update book_content.md, construct_toc.py

Author: kantundpeterpan

I/ToC.md

@@ -5,13 +5,14 @@ title: "Table of Contents"
 
 
 **[Proofs](/P/-temp-)** are printed in **bold** – *[Definitions](/D/-temp-)* are set in *italics* <br>
-**Proofs**: [by Number](/I/PbN), [by Topic](/I/PbT) – *Definitions*:  [by Number](/I/DbN), [by Topic](/I/DbT) <br>
+**Proofs**: [by Number](/I/PbN), [by Topic](/I/PbT) – *Definitions*:  [by Number](/I/DbN), [by Topic](/D/DbT) <br>
 <u>Specials:</u> [General Theorems](/S/ChI), [Probability Distributions](/S/ChII), [Statistical Models](/S/ChIII), [Model Selection Criteria](/S/ChIV) <br>
 
 
 <br>
 <h3 id="General Theorems">Chapter I: General Theorems</h3>
 
+   
 1. <p id="Probability theory">Probability theory</p>
 
    <p id="Random experiments"></p>
@@ -110,10 +111,10 @@ title: "Table of Contents"
    &emsp;&ensp; 1.8.5. **[Cumulative distribution function of discrete random variable](/P/cdf-pmf)** <br>
    &emsp;&ensp; 1.8.6. **[Cumulative distribution function of continuous random variable](/P/cdf-pdf)** <br>
    &emsp;&ensp; 1.8.7. **[Exceedance probability based on cumulative distribution function](/P/cdf-probexc)** <br>
-   &emsp;&ensp; 1.8.7. **[Probability integral transform](/P/cdf-pit)** <br>
-   &emsp;&ensp; 1.8.8. **[Inverse transformation method](/P/cdf-itm)** <br>
-   &emsp;&ensp; 1.8.9. **[Distributional transformation](/P/cdf-dt)** <br>
-   &emsp;&ensp; 1.8.10. *[Joint cumulative distribution function](/D/cdf-joint)* <br>
+   &emsp;&ensp; 1.8.8. **[Probability integral transform](/P/cdf-pit)** <br>
+   &emsp;&ensp; 1.8.9. **[Inverse transformation method](/P/cdf-itm)** <br>
+   &emsp;&ensp; 1.8.10. **[Distributional transformation](/P/cdf-dt)** <br>
+   &emsp;&ensp; 1.8.11. *[Joint cumulative distribution function](/D/cdf-joint)* <br>
 
    <p id="Moment-generating function"></p>
    1.9. Moment-generating function <br>
@@ -166,16 +167,16 @@ title: "Table of Contents"
    &emsp;&ensp; 1.13.1. *[Definition](/D/var)* <br>
    &emsp;&ensp; 1.13.2. *[Sample variance](/D/var-samp)* <br>
    &emsp;&ensp; 1.13.3. *[Pooled sample variance](/D/var-pool)* <br>
-   &emsp;&ensp; 1.13.3. **[Partition into expected values](/P/var-mean)** <br>
-   &emsp;&ensp; 1.13.4. **[Non-negativity](/P/var-nonneg)** <br>
-   &emsp;&ensp; 1.13.5. **[Variance of a constant](/P/var-const)** <br>
-   &emsp;&ensp; 1.13.6. **[Invariance under addition](/P/var-inv)** <br>
-   &emsp;&ensp; 1.13.7. **[Scaling upon multiplication](/P/var-scal)** <br>
-   &emsp;&ensp; 1.13.8. **[Variance of a sum](/P/var-sum)** <br>
-   &emsp;&ensp; 1.13.9. **[Variance of linear combination](/P/var-lincomb)** <br>
-   &emsp;&ensp; 1.13.10. **[Additivity under independence](/P/var-add)** <br>
-   &emsp;&ensp; 1.13.11. **[Law of total variance](/P/var-tot)** <br>
-   &emsp;&ensp; 1.13.12. *[Precision](/D/prec)* <br>
+   &emsp;&ensp; 1.13.4. **[Partition into expected values](/P/var-mean)** <br>
+   &emsp;&ensp; 1.13.5. **[Non-negativity](/P/var-nonneg)** <br>
+   &emsp;&ensp; 1.13.6. **[Variance of a constant](/P/var-const)** <br>
+   &emsp;&ensp; 1.13.7. **[Invariance under addition](/P/var-inv)** <br>
+   &emsp;&ensp; 1.13.8. **[Scaling upon multiplication](/P/var-scal)** <br>
+   &emsp;&ensp; 1.13.9. **[Variance of a sum](/P/var-sum)** <br>
+   &emsp;&ensp; 1.13.10. **[Variance of linear combination](/P/var-lincomb)** <br>
+   &emsp;&ensp; 1.13.11. **[Additivity under independence](/P/var-add)** <br>
+   &emsp;&ensp; 1.13.12. **[Law of total variance](/P/var-tot)** <br>
+   &emsp;&ensp; 1.13.13. *[Precision](/D/prec)* <br>
 
