updated index pages

The index pages were updated with the recently added proofs/definitions.

Author: JoramSoch

I/DbA.md

@@ -8,14 +8,16 @@ title: "Definition by Author"
 
 - [Sample covariance](/D/cov-samp)
 
-### JoramSoch (170 definitions)
+### JoramSoch (174 definitions)
 
 - [Akaike information criterion](/D/aic)
 - [Alternative hypothesis](/D/h1)
 - [Bayesian information criterion](/D/bic)
 - [Bayesian model averaging](/D/bma)
 - [Bernoulli distribution](/D/bern)
 - [Beta distribution](/D/beta)
+- [Beta-binomial data](/D/betabin-data)
+- [Beta-binomial distribution](/D/betabin)
 - [Beta-distributed data](/D/beta-data)
 - [Binomial distribution](/D/bin)
 - [Binomial observations](/D/bin-data)
@@ -64,6 +66,7 @@ title: "Definition by Author"
 - [Explained sum of squares](/D/ess)
 - [Exponential distribution](/D/exp)
 - [F-distribution](/D/f)
+- [Family evidence](/D/fe)
 - [Flat, hard and soft prior distribution](/D/prior-flat)
 - [Full probability model](/D/fpm)
 - [Full width at half maximum](/D/fwhm)
@@ -100,6 +103,7 @@ title: "Definition by Author"
 - [Method-of-moments estimation](/D/mome)
 - [Minimum](/D/min)
 - [Mode](/D/mode)
+- [Model evidence](/D/me)
 - [Moment](/D/mom)
 - [Moment-generating function](/D/mgf)
 - [Multinomial distribution](/D/mult)

I/DbN.md

@@ -183,3 +183,7 @@ title: "Definition by Number"
 | D174 | ci | [Confidence interval](/D/ci) | JoramSoch | 2022-03-27 |
 | D175 | nw | [Normal-Wishart distribution](/D/nw) | JoramSoch | 2022-05-14 |
 | D176 | covmat-cross | [Cross-covariance matrix](/D/covmat-cross) | JoramSoch | 2022-09-26 |
+| D177 | betabin | [Beta-binomial distribution](/D/betabin) | JoramSoch | 2022-10-20 |
+| D178 | betabin-data | [Beta-binomial data](/D/betabin-data) | JoramSoch | 2022-10-20 |
+| D179 | me | [Model evidence](/D/me) | JoramSoch | 2022-10-20 |
+| D180 | fe | [Family evidence](/D/fe) | JoramSoch | 2022-10-20 |

I/DbT.md

@@ -16,6 +16,8 @@ title: "Definition by Topic"
 - [Bayesian model averaging](/D/bma)
 - [Bernoulli distribution](/D/bern)
 - [Beta distribution](/D/beta)
+- [Beta-binomial data](/D/betabin-data)
+- [Beta-binomial distribution](/D/betabin)
 - [Beta-distributed data](/D/beta-data)
 - [Binomial distribution](/D/bin)
 - [Binomial observations](/D/bin-data)
@@ -79,6 +81,7 @@ title: "Definition by Topic"
 ### F
 
 - [F-distribution](/D/f)
+- [Family evidence](/D/fe)
 - [Flat, hard and soft prior distribution](/D/prior-flat)
 - [Full probability model](/D/fpm)
 - [Full width at half maximum](/D/fwhm)
@@ -134,6 +137,7 @@ title: "Definition by Topic"
 - [Method-of-moments estimation](/D/mome)
 - [Minimum](/D/min)
 - [Mode](/D/mode)
+- [Model evidence](/D/me)
 - [Moment](/D/mom)
 - [Moment-generating function](/D/mgf)
 - [Multinomial distribution](/D/mult)

I/DwS.md

@@ -4,6 +4,7 @@ title: "Definitions without Source"
 ---
 
 
+- [Beta-binomial data](/D/betabin-data)
 - [Beta-distributed data](/D/beta-data)
 - [Binomial observations](/D/bin-data)
 - [Conditional differential entropy](/D/dent-cond)

