统计学概论_目录

这是一篇关于统计学概论的思维导图，主要内容有1.Basics in statistics2.Bivariats Analysis3.Sampling4.Estimation5.Confidence lntervals。

Introduction to Statistics

• 1. Basics in statistics
  • 1.1. basic concept
    • 1.1.1. population
    • 1.1.2. variable
      • 1.1.2.1. Quantitative
      • 1.1.2.2. Qualitative
    • 1.1.3. Probabilities on finite pop
    • 1.1.4. Union, intersection
    • 1.1.5. Conditional probability
    • 1.1.6. Distribution
    • 1.1.7. Graphical representation
      • 1.1.7.1. pie charts
      • 1.1.7.2. histogram
      • 1.1.7.3. box-plot
    • 1.1.8. Cumulative distribution function
    • 1.1.9. Probability density function
  • 1.2. Digital features and their properties
    • 1.2.1. exceptation
    • 1.2.2. Variance
    • 1.2.3. Median
    • 1.2.4. Quantiles
  • 1.3. analysis
    • 1.3.1. Univariate analysis
  • 1.4. Summary
• 2. Bivariate Analysis
  • 2.1. Qualitative - Qualitative
  • 2.2. Quantitative - Qualitative
  • 2.3. Covariance
  • 2.4. Correlation
  • 2.5. About interpretation
  • 2.6. About the effect of the outlier
  • 2.7. Summary
• 3. Sampling
  • 3.1. Technical results
    • 3.1.1. Refresher
      • 3.1.1.1. Expectation of f(Y)
      • 3.1.1.2. Expectation of f(Y1,Y2)
      • 3.1.1.3. Another formula for the variance
      • serve to
        • Special case of independent variables
        • Variance of a sum
        • Sum of independent random variables
        • Application to the Binomial distribution
  • 3.2. A first try at estimation
    • 3.2.1. EX：The Circle dataset
      • 3.2.1.1. three steps to obtain an estimate
    • 3.2.2. Several ways to "sample at random"
    • 3.2.3. Performance evaluation
      • 3.2.3.1. MSE
  • 3.3. SRS in finite population
  • 3.4. Stratified sampling
  • 3.5. IID sampling in infinite populations
  • 3.6. Summary
• 4. Estimation
  • 4.1. Technical detour
    • 4.1.1. gaussian variables
      • 4.1.1.1. Algebraic properties
      • 4.1.1.2. Link with random variables
    • 4.1.2. Scaling
    • 4.1.3. Standard normal gaussian
      • 4.1.3.1. Mean and variance
      • 4.1.3.2. Sum of independent gaussians
  • 4.2. Chi-square distribution
    • 4.2.1. First example: infering allelic frequency
  • 4.3. Likelihood
    • 4.3.1. Maximizing the likelihood
    • 4.3.2. The log "monotonicity" property
    • 4.3.3. Maximum likelihood estimator
    • 4.3.4. Second example: maize yield analysis
    • 4.3.5. Properties of the ML estimators
  • 4.4. Debiasing
  • 4.5. Summary
• 5. Confidence Intervals
  • 5.1. Warm-up
    • 5.1.1. Gaussian variable manipulation
    • 5.1.2. An important result
  • 5.2. Introducing the Student distribution
    • 5.2.1. Student density
  • 5.3. Confidence interval
    • 5.3.1. Pivotal statistic
  • 5.4. EX_1:Weighing scale precision
  • 5.5. Ex_2:Number of bacteriophages
    • 5.5.1. First strategy: exact computation
    • 5.5.2. Second strategy: plug-in approximation
  • 5.6. Summary