    <p id="Skewness"></p>
    1.14. Skewness <br>
@@ -249,7 +250,7 @@ title: "Table of Contents"
    &emsp;&ensp; 1.21.7. **[First central moment is zero](/P/momcent-1st)** <br>
    &emsp;&ensp; 1.21.8. **[Second central moment is variance](/P/momcent-2nd)** <br>
    &emsp;&ensp; 1.21.9. *[Standardized moment](/D/mom-stand)* <br>
-
+   
 2. <p id="Information theory">Information theory</p>
 
    <p id="Shannon entropy"></p>
@@ -302,7 +303,7 @@ title: "Table of Contents"
    &emsp;&ensp; 2.5.8. **[Invariance under parameter transformation](/P/kl-inv)** <br>
    &emsp;&ensp; 2.5.9. **[Relation to discrete entropy](/P/kl-ent)** <br>
    &emsp;&ensp; 2.5.10. **[Relation to differential entropy](/P/kl-dent)** <br>
-
+   
 3. <p id="Estimation theory">Estimation theory</p>
 
    <p id="Basic concepts of estimation"></p>
@@ -319,7 +320,7 @@ title: "Table of Contents"
    3.3. Interval estimates <br>
    &emsp;&ensp; 3.3.1. *[Confidence interval](/D/ci)* <br>
    &emsp;&ensp; 3.3.2. **[Construction of confidence intervals using Wilks' theorem](/P/ci-wilks)** <br>
-
+   
 4. <p id="Frequentist statistics">Frequentist statistics</p>
 
    <p id="Likelihood theory"></p>
@@ -355,7 +356,7 @@ title: "Table of Contents"
    &emsp;&ensp; 4.3.11. **[Distribution of p-value under null hypothesis](/P/pval-h0)** <br>
    &emsp;&ensp; 4.3.12. *[Minimum detectable effect](/D/mde)* <br>
    &emsp;&ensp; 4.3.13. *[Minimum required sample size](/D/mrss)* <br>
-
+   
 5. <p id="Bayesian statistics">Bayesian statistics</p>
 
    <p id="Probabilistic modeling"></p>
@@ -397,7 +398,7 @@ title: "Table of Contents"
    &emsp;&ensp; 5.3.5. *[Variational Bayes](/D/vb)* <br>
    &emsp;&ensp; 5.3.6. **[Decomposition of the free energy](/P/fren-dec)** <br>
    &emsp;&ensp; 5.3.7. **[Free energy is lower bound on log model evidence](/P/fren-lme)** <br>
-
+   
 6. <p id="Machine learning">Machine learning</p>
 
    <p id="Scoring rules"></p>
@@ -414,6 +415,7 @@ title: "Table of Contents"
 <br>
 <h3 id="Probability Distributions">Chapter II: Probability Distributions</h3>
 
+   
 1. <p id="Univariate discrete distributions">Univariate discrete distributions</p>
 
    <p id="Discrete uniform distribution"></p>
@@ -465,7 +467,7 @@ title: "Table of Contents"
    &emsp;&ensp; 1.5.3. **[Mean](/P/poiss-mean)** <br>
    &emsp;&ensp; 1.5.4. **[Variance](/P/poiss-var)** <br>
    &emsp;&ensp; 1.5.5. **[Shannon entropy](/P/poiss-ent)** <br>
-
+   
 2. <p id="Multivariate discrete distributions">Multivariate discrete distributions</p>
 
    <p id="Categorical distribution"></p>
@@ -485,7 +487,7 @@ title: "Table of Contents"
    &emsp;&ensp; 2.2.5. **[Covariance](/P/mult-cov)** <br>
    &emsp;&ensp; 2.2.6. **[Shannon entropy](/P/mult-ent)** <br>
    &emsp;&ensp; 2.2.7. **[Marginal distributions](/P/mult-marg)** <br>
-
+   
 3. <p id="Univariate continuous distributions">Univariate continuous distributions</p>
 
