updated index pages

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

Author: JoramSoch

I/Definition_by_Author.md

@@ -4,7 +4,7 @@ title: "Definition by Author"
 ---
 
 
-### JoramSoch (111 definitions)
+### JoramSoch (119 definitions)
 
 - [Akaike information criterion](/D/aic)
 - [Bayesian information criterion](/D/bic)
@@ -21,6 +21,7 @@ title: "Definition by Author"
 - [Conditional entropy](/D/ent-cond)
 - [Conditional independence](/D/ind-cond)
 - [Conditional probability distribution](/D/dist-cond)
+- [Conjugate and non-conjugate prior distribution](/D/prior-conj)
 - [Constant](/D/const)
 - [Continuous uniform distribution](/D/cuni)
 - [Correlation](/D/corr)
@@ -38,17 +39,21 @@ title: "Definition by Author"
 - [Dirichlet-distributed data](/D/dir-data)
 - [Discrete and continuous random variable](/D/rvar-disc)
 - [Discrete uniform distribution](/D/duni)
+- [Empirical Bayes prior distribution](/D/prior-eb)
 - [Empirical Bayesian log model evidence](/D/eblme)
+- [Empirical and theoretical prior distribution](/D/prior-emp)
 - [Estimation matrix](/D/emat)
 - [Exceedance probability](/D/prob-exc)
 - [Expected value](/D/mean)
 - [Explained sum of squares](/D/ess)
 - [Exponential distribution](/D/exp)
+- [Flat, hard and soft prior distribution](/D/prior-flat)
 - [Full probability model](/D/fpm)
 - [Full width at half maximum](/D/fwhm)
 - [Gamma distribution](/D/gam)
 - [General linear model](/D/glm)
 - [Generative model](/D/gm)
+- [Informative and non-informative prior distribution](/D/prior-inf)
 - [Joint differential entropy](/D/dent-joint)
 - [Joint entropy](/D/ent-joint)
 - [Joint likelihood](/D/jl)
@@ -67,6 +72,7 @@ title: "Definition by Author"
 - [Marginal probability distribution](/D/dist-marg)
 - [Matrix-normal distribution](/D/matn)
 - [Maximum](/D/max)
+- [Maximum entropy prior distribution](/D/prior-maxent)
 - [Maximum likelihood estimation](/D/mle)
 - [Maximum log-likelihood](/D/mll)
 - [Median](/D/med)
@@ -102,6 +108,7 @@ title: "Definition by Author"
 - [Random variable](/D/rvar)
 - [Random vector](/D/rvec)
 - [Raw moment](/D/mom-raw)
+- [Reference prior distribution](/D/prior-ref)
 - [Residual sum of squares](/D/rss)
 - [Residual variance](/D/resvar)
 - [Residual-forming matrix](/D/rfmat)
@@ -112,6 +119,7 @@ title: "Definition by Author"
 - [Standardized moment](/D/mom-stand)
 - [Statistical independence](/D/ind)
 - [Total sum of squares](/D/tss)
+- [Uniform and non-uniform prior distribution](/D/prior-uni)
 - [Uniform-prior log model evidence](/D/uplme)
 - [Univariate and multivariate random variable](/D/rvar-uni)
 - [Variance](/D/var)

I/Definition_by_Number.md

@@ -122,3 +122,11 @@ title: "Definition by Number"
 | D113 | uplme | [Uniform-prior log model evidence](/D/uplme) | JoramSoch | 2020-11-25 |
 | D114 | eblme | [Empirical Bayesian log model evidence](/D/eblme) | JoramSoch | 2020-11-25 |
 | D115 | vblme | [Variational Bayesian log model evidence](/D/vblme) | JoramSoch | 2020-11-25 |
+| D116 | prior-flat | [Flat, hard and soft prior distribution](/D/prior-flat) | JoramSoch | 2020-12-02 |
+| D117 | prior-uni | [Uniform and non-uniform prior distribution](/D/prior-uni) | JoramSoch | 2020-12-02 |
+| D118 | prior-inf | [Informative and non-informative prior distribution](/D/prior-inf) | JoramSoch | 2020-12-02 |
+| D119 | prior-emp | [Empirical and theoretical prior distribution](/D/prior-emp) | JoramSoch | 2020-12-02 |
+| D120 | prior-conj | [Conjugate and non-conjugate prior distribution](/D/prior-conj) | JoramSoch | 2020-12-02 |
+| D121 | prior-maxent | [Maximum entropy prior distribution](/D/prior-maxent) | JoramSoch | 2020-12-02 |
+| D122 | prior-eb | [Empirical Bayes prior distribution](/D/prior-eb) | JoramSoch | 2020-12-02 |
+| D123 | prior-ref | [Reference prior distribution](/D/prior-ref) | JoramSoch | 2020-12-02 |

