the continuous uniform distribution" (cuni-qf) #RandomProof
statproofbook.github.io/P/cuni-qf
statproofbook.github.io/P/cuni-qf
Quantile function of the continuous uniform distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 12, 2025 at 8:30 AM
Proof #39: "Quantile function of the continuous uniform distribution" (cuni-qf) #RandomProof
statproofbook.github.io/P/cuni-qf
statproofbook.github.io/P/cuni-qf
Proof #311: "Mode of the log-normal distribution" (lognorm-mode) #RandomProof
statproofbook.github.io/P/lognorm-mode
statproofbook.github.io/P/lognorm-mode
Mode of the log-normal distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 11, 2025 at 9:22 AM
Proof #311: "Mode of the log-normal distribution" (lognorm-mode) #RandomProof
statproofbook.github.io/P/lognorm-mode
statproofbook.github.io/P/lognorm-mode
Proof #421: "Skewness of the Wald distribution" (wald-skew) #RandomProof
statproofbook.github.io/P/wald-skew
statproofbook.github.io/P/wald-skew
Skewness of the Wald distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 10, 2025 at 7:55 AM
Proof #421: "Skewness of the Wald distribution" (wald-skew) #RandomProof
statproofbook.github.io/P/wald-skew
statproofbook.github.io/P/wald-skew
Proof #254: "Probability density function of an invertible function of a continuous random vector" (pdf-invfct) #RandomProof
statproofbook.github.io/P/pdf-invfct
statproofbook.github.io/P/pdf-invfct
Probability density function of an invertible function of a continuous random vector
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 9, 2025 at 8:33 AM
Proof #254: "Probability density function of an invertible function of a continuous random vector" (pdf-invfct) #RandomProof
statproofbook.github.io/P/pdf-invfct
statproofbook.github.io/P/pdf-invfct
Proof #224: "Maximum likelihood estimation for the Poisson distribution with exposure values" (poissexp-mle) #RandomProof
statproofbook.github.io/P/poissexp-mle
statproofbook.github.io/P/poissexp-mle
Maximum likelihood estimation for the Poisson distribution with exposure values
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 8, 2025 at 1:30 PM
Proof #224: "Maximum likelihood estimation for the Poisson distribution with exposure values" (poissexp-mle) #RandomProof
statproofbook.github.io/P/poissexp-mle
statproofbook.github.io/P/poissexp-mle