    <p id="Continuous uniform distribution"></p>
@@ -635,7 +637,7 @@ title: "Table of Contents"
    &emsp;&ensp; 3.11.5. **[Variance](/P/exg-var)** <br>
    &emsp;&ensp; 3.11.6. **[Skewness](/P/exg-skew)** <br>
    &emsp;&ensp; 3.11.7. **[Method of moments](/P/exg-mome)** <br>
-
+   
 4. <p id="Multivariate continuous distributions">Multivariate continuous distributions</p>
 
    <p id="Multivariate normal distribution"></p>
@@ -694,7 +696,7 @@ title: "Table of Contents"
    &emsp;&ensp; 4.5.2. **[Probability density function](/P/dir-pdf)** <br>
    &emsp;&ensp; 4.5.3. **[Kullback-Leibler divergence](/P/dir-kl)** <br>
    &emsp;&ensp; 4.5.4. **[Exceedance probabilities](/P/dir-ep)** <br>
-
+   
 5. <p id="Matrix-variate continuous distributions">Matrix-variate continuous distributions</p>
 
    <p id="Matrix-normal distribution"></p>
@@ -728,6 +730,7 @@ title: "Table of Contents"
 <br>
 <h3 id="Statistical Models">Chapter III: Statistical Models</h3>
 
+   
 1. <p id="Univariate normal data">Univariate normal data</p>
 
    <p id="Univariate Gaussian"></p>
@@ -872,7 +875,7 @@ title: "Table of Contents"
    &emsp;&ensp; 1.7.4. **[Accuracy and complexity](/P/blrkc-anc)** <br>
 
 2. <p id="Multivariate normal data">Multivariate normal data</p>
-
+   
    <p id="Multivariate Gaussian"></p>
    2.1. Multivariate Gaussian <br>
    &emsp;&ensp; 2.1.1. *[Bivariate normally distributed data](/D/bvn-data)* <br>
@@ -912,7 +915,7 @@ title: "Table of Contents"
    &emsp;&ensp; 2.5.1. **[Conjugate prior distribution](/P/mblr-prior)** <br>
    &emsp;&ensp; 2.5.2. **[Posterior distribution](/P/mblr-post)** <br>
    &emsp;&ensp; 2.5.3. **[Log model evidence](/P/mblr-lme)** <br>
-
+   
 3. <p id="Count data">Count data</p>
 
    <p id="Binomial observations"></p>
@@ -958,7 +961,7 @@ title: "Table of Contents"
    &emsp;&ensp; 3.4.3. **[Conjugate prior distribution](/P/poissexp-prior)** <br>
    &emsp;&ensp; 3.4.4. **[Posterior distribution](/P/poissexp-post)** <br>
    &emsp;&ensp; 3.4.5. **[Log model evidence](/P/poissexp-lme)** <br>
-
+   
 4. <p id="Frequency data">Frequency data</p>
 
    <p id="Beta-distributed data"></p>
@@ -975,7 +978,7 @@ title: "Table of Contents"
    4.3. Beta-binomial data <br>
    &emsp;&ensp; 4.3.1. *[Definition](/D/betabin-data)* <br>
    &emsp;&ensp; 4.3.2. **[Method of moments](/P/betabin-mome)** <br>
-
+   
 5. <p id="Categorical data">Categorical data</p>
 
    <p id="Logistic regression"></p>
@@ -988,6 +991,7 @@ title: "Table of Contents"
 <br>
 <h3 id="Model Selection">Chapter IV: Model Selection</h3>
 
+   
 1. <p id="Goodness-of-fit measures">Goodness-of-fit measures</p>
 
    <p id="Residual variance"></p>
@@ -1020,7 +1024,7 @@ title: "Table of Contents"
    &emsp;&ensp; 1.4.1. *[Definition](/D/snr)* <br>
    &emsp;&ensp; 1.4.2. **[Relationship to coefficient of determination](/P/snr-rsq)** <br>
    &emsp;&ensp; 1.4.3. **[Relationship to maximum log-likelihood](/P/snr-mll)** <br>
-
+   
 2. <p id="Classical information criteria">Classical information criteria</p>
 