I/Definition_by_Topic.md

@@ -29,6 +29,7 @@ title: "Definition by Topic"
 - [Conditional entropy](/D/ent-cond)
 - [Conditional independence](/D/ind-cond)
 - [Conditional probability distribution](/D/dist-cond)
+- [Conjugate and non-conjugate prior distribution](/D/prior-conj)
 - [Constant](/D/const)
 - [Continuous uniform distribution](/D/cuni)
 - [Correlation](/D/corr)
@@ -53,7 +54,9 @@ title: "Definition by Topic"
 
 ### E
 
+- [Empirical Bayes prior distribution](/D/prior-eb)
 - [Empirical Bayesian log model evidence](/D/eblme)
+- [Empirical and theoretical prior distribution](/D/prior-emp)
 - [Encompassing model](/D/encm)
 - [Estimation matrix](/D/emat)
 - [Exceedance probability](/D/prob-exc)
@@ -63,6 +66,7 @@ title: "Definition by Topic"
 
 ### F
 
+- [Flat, hard and soft prior distribution](/D/prior-flat)
 - [Full probability model](/D/fpm)
 - [Full width at half maximum](/D/fwhm)
 
@@ -72,6 +76,10 @@ title: "Definition by Topic"
 - [General linear model](/D/glm)
 - [Generative model](/D/gm)
 
+### I
+
+- [Informative and non-informative prior distribution](/D/prior-inf)
+
 ### J
 
 - [Joint differential entropy](/D/dent-joint)
@@ -101,6 +109,7 @@ title: "Definition by Topic"
 - [Marginal probability distribution](/D/dist-marg)
 - [Matrix-normal distribution](/D/matn)
 - [Maximum](/D/max)
+- [Maximum entropy prior distribution](/D/prior-maxent)
 - [Maximum likelihood estimation](/D/mle)
 - [Maximum log-likelihood](/D/mll)
 - [Median](/D/med)
@@ -148,6 +157,7 @@ title: "Definition by Topic"
 - [Random variable](/D/rvar)
 - [Random vector](/D/rvec)
 - [Raw moment](/D/mom-raw)
+- [Reference prior distribution](/D/prior-ref)
 - [Residual sum of squares](/D/rss)
 - [Residual variance](/D/resvar)
 - [Residual-forming matrix](/D/rfmat)
@@ -167,6 +177,7 @@ title: "Definition by Topic"
 
 ### U
 
+- [Uniform and non-uniform prior distribution](/D/prior-uni)
 - [Uniform-prior log model evidence](/D/uplme)
 - [Univariate and multivariate random variable](/D/rvar-uni)
 

I/Proof_by_Author.md

@@ -4,9 +4,10 @@ title: "Proof by Author"
 ---
 
 
-### JoramSoch (189 proofs)
+### JoramSoch (191 proofs)
 
 - [(Non-)Multiplicativity of the expected value](/P/mean-mult)
+- [Addition of the differential entropy upon multiplication with a constant](/P/dent-add)
 - [Additivity of the Kullback-Leibler divergence for independent distributions](/P/kl-add)
 - [Additivity of the variance for independent random variables](/P/var-add)
 - [Bayes' rule](/P/bayes-rule)
@@ -58,6 +59,7 @@ title: "Proof by Author"
 - [Gaussian integral](/P/norm-gi)
 - [Gibbs' inequality](/P/gibbs-ineq)
 - [Invariance of the Kullback-Leibler divergence under parameter transformation](/P/kl-inv)
+- [Invariance of the differential entropy under addition of a constant](/P/dent-inv)
 - [Invariance of the variance under addition of a constant](/P/var-inv)
 - [Joint likelihood is the product of likelihood function and prior density](/P/jl-lfnprior)
 - [Kullback-Leibler divergence for the gamma distribution](/P/gam-kl)

I/Proof_by_Number.md

@@ -205,3 +205,5 @@ title: "Proof by Number"
 | P196 | norm-gi | [Gaussian integral](/P/norm-gi) | JoramSoch | 2020-11-25 |
 | P197 | chi2-pdf | [Probability density function of the chi-square distribution](/P/chi2-pdf) | JoramSoch | 2020-11-25 |
 | P198 | beta-mgf | [Moment-generating function of the beta distribution](/P/beta-mgf) | JoramSoch | 2020-11-25 |
+| P199 | dent-inv | [Invariance of the differential entropy under addition of a constant](/P/dent-inv) | JoramSoch | 2020-12-02 |
+| P200 | dent-add | [Addition of the differential entropy upon multiplication with a constant](/P/dent-add) | JoramSoch | 2020-12-02 |

I/Proof_by_Topic.md

@@ -10,6 +10,7 @@ title: "Proof by Topic"
 
 ### A
 
+- [Addition of the differential entropy upon multiplication with a constant](/P/dent-add)
 - [Additivity of the Kullback-Leibler divergence for independent distributions](/P/kl-add)
 - [Additivity of the variance for independent random variables](/P/var-add)
 
@@ -84,6 +85,7 @@ title: "Proof by Topic"
 ### I
 
 - [Invariance of the Kullback-Leibler divergence under parameter transformation](/P/kl-inv)
+- [Invariance of the differential entropy under addition of a constant](/P/dent-inv)
 - [Invariance of the variance under addition of a constant](/P/var-inv)
 
 ### J