Read the summary and the most important questions on multivariate statistics and machine learning

• 1 basics and matrices

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• What is multivariate statistics?

  a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable.

• What is the use of a statistical model in psychology?

  • empirical sciences are fraught with uncertainty about relations between variables.
  • statistical models help us to quentify this uncertainty
  • it helps us to reason about the relations between variables
    

  • it helps us to predict what happens when things change.

• What can we deduce from a linear model?

  • The expected variance of y
    
  • the expected values of y
  • the expected covariance of y

• What is the covariance of two variables?

  Basically the correlation, but unstandardized for the sd's of both variables.
  

  • if sd of x = sd of y, cor(x,y) = cov(x,y)

• What is the difference between causal and descriptive models?

  • Statistical models may be based on causal reasoning, then the model describes the theory about why two variables are related
    
  • statistical models can be descriptive, then they simply give a summary of the data

• What are the characteristics of statistical models in multivariate statistics?

  • Multivariate data require more sophisticated statistical models, models with multiple independent and dependent variables
  • statistical analysis among others are;
  • Latent variable models (Factor Analysis), PCA

  • Multivariate (normal) probability distribution
  • Clustering
