Merge pull request #9 from RuiDongDR/main

add EM notebook, revise HMM, and merge the toc changes

Author: gaow

README.md

@@ -14,9 +14,6 @@ The goal is to bridge the knowledge gap between these existing backgrounds and t
 | **Correlation** | Between variants | [Linkage Disequilibrium](https://statfungen.github.io/statgen-primer/linkage_disequilibrium.html) |
 | | | [Linkage Disequilibrium Score](https://statfungen.github.io/statgen-primer/linkage_disequilibrium_score.html) |
 | | Between individuals | [Genetic Relationship Matrix](https://statfungen.github.io/statgen-primer/genetic_relationship_matrix.html) |
-| | Between variables | [Factor Analysis](https://statfungen.github.io/statgen-primer/factor_analysis.html) |
-| | | [Principal Component Analysis](https://statfungen.github.io/statgen-primer/principal_component_analysis.html) |
-| | | [Hidden Markov Model](https://statfungen.github.io/statgen-primer/hidden_Markov_model.html) |
 | **Genetic Associations** | Basic model | [Ordinary Least Squares](https://statfungen.github.io/statgen-primer/ordinary_least_squares.html) |
 | | Extend to binary outcome | [Odds Ratio](https://statfungen.github.io/statgen-primer/odds_ratio.html) |
 | | Extend to multiple variables| [Marginal vs. Joint Effects](https://statfungen.github.io/statgen-primer/marginal_joint_effects.html) |
@@ -29,9 +26,10 @@ The goal is to bridge the knowledge gap between these existing backgrounds and t
 | | | [Mediator](https://statfungen.github.io/statgen-primer/mediator.html) |
 | | Multiple studies | [Meta Analysis Fixed Effect](https://statfungen.github.io/statgen-primer/meta_analysis_fixed_effect.html) |
 | | | [Meta Analysis Random Effect](https://statfungen.github.io/statgen-primer/meta_analysis_random_effect.html) |
-| **Statistical Inference** | Likelihood and MLE | [Likelihood](https://statfungen.github.io/statgen-primer/likelihood.html) |
+| **Statistical Inference** | Likelihood | [Likelihood](https://statfungen.github.io/statgen-primer/likelihood.html) |
 | | | [Maximum Likelihood Estimation](https://statfungen.github.io/statgen-primer/maximum_likelihood_estimation.html) |
-| | LR and LRT | [Likelihood Ratio](https://statfungen.github.io/statgen-primer/likelihood_ratio.html) |
+| | | [Likelihood Ratio](https://statfungen.github.io/statgen-primer/likelihood_ratio.html) |
+| | | [Expectation-Maximum Algorithm](https://statfungen.github.io/statgen-primer/expectation_maximum.html) |
 | | Bayesian versus Frequentist | [Bayesian and Frequentist](https://statfungen.github.io/statgen-primer/Bayesian_frequentist.html) |
 | | | [Bayes Rule](https://statfungen.github.io/statgen-primer/Bayes_rule.html) |
 | | | [Bayes Factor](https://statfungen.github.io/statgen-primer/Bayes_factor.html) |
@@ -40,5 +38,8 @@ The goal is to bridge the knowledge gap between these existing backgrounds and t
 | | | [Bayesian Multivariate Normal Mean Model](https://statfungen.github.io/statgen-primer/Bayesian_multivariate_normal_mean_model.html) |
 | | Multiple Bayesian Models | [Bayesian Model Comparison](https://statfungen.github.io/statgen-primer/Bayesian_model_comparison.html) |
 | | | [Bayesian Mixture Model](https://statfungen.github.io/statgen-primer/Bayesian_mixture_model.html) |
+| | Latent Structures in Data | [Factor Analysis](https://statfungen.github.io/statgen-primer/factor_analysis.html) |
+| | | [Principal Component Analysis](https://statfungen.github.io/statgen-primer/principal_component_analysis.html) |
+| | | [Hidden Markov Model](https://statfungen.github.io/statgen-primer/hidden_Markov_model.html) |
 
 These notes draw inspiration from [fiveMinuteStats](https://stephens999.github.io/fiveMinuteStats/index.html) by Matthew Stephens and [statistical genetics equations](https://rawgit.com/uqrmaie1/statgen_equations/master/statgen_equations.html) by Robert Maier. Compared to Matthew's materials, these notes are more narrowly focused on human and statistical genetics with only as much statistical details to understand the applications. Compared to Robert's materials, these notes include a slightly stronger statistical component to serve as "primer" for readers to advance into details in advanced statistical genetics methods in practice.