updated index pages

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

Author: JoramSoch

I/PbA.md

@@ -8,7 +8,7 @@ title: "Proof by Author"
 
 - [Covariance matrix of the multinomial distribution](/P/mult-cov)
 
-### JoramSoch (361 proofs)
+### JoramSoch (369 proofs)
 
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
 - [Accuracy and complexity for the univariate Gaussian with known variance](/P/ugkv-anc)
@@ -142,6 +142,8 @@ title: "Proof by Author"
 - [Linear transformation theorem for the moment-generating function](/P/mgf-ltt)
 - [Linear transformation theorem for the multivariate normal distribution](/P/mvn-ltt)
 - [Linearity of the expected value](/P/mean-lin)
+- [Log Bayes factor for binomial observations](/P/bin-lbf)
+- [Log Bayes factor for multinomial observations](/P/mult-lbf)
 - [Log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-lbf)
 - [Log Bayes factor in terms of log model evidences](/P/lbf-lme)
 - [Log family evidences in terms of log model evidences](/P/lfe-lme)
@@ -163,7 +165,9 @@ title: "Proof by Author"
 - [Marginal distributions of the normal-gamma distribution](/P/ng-marg)
 - [Marginal likelihood is a definite integral of joint likelihood](/P/ml-jl)
 - [Maximum likelihood estimation can result in biased estimates](/P/mle-bias)
+- [Maximum likelihood estimation for binomial observations](/P/bin-mle)
 - [Maximum likelihood estimation for Dirichlet-distributed data](/P/dir-mle)
+- [Maximum likelihood estimation for multinomial observations](/P/mult-mle)
 - [Maximum likelihood estimation for multiple linear regression](/P/mlr-mle)
 - [Maximum likelihood estimation for Poisson-distributed data](/P/poiss-mle)
 - [Maximum likelihood estimation for simple linear regression](/P/slr-mle)
@@ -173,6 +177,8 @@ title: "Proof by Author"
 - [Maximum likelihood estimation for the univariate Gaussian](/P/ug-mle)
 - [Maximum likelihood estimation for the univariate Gaussian with known variance](/P/ugkv-mle)
 - [Maximum likelihood estimator of variance is biased](/P/resvar-bias)
+- [Maximum log-likelihood for binomial observations](/P/bin-mll)
+- [Maximum log-likelihood for multinomial observations](/P/mult-mll)
 - [Maximum log-likelihood for multiple linear regression](/P/mlr-mll)
 - [Mean of the Bernoulli distribution](/P/bern-mean)
 - [Mean of the beta distribution](/P/beta-mean)
@@ -252,6 +258,8 @@ title: "Proof by Author"
 - [Posterior model probabilities in terms of log model evidences](/P/pmp-lme)
 - [Posterior model probability in terms of log Bayes factor](/P/pmp-lbf)
 - [Posterior probability of the alternative hypothesis for Bayesian linear regression](/P/blr-pp)
+- [Posterior probability of the alternative model for binomial observations](/P/bin-pp)
+- [Posterior probability of the alternative model for multinomial observations](/P/mult-pp)
 - [Probability and log-odds in logistic regression](/P/logreg-pnlo)
 - [Probability density function is first derivative of cumulative distribution function](/P/pdf-cdf)
 - [Probability density function of a linear function of a continuous random vector](/P/pdf-linfct)

I/PbN.md

@@ -386,3 +386,11 @@ title: "Proof by Number"
 | P378 | anova2-cochran | [Application of Cochran's theorem to two-way analysis of variance](/P/anova2-cochran) | JoramSoch | 2022-11-16 |
 | P379 | anova2-pss | [Partition of sums of squares in two-way analysis of variance](/P/anova2-pss) | JoramSoch | 2022-11-16 |
 | P380 | anova2-fols | [F-statistics in terms of ordinary least squares estimates in two-way analysis of variance](/P/anova2-fols) | JoramSoch | 2022-11-16 |
+| P381 | bin-mle | [Maximum likelihood estimation for binomial observations](/P/bin-mle) | JoramSoch | 2022-11-23 |
+| P382 | bin-mll | [Maximum log-likelihood for binomial observations](/P/bin-mll) | JoramSoch | 2022-11-24 |
+| P383 | bin-lbf | [Log Bayes factor for binomial observations](/P/bin-lbf) | JoramSoch | 2022-11-25 |
+| P384 | bin-pp | [Posterior probability of the alternative model for binomial observations](/P/bin-pp) | JoramSoch | 2022-11-26 |
+| P385 | mult-mle | [Maximum likelihood estimation for multinomial observations](/P/mult-mle) | JoramSoch | 2022-12-02 |
+| P386 | mult-mll | [Maximum log-likelihood for multinomial observations](/P/mult-mll) | JoramSoch | 2022-12-02 |
+| P387 | mult-lbf | [Log Bayes factor for multinomial observations](/P/mult-lbf) | JoramSoch | 2022-12-02 |
+| P388 | mult-pp | [Posterior probability of the alternative model for multinomial observations](/P/mult-pp) | JoramSoch | 2022-12-02 |

I/PbT.md

@@ -172,6 +172,8 @@ title: "Proof by Topic"
 - [Linear transformation theorem for the moment-generating function](/P/mgf-ltt)
 - [Linear transformation theorem for the multivariate normal distribution](/P/mvn-ltt)
 - [Linearity of the expected value](/P/mean-lin)
+- [Log Bayes factor for binomial observations](/P/bin-lbf)
+- [Log Bayes factor for multinomial observations](/P/mult-lbf)
 - [Log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-lbf)
 - [Log Bayes factor in terms of log model evidences](/P/lbf-lme)
 - [Log family evidences in terms of log model evidences](/P/lfe-lme)
@@ -196,7 +198,9 @@ title: "Proof by Topic"
 - [Marginal distributions of the normal-gamma distribution](/P/ng-marg)
 - [Marginal likelihood is a definite integral of joint likelihood](/P/ml-jl)
 - [Maximum likelihood estimation can result in biased estimates](/P/mle-bias)
+- [Maximum likelihood estimation for binomial observations](/P/bin-mle)
 - [Maximum likelihood estimation for Dirichlet-distributed data](/P/dir-mle)
+- [Maximum likelihood estimation for multinomial observations](/P/mult-mle)
 - [Maximum likelihood estimation for multiple linear regression](/P/mlr-mle)
 - [Maximum likelihood estimation for Poisson-distributed data](/P/poiss-mle)
 - [Maximum likelihood estimation for simple linear regression](/P/slr-mle)
@@ -206,6 +210,8 @@ title: "Proof by Topic"
 - [Maximum likelihood estimation for the univariate Gaussian](/P/ug-mle)
 - [Maximum likelihood estimation for the univariate Gaussian with known variance](/P/ugkv-mle)
 - [Maximum likelihood estimator of variance is biased](/P/resvar-bias)
+- [Maximum log-likelihood for binomial observations](/P/bin-mll)
+- [Maximum log-likelihood for multinomial observations](/P/mult-mll)
 - [Maximum log-likelihood for multiple linear regression](/P/mlr-mll)
 - [Mean of the Bernoulli distribution](/P/bern-mean)
 - [Mean of the beta distribution](/P/beta-mean)
@@ -301,6 +307,8 @@ title: "Proof by Topic"
 - [Posterior model probabilities in terms of log model evidences](/P/pmp-lme)
 - [Posterior model probability in terms of log Bayes factor](/P/pmp-lbf)
 - [Posterior probability of the alternative hypothesis for Bayesian linear regression](/P/blr-pp)
+- [Posterior probability of the alternative model for binomial observations](/P/bin-pp)
+- [Posterior probability of the alternative model for multinomial observations](/P/mult-pp)
 - [Probability and log-odds in logistic regression](/P/logreg-pnlo)
 - [Probability density function is first derivative of cumulative distribution function](/P/pdf-cdf)
 - [Probability density function of a linear function of a continuous random vector](/P/pdf-linfct)

I/PwS.md

@@ -46,6 +46,8 @@ title: "Proofs without Source"
 - [Kullback-Leibler divergence for the normal distribution](/P/norm-kl)
 - [Linear combination of independent normal random variables](/P/norm-lincomb)
 - [Linear transformation theorem for the matrix-normal distribution](/P/matn-ltt)
+- [Log Bayes factor for binomial observations](/P/bin-lbf)
+- [Log Bayes factor for multinomial observations](/P/mult-lbf)
 - [Log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-lbf)
 - [Log model evidence for multinomial observations](/P/mult-lme)
 - [Log model evidence for multivariate Bayesian linear regression](/P/mblr-lme)
@@ -58,12 +60,15 @@ title: "Proofs without Source"
 - [Marginal distributions of the normal-gamma distribution](/P/ng-marg)
 - [Marginal likelihood is a definite integral of joint likelihood](/P/ml-jl)
 - [Maximum likelihood estimation can result in biased estimates](/P/mle-bias)
+- [Maximum likelihood estimation for multinomial observations](/P/mult-mle)
 - [Maximum likelihood estimation for multiple linear regression](/P/mlr-mle)
 - [Maximum likelihood estimation for Poisson-distributed data](/P/poiss-mle)
 - [Maximum likelihood estimation for simple linear regression](/P/slr-mle)
 - [Maximum likelihood estimation for simple linear regression](/P/slr-mle2)
 - [Maximum likelihood estimation for the general linear model](/P/glm-mle)
 - [Maximum likelihood estimation for the Poisson distribution with exposure values](/P/poissexp-mle)
+- [Maximum log-likelihood for binomial observations](/P/bin-mll)
+- [Maximum log-likelihood for multinomial observations](/P/mult-mll)
 - [Mean of the categorical distribution](/P/cat-mean)
 - [Mean of the continuous uniform distribution](/P/cuni-mean)
 - [Mean of the multinomial distribution](/P/mult-mean)
@@ -84,6 +89,8 @@ title: "Proofs without Source"
 - [Ordinary least squares for the general linear model](/P/glm-ols)
 - [Parameter estimates for simple linear regression are uncorrelated after mean-centering](/P/slr-olscorr)
 - [Posterior density is proportional to joint likelihood](/P/post-jl)
+- [Posterior probability of the alternative model for binomial observations](/P/bin-pp)
+- [Posterior probability of the alternative model for multinomial observations](/P/mult-pp)
 - [Probability density function of the beta distribution](/P/beta-pdf)
 - [Probability density function of the continuous uniform distribution](/P/cuni-pdf)
 - [Probability density function of the Dirichlet distribution](/P/dir-pdf)