Statistical Genetics and Genomics

Statistical Genetics and Genomics is a specialized field that develops and applies statistical and computational methods to analyze genetic and genomic data. Its central aim is to decipher the complex relationship between genetic variation and observable traits, such as height, or susceptibility to diseases like diabetes. By building sophisticated mathematical models, researchers can identify specific genes linked to these traits, quantify the influence of heredity, trace evolutionary histories of populations, and ultimately create tools to predict disease risk from an individual's genetic information.

1. Foundations of Statistical Genetics
   1. Core Concepts in Molecular Genetics
      1. DNA Structure and Organization
         1. Chemical Structure of DNA
         2. Double Helix Model
         3. Base Pairing Rules
         4. DNA Packaging in Chromosomes
         5. Chromatin Structure
         6. Histone Modifications
      2. Gene Structure and Organization
         1. Gene Definition and Components
         2. Exons and Introns
         3. Promoter Regions
         4. Regulatory Elements
         5. Gene Families
         6. Pseudogenes
      3. Chromosomal Organization
         1. Chromosome Structure
         2. Karyotypes
         3. Centromeres and Telomeres
         4. Heterochromatin and Euchromatin
         5. Chromosome Banding Patterns
      4. Non-Nuclear Genomes
         1. Mitochondrial Genome Structure
         2. Chloroplast Genome Organization
         3. Inheritance Patterns of Organellar DNA
      5. Central Dogma of Molecular Biology
         1. DNA Replication
            1. Replication Machinery
            2. Leading and Lagging Strands
            3. Proofreading Mechanisms
         2. Transcription
            1. RNA Polymerases
            2. Transcription Initiation
            3. Transcription Elongation and Termination
         3. RNA Processing
            1. 5' Capping
            2. 3' Polyadenylation
            3. Splicing Mechanisms
            4. Alternative Splicing
         4. Translation
            1. Ribosome Structure and Function
            2. Genetic Code
            3. Translation Initiation, Elongation, and Termination
         5. Gene Expression Regulation
            1. Transcriptional Control
            2. Post-transcriptional Regulation
            3. Epigenetic Modifications
      6. Types of Genetic Variation
         1. Single Nucleotide Polymorphisms
            1. Definition and Classification
            2. Transition and Transversion Mutations
            3. Synonymous and Non-synonymous SNPs
            4. Regulatory SNPs
         2. Insertions and Deletions
            1. Small Indels
            2. Large Indels
            3. Frameshift vs In-frame Indels
            4. Detection Challenges
         3. Structural Variants
            1. Copy Number Variants
            2. Inversions
            3. Translocations
            4. Duplications and Deletions
            5. Complex Rearrangements
         4. Tandem Repeats
            1. Short Tandem Repeats
            2. Variable Number Tandem Repeats
            3. Trinucleotide Repeat Expansions
      7. Patterns of Inheritance
         1. Mendelian Inheritance
            1. Mendel's Laws
            2. Autosomal Dominant Inheritance
            3. Autosomal Recessive Inheritance
            4. X-linked Inheritance
            5. Y-linked Inheritance
            6. Codominance and Incomplete Dominance
         2. Non-Mendelian Inheritance
            1. Mitochondrial Inheritance
            2. Genomic Imprinting
            3. Anticipation
            4. Mosaicism
            5. Uniparental Disomy
   2. Mathematical and Statistical Foundations
      1. Probability Theory
         1. Basic Probability Rules
         2. Conditional Probability
         3. Bayes' Theorem
         4. Independence and Dependence
      2. Probability Distributions
         1. Discrete Distributions
            1. Binomial Distribution
            2. Poisson Distribution
            3. Multinomial Distribution
            4. Hypergeometric Distribution
         2. Continuous Distributions
            1. Normal Distribution
            2. Chi-squared Distribution
            3. t-Distribution
            4. F-Distribution
            5. Beta Distribution
      3. Statistical Inference
         1. Point Estimation
            1. Method of Moments
            2. Maximum Likelihood Estimation
            3. Properties of Estimators
         2. Interval Estimation
            1. Confidence Intervals
            2. Credible Intervals
            3. Bootstrap Methods
         3. Hypothesis Testing
            1. Null and Alternative Hypotheses
            2. Test Statistics
            3. P-values
            4. Type I and Type II Errors
            5. Statistical Power
            6. Multiple Testing Corrections
      4. Bayesian Statistics
         1. Bayes' Theorem in Statistics
         2. Prior and Posterior Distributions
         3. Conjugate Priors
         4. Markov Chain Monte Carlo Methods
         5. Gibbs Sampling
         6. Metropolis-Hastings Algorithm
      5. Linear Models
         1. Simple Linear Regression
            1. Model Assumptions
            2. Parameter Estimation
            3. Model Diagnostics
            4. Residual Analysis
         2. Multiple Linear Regression
            1. Model Selection
            2. Multicollinearity
            3. Interaction Terms
         3. Generalized Linear Models
            1. Link Functions
            2. Logistic Regression
            3. Poisson Regression
            4. Model Fitting and Diagnostics
         4. Mixed Effects Models
            1. Fixed and Random Effects
            2. Variance Components
            3. BLUP Estimation