updated index pages

The index pages were updated with the recently added proofs.

Author: JoramSoch

I/PbA.md

@@ -16,7 +16,7 @@ title: "Proof by Author"
 
 - [Posterior predictive distribution is a marginal distribution of the joint likelihood](/P/postpred-jl)
 
-### JoramSoch (508 proofs)
+### JoramSoch (509 proofs)
 
 - [Accuracy and complexity for Bayesian linear regression](/P/blr-anc)
 - [Accuracy and complexity for Bayesian linear regression with known covariance](/P/blrkc-anc)
@@ -136,6 +136,7 @@ title: "Proof by Author"
 - [Entropy of the discrete uniform distribution](/P/duni-ent)
 - [Entropy of the multinomial distribution](/P/mult-ent)
 - [Entropy of the Poisson distribution](/P/poiss-ent)
+- [Equivalence of conditional and partial correlation for the multivariate normal distribution](/P/mvn-ecpc)
 - [Equivalence of log-likelihood ratio and mutual information for the general linear model](/P/glm-llrmi)
 - [Equivalence of log-likelihood ratios for regular and inverse general linear model](/P/iglm-llrs)
 - [Equivalence of matrix-normal distribution and multivariate normal distribution](/P/matn-mvn)

I/PbN.md

@@ -552,3 +552,4 @@ title: "Proof by Number"
 | P544 | glbf-der | [Derivation of the group log Bayes factor](/P/glbf-der) | JoramSoch | 2026-06-14 |
 | P545 | bmsrfx-freqpost | [Posterior frequencies for random-effects Bayesian model selection using Dirichlet posterior distribution](/P/bmsrfx-freqpost) | JoramSoch | 2026-06-29 |
 | P545 | bmsrfx-vb | [Variational Bayesian estimation of random-effects Bayesian model selection using the mean-field approximation](/P/bmsrfx-vb) | JoramSoch | 2026-06-24 |
+| P546 | mvn-ecpc | [Equivalence of conditional and partial correlation for the multivariate normal distribution](/P/mvn-ecpc) | JoramSoch | 2026-08-28 |

I/PbT.md

@@ -142,6 +142,7 @@ title: "Proof by Topic"
 - [Entropy of the discrete uniform distribution](/P/duni-ent)
 - [Entropy of the multinomial distribution](/P/mult-ent)
 - [Entropy of the Poisson distribution](/P/poiss-ent)
+- [Equivalence of conditional and partial correlation for the multivariate normal distribution](/P/mvn-ecpc)
 - [Equivalence of log-likelihood ratio and mutual information for the general linear model](/P/glm-llrmi)
 - [Equivalence of log-likelihood ratios for regular and inverse general linear model](/P/iglm-llrs)
 - [Equivalence of matrix-normal distribution and multivariate normal distribution](/P/matn-mvn)

I/PwS.md

@@ -4,7 +4,7 @@ title: "Proofs without Source"
 ---
 
 
-### Missing source (195 proofs)
+### Missing source (196 proofs)
 
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
 - [Accuracy and complexity for the univariate Gaussian with known variance](/P/ugkv-anc)
@@ -53,6 +53,7 @@ title: "Proofs without Source"
 - [Entropy of the discrete uniform distribution](/P/duni-ent)
 - [Entropy of the multinomial distribution](/P/mult-ent)
 - [Entropy of the Poisson distribution](/P/poiss-ent)
+- [Equivalence of conditional and partial correlation for the multivariate normal distribution](/P/mvn-ecpc)
 - [Expectation of a bilinear form](/P/mean-blf)
 - [Expectation of a quadratic form for the multivariate normal distribution](/P/mvn-meanqf)
 - [Expectation of the cross-validated log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-cvlbfmean)

I/ToC.md

@@ -675,16 +675,17 @@ title: "Table of Contents"
    &emsp;&ensp; 4.1.9. **[Expectation of a quadratic form](/P/mvn-meanqf)** <br>
    &emsp;&ensp; 4.1.10. **[Conditional correlation](/P/mvn-corrcond)** <br>
    &emsp;&ensp; 4.1.11. **[Partial correlation](/P/mvn-corrpart)** <br>
-   &emsp;&ensp; 4.1.12. **[Differential entropy](/P/mvn-dent)** <br>
-   &emsp;&ensp; 4.1.13. **[Mutual information](/P/mvn-mi)** <br>
-   &emsp;&ensp; 4.1.14. **[Kullback-Leibler divergence](/P/mvn-kl)** <br>
-   &emsp;&ensp; 4.1.15. **[Maximum entropy distribution](/P/mvn-maxent)** <br>
-   &emsp;&ensp; 4.1.16. **[Linear transformation](/P/mvn-ltt)** <br>
-   &emsp;&ensp; 4.1.17. **[Marginal distributions](/P/mvn-marg)** <br>
-   &emsp;&ensp; 4.1.18. **[Conditional distributions](/P/mvn-cond)** <br>
-   &emsp;&ensp; 4.1.19. **[Conditions for independence](/P/mvn-ind)** <br>
-   &emsp;&ensp; 4.1.20. **[Independence of products](/P/mvn-indprod)** <br>
-   &emsp;&ensp; 4.1.21. **[Drawing samples](/P/mvn-samp)** <br>
+   &emsp;&ensp; 4.1.12. **[Conditional and partial correlation](/P/mvn-ecpc)** <br>
+   &emsp;&ensp; 4.1.13. **[Differential entropy](/P/mvn-dent)** <br>
+   &emsp;&ensp; 4.1.14. **[Mutual information](/P/mvn-mi)** <br>
+   &emsp;&ensp; 4.1.15. **[Kullback-Leibler divergence](/P/mvn-kl)** <br>
+   &emsp;&ensp; 4.1.16. **[Maximum entropy distribution](/P/mvn-maxent)** <br>
+   &emsp;&ensp; 4.1.17. **[Linear transformation](/P/mvn-ltt)** <br>
+   &emsp;&ensp; 4.1.18. **[Marginal distributions](/P/mvn-marg)** <br>
+   &emsp;&ensp; 4.1.19. **[Conditional distributions](/P/mvn-cond)** <br>
+   &emsp;&ensp; 4.1.20. **[Conditions for independence](/P/mvn-ind)** <br>
+   &emsp;&ensp; 4.1.21. **[Independence of products](/P/mvn-indprod)** <br>
+   &emsp;&ensp; 4.1.22. **[Drawing samples](/P/mvn-samp)** <br>
 
    <p id="Bivariate normal distribution"></p>
    4.2. Bivariate normal distribution <br>