I/PbA.md

@@ -8,7 +8,7 @@ title: "Proof by Author"
 
 - [Covariance matrix of the multinomial distribution](/P/mult-cov)
 
-### JoramSoch (344 proofs)
+### JoramSoch (349 proofs)
 
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
 - [Accuracy and complexity for the univariate Gaussian with known variance](/P/ugkv-anc)
@@ -58,6 +58,7 @@ title: "Proof by Author"
 - [Cumulative distribution function of a strictly increasing function of a random variable](/P/cdf-sifct)
 - [Cumulative distribution function of a sum of independent random variables](/P/cdf-sumind)
 - [Cumulative distribution function of the beta distribution](/P/beta-cdf)
+- [Cumulative distribution function of the beta-binomial distribution](/P/betabin-cdf)
 - [Cumulative distribution function of the continuous uniform distribution](/P/cuni-cdf)
 - [Cumulative distribution function of the discrete uniform distribution](/P/duni-cdf)
 - [Cumulative distribution function of the exponential distribution](/P/exp-cdf)
@@ -66,9 +67,11 @@ title: "Proof by Author"
 - [Derivation of Bayesian model averaging](/P/bma-der)
 - [Derivation of R² and adjusted R²](/P/rsq-der)
 - [Derivation of the Bayesian information criterion](/P/bic-der)
+- [Derivation of the family evidence](/P/fe-der)
 - [Derivation of the log Bayes factor](/P/lbf-der)
 - [Derivation of the log family evidence](/P/lfe-der)
 - [Derivation of the log model evidence](/P/lme-der)
+- [Derivation of the model evidence](/P/me-der)
 - [Derivation of the posterior model probability](/P/pmp-der)
 - [Deviance for multiple linear regression](/P/mlr-dev)
 - [Deviance information criterion for multiple linear regression](/P/blr-dic)
@@ -100,6 +103,7 @@ title: "Proof by Author"
 - [Expected value of x times ln(x) for a gamma distribution](/P/gam-xlogx)
 - [Exponential distribution is a special case of gamma distribution](/P/exp-gam)
 - [Expression of the cumulative distribution function of the normal distribution without the error function](/P/norm-cdfwerf)
+- [Expression of the probability mass function of the beta-binomial distribution using only the gamma function](/P/betabin-pmfitogf)
 - [Extreme points of the probability density function of the normal distribution](/P/norm-extr)
 - [First central moment is zero](/P/momcent-1st)
 - [First raw moment is mean](/P/momraw-1st)
@@ -264,6 +268,7 @@ title: "Proof by Author"
 - [Probability mass function of a sum of independent discrete random variables](/P/pmf-sumind)
 - [Probability mass function of an invertible function of a random vector](/P/pmf-invfct)
 - [Probability mass function of the Bernoulli distribution](/P/bern-pmf)
+- [Probability mass function of the beta-binomial distribution](/P/betabin-pmf)
 - [Probability mass function of the binomial distribution](/P/bin-pmf)
 - [Probability mass function of the categorical distribution](/P/cat-pmf)
 - [Probability mass function of the discrete uniform distribution](/P/duni-pmf)
@@ -380,10 +385,10 @@ title: "Proof by Author"
 
 ### tomfaulkenberry (7 proofs)
 
-- [Encompassing Prior Method for computing Bayes Factors](/P/bf-ep)
+- [Encompassing prior method for computing Bayes factors](/P/bf-ep)
 - [Mean of the Wald distribution](/P/wald-mean)
 - [Moment-generating function of the Wald distribution](/P/wald-mgf)
 - [Probability density function of the Wald distribution](/P/wald-pdf)
-- [Savage-Dickey Density Ratio for computing Bayes Factors](/P/bf-sddr)
+- [Savage-Dickey density ratio for computing Bayes factors](/P/bf-sddr)
 - [Transitivity of Bayes Factors](/P/bf-trans)
 - [Variance of the Wald distribution](/P/wald-var)

I/PbN.md

@@ -161,8 +161,8 @@ title: "Proof by Number"
 | P153 | mom-mgf | [Moment in terms of moment-generating function](/P/mom-mgf) | JoramSoch | 2020-08-19 |
 | P154 | mgf-ltt | [Linear transformation theorem for the moment-generating function](/P/mgf-ltt) | JoramSoch | 2020-08-19 |
 | P155 | mgf-lincomb | [Moment-generating function of linear combination of independent random variables](/P/mgf-lincomb) | JoramSoch | 2020-08-19 |
-| P156 | bf-sddr | [Savage-Dickey Density Ratio for computing Bayes Factors](/P/bf-sddr) | tomfaulkenberry | 2020-08-26 |
-| P157 | bf-ep | [Encompassing Prior Method for computing Bayes Factors](/P/bf-ep) | tomfaulkenberry | 2020-09-02 |
+| P156 | bf-sddr | [Savage-Dickey density ratio for computing Bayes factors](/P/bf-sddr) | tomfaulkenberry | 2020-08-26 |
+| P157 | bf-ep | [Encompassing prior method for computing Bayes factors](/P/bf-ep) | tomfaulkenberry | 2020-09-02 |
 | P158 | cov-ind | [Covariance of independent random variables](/P/cov-ind) | JoramSoch | 2020-09-03 |
 | P159 | mblr-prior | [Conjugate prior distribution for multivariate Bayesian linear regression](/P/mblr-prior) | JoramSoch | 2020-09-03 |
 | P160 | mblr-post | [Posterior distribution for multivariate Bayesian linear regression](/P/mblr-post) | JoramSoch | 2020-09-03 |
@@ -369,3 +369,8 @@ title: "Proof by Number"
 | P361 | pgf-zero | [Value of the probability-generating function for argument zero](/P/pgf-zero) | JoramSoch | 2022-10-11 |
 | P362 | pgf-one | [Value of the probability-generating function for argument one](/P/pgf-one) | JoramSoch | 2022-10-11 |
 | P363 | bin-pgf | [Probability-generating function of the binomial distribution](/P/bin-pgf) | JoramSoch | 2022-10-11 |
+| P364 | betabin-pmf | [Probability mass function of the beta-binomial distribution](/P/betabin-pmf) | JoramSoch | 2022-10-20 |
+| P365 | betabin-pmfitogf | [Expression of the probability mass function of the beta-binomial distribution using only the gamma function](/P/betabin-pmfitogf) | JoramSoch | 2022-10-20 |
+| P366 | betabin-cdf | [Cumulative distribution function of the beta-binomial distribution](/P/betabin-cdf) | JoramSoch | 2022-10-22 |
+| P367 | me-der | [Derivation of the model evidence](/P/me-der) | JoramSoch | 2022-10-20 |
+| P368 | fe-der | [Derivation of the family evidence](/P/fe-der) | JoramSoch | 2022-10-20 |

I/PbT.md

@@ -62,6 +62,7 @@ title: "Proof by Topic"
 - [Cumulative distribution function of a strictly increasing function of a random variable](/P/cdf-sifct)
 - [Cumulative distribution function of a sum of independent random variables](/P/cdf-sumind)
 - [Cumulative distribution function of the beta distribution](/P/beta-cdf)
+- [Cumulative distribution function of the beta-binomial distribution](/P/betabin-cdf)
 - [Cumulative distribution function of the continuous uniform distribution](/P/cuni-cdf)
 - [Cumulative distribution function of the discrete uniform distribution](/P/duni-cdf)
 - [Cumulative distribution function of the exponential distribution](/P/exp-cdf)
@@ -74,9 +75,11 @@ title: "Proof by Topic"
 - [Derivation of Bayesian model averaging](/P/bma-der)
 - [Derivation of R² and adjusted R²](/P/rsq-der)
 - [Derivation of the Bayesian information criterion](/P/bic-der)
+- [Derivation of the family evidence](/P/fe-der)
 - [Derivation of the log Bayes factor](/P/lbf-der)
 - [Derivation of the log family evidence](/P/lfe-der)
 - [Derivation of the log model evidence](/P/lme-der)
+- [Derivation of the model evidence](/P/me-der)
 - [Derivation of the posterior model probability](/P/pmp-der)
 - [Deviance for multiple linear regression](/P/mlr-dev)
 - [Deviance information criterion for multiple linear regression](/P/blr-dic)
@@ -94,7 +97,7 @@ title: "Proof by Topic"
 ### E
 
 - [Effects of mean-centering on parameter estimates for simple linear regression](/P/slr-meancent)
-- [Encompassing Prior Method for computing Bayes Factors](/P/bf-ep)
+- [Encompassing prior method for computing Bayes factors](/P/bf-ep)
 - [Entropy of the Bernoulli distribution](/P/bern-ent)
 - [Entropy of the binomial distribution](/P/bin-ent)
 - [Entropy of the categorical distribution](/P/cat-ent)
@@ -112,6 +115,7 @@ title: "Proof by Topic"
 - [Expected value of x times ln(x) for a gamma distribution](/P/gam-xlogx)
 - [Exponential distribution is a special case of gamma distribution](/P/exp-gam)
 - [Expression of the cumulative distribution function of the normal distribution without the error function](/P/norm-cdfwerf)
+- [Expression of the probability mass function of the beta-binomial distribution using only the gamma function](/P/betabin-pmfitogf)
 - [Extreme points of the probability density function of the normal distribution](/P/norm-extr)
 
 ### F
@@ -315,6 +319,7 @@ title: "Proof by Topic"
 - [Probability mass function of a sum of independent discrete random variables](/P/pmf-sumind)
 - [Probability mass function of an invertible function of a random vector](/P/pmf-invfct)
 - [Probability mass function of the Bernoulli distribution](/P/bern-pmf)
+- [Probability mass function of the beta-binomial distribution](/P/betabin-pmf)
 - [Probability mass function of the binomial distribution](/P/bin-pmf)
 - [Probability mass function of the categorical distribution](/P/cat-pmf)
 - [Probability mass function of the discrete uniform distribution](/P/duni-pmf)
@@ -380,7 +385,7 @@ title: "Proof by Topic"
 
 - [Sampling from the matrix-normal distribution](/P/matn-samp)
 - [Sampling from the normal-gamma distribution](/P/ng-samp)
-- [Savage-Dickey Density Ratio for computing Bayes Factors](/P/bf-sddr)
+- [Savage-Dickey density ratio for computing Bayes factors](/P/bf-sddr)
 - [Scaling of the covariance matrix upon multiplication with constant matrix](/P/covmat-scal)
 - [Scaling of the variance upon multiplication with a constant](/P/var-scal)
 - [Second central moment is variance](/P/momcent-2nd)

I/PwS.md

@@ -15,13 +15,16 @@ title: "Proofs without Source"
 - [Cross-validated log model evidence for the univariate Gaussian with known variance](/P/ugkv-cvlme)
 - [Cumulative distribution function in terms of probability density function of a continuous random variable](/P/cdf-pdf)
 - [Cumulative distribution function in terms of probability mass function of a discrete random variable](/P/cdf-pmf)
+- [Cumulative distribution function of the beta-binomial distribution](/P/betabin-cdf)
 - [Cumulative distribution function of the continuous uniform distribution](/P/cuni-cdf)
 - [Cumulative distribution function of the discrete uniform distribution](/P/duni-cdf)
 - [Cumulative distribution function of the exponential distribution](/P/exp-cdf)
 - [Derivation of Bayesian model averaging](/P/bma-der)
+- [Derivation of the family evidence](/P/fe-der)
 - [Derivation of the log Bayes factor](/P/lbf-der)
 - [Derivation of the log family evidence](/P/lfe-der)
 - [Derivation of the log model evidence](/P/lme-der)
+- [Derivation of the model evidence](/P/me-der)
 - [Derivation of the posterior model probability](/P/pmp-der)
 - [Deviance for multiple linear regression](/P/mlr-dev)
 - [Deviance information criterion for multiple linear regression](/P/blr-dic)