    <p id="Akaike information criterion"></p>
@@ -1039,7 +1043,7 @@ title: "Table of Contents"
    2.3. Deviance information criterion <br>
    &emsp;&ensp; 2.3.1. *[Definition](/D/dic)* <br>
    &emsp;&ensp; 2.3.2. *[Deviance](/D/dev)* <br>
-
+   
 3. <p id="Bayesian model selection">Bayesian model selection</p>
 
    <p id="Model evidence"></p>
@@ -1088,4 +1092,4 @@ title: "Table of Contents"
    3.5. Bayesian model averaging <br>
    &emsp;&ensp; 3.5.1. *[Definition](/D/bma)* <br>
    &emsp;&ensp; 3.5.2. **[Derivation](/P/bma-der)** <br>
-   &emsp;&ensp; 3.5.3. **[Calculation from log model evidences](/P/bma-lme)** <br>
+   &emsp;&ensp; 3.5.3. **[Calculation from log model evidences](/P/bma-lme)** <br>

book_content.md

@@ -33,18 +33,18 @@
 - **[Probability under exclusivity](/P/prob-exc)**
 ### Probability axioms
 - *[Axioms of probability](/D/prob-ax)*
-- **[Monotonicity of probability](/P/prob-mon)**
-- **[Monotonicity of probability](/P/prob-mon2)**
-- **[Probability of the empty set](/P/prob-emp)**
-- **[Probability of the empty set](/P/prob-emp2)**
+- **[Monotonicity of probability](/P/prob-mon)** (1) 
+- **[Monotonicity of probability](/P/prob-mon2)** (2) 
+- **[Probability of the empty set](/P/prob-emp)** (1) 
+- **[Probability of the empty set](/P/prob-emp2)** (2) 
 - **[Probability of the complement](/P/prob-comp)**
 - **[Range of probability](/P/prob-range)**
 - **[Addition law of probability](/P/prob-add)**
 - **[Bonferroni's inequality](/P/bonf-ineq)**
 - **[Boole's inequality](/P/bool-ineq)**
 - **[Law of total probability](/P/prob-tot)**
-- **[Probability of exhaustive events](/P/prob-exh)**
-- **[Probability of exhaustive events](/P/prob-exh2)**
+- **[Probability of exhaustive events](/P/prob-exh)** (1) 
+- **[Probability of exhaustive events](/P/prob-exh2)** (2) 
 ### Probability distributions
 - *[Probability distribution](/D/dist)*
 - *[Joint distribution](/D/dist-joint)*
@@ -227,9 +227,9 @@
 - **[Relation to joint and conditional differential entropy](/P/cmi-jcde)**
 ### Kullback-Leibler divergence
 - *[Definition](/D/kl)*
-- **[Non-negativity](/P/kl-nonneg)**
-- **[Non-negativity](/P/kl-nonneg2)**
-- **[Non-negativity](/P/kl-nonneg3)**
+- **[Non-negativity](/P/kl-nonneg)** (1) 
+- **[Non-negativity](/P/kl-nonneg2)** (2) 
+- **[Non-negativity](/P/kl-nonneg3)** (3) 
 - **[Non-symmetry](/P/kl-nonsymm)**
 - **[Convexity](/P/kl-conv)**
 - **[Additivity for independent distributions](/P/kl-add)**
@@ -395,9 +395,9 @@
 - *[Definition](/D/norm)*
 - **[Special case of multivariate normal distribution](/P/norm-mvn)**
 - *[Standard normal distribution](/D/snorm)*
-- **[Relationship to standard normal distribution](/P/norm-snorm)**
-- **[Relationship to standard normal distribution](/P/norm-snorm2)**
-- **[Relationship to standard normal distribution](/P/norm-snorm3)**
+- **[Relationship to standard normal distribution](/P/norm-snorm)** (1) 
+- **[Relationship to standard normal distribution](/P/norm-snorm2)** (2) 
+- **[Relationship to standard normal distribution](/P/norm-snorm3)** (3) 
 - **[Relationship to chi-squared distribution](/P/norm-chi2)**
 - **[Relationship to t-distribution](/P/norm-t)**
 - **[Gaussian integral](/P/norm-gi)**
@@ -430,8 +430,8 @@
 - *[Definition](/D/gam)*
 - **[Special case of Wishart distribution](/P/gam-wish)**
 - *[Standard gamma distribution](/D/sgam)*
-- **[Relationship to standard gamma distribution](/P/gam-sgam)**
-- **[Relationship to standard gamma distribution](/P/gam-sgam2)**
+- **[Relationship to standard gamma distribution](/P/gam-sgam)** (1) 
+- **[Relationship to standard gamma distribution](/P/gam-sgam2)** (2) 
 - **[Scaling of a gamma random variable](/P/gam-scal)**
 - **[Probability density function](/P/gam-pdf)**
 - **[Moment-generating function](/P/gam-mgf)**
@@ -564,8 +564,8 @@
 - **[Transposition](/P/matn-trans)**
 - **[Linear transformation](/P/matn-ltt)**
 - **[Marginal distributions](/P/matn-marg)**
-- **[Redundancy of parameters](/P/matn-red)**
-- **[Redundancy of parameters](/P/matn-red2)**
+- **[Redundancy of parameters](/P/matn-red)** (1) 
+- **[Redundancy of parameters](/P/matn-red2)** (2) 
 - **[Drawing samples](/P/matn-samp)**
 ### Wishart distribution
 - *[Definition](/D/wish)*
@@ -626,8 +626,8 @@
 ### Simple linear regression
 - *[Definition](/D/slr)*
 - **[Special case of multiple linear regression](/P/slr-mlr)**
-- **[Ordinary least squares](/P/slr-ols)**
-- **[Ordinary least squares](/P/slr-ols2)**
+- **[Ordinary least squares](/P/slr-ols)** (1) 
+- **[Ordinary least squares](/P/slr-ols2)** (2) 
 - **[Expectation of estimates](/P/slr-olsmean)**
 - **[Variance of estimates](/P/slr-olsvar)**
 - **[Distribution of estimates](/P/slr-olsdist)**
@@ -639,10 +639,10 @@
 - **[Sums of squares](/P/slr-sss)**
 - **[Partition of sums of squares](/P/slr-pss)**
 - **[Transformation matrices](/P/slr-mat)**
-- **[Weighted least squares](/P/slr-wls)**
-- **[Weighted least squares](/P/slr-wls2)**
-- **[Maximum likelihood estimation](/P/slr-mle)**
-- **[Maximum likelihood estimation](/P/slr-mle2)**
+- **[Weighted least squares](/P/slr-wls)** (1) 
+- **[Weighted least squares](/P/slr-wls2)** (2) 
+- **[Maximum likelihood estimation](/P/slr-mle)** (1) 
+- **[Maximum likelihood estimation](/P/slr-mle2)** (2) 
 - **[t-test for intercept parameter](/P/slr-tint)**
 - **[t-test for slope parameter](/P/slr-tslo)**
 - **[F-test for model comparison](/P/slr-fcomp)**
@@ -654,9 +654,9 @@
 ### Multiple linear regression
 - *[Definition](/D/mlr)*
 - **[Special case of general linear model](/P/mlr-glm)**
-- **[Ordinary least squares](/P/mlr-ols)**
-- **[Ordinary least squares](/P/mlr-ols2)**
-- **[Ordinary least squares](/P/mlr-ols3)**
+- **[Ordinary least squares](/P/mlr-ols)** (1) 
+- **[Ordinary least squares](/P/mlr-ols2)** (2) 
+- **[Ordinary least squares](/P/mlr-ols3)** (3) 
 - **[Ordinary least squares for two regressors](/P/mlr-olstr)**
 - *[Total sum of squares](/D/tss)*
 - *[Explained sum of squares](/D/ess)*
@@ -672,8 +672,8 @@
 - **[Distribution of OLS estimates, signal and residuals](/P/mlr-olsdist)**
 - **[Distribution of WLS estimates, signal and residuals](/P/mlr-wlsdist)**
 - **[Distribution of residual sum of squares](/P/mlr-rssdist)**
-- **[Weighted least squares](/P/mlr-wls)**
-- **[Weighted least squares](/P/mlr-wls2)**
+- **[Weighted least squares](/P/mlr-wls)** (1) 
+- **[Weighted least squares](/P/mlr-wls2)** (2) 
 - **[Maximum likelihood estimation](/P/mlr-mle)**
 - **[Maximum log-likelihood](/P/mlr-mll)**
 - **[Log-likelihood ratio](/P/mlr-llr)**

construct_toc.py

@@ -100,7 +100,7 @@ def to_roman(num):
 
 if __name__ == '__main__':
 
-    with open('./structure.md', 'r') as f:
+    with open('./book_content.md', 'r') as f:
         md = f.read()
 
     with open("./I/ToC.md", 'w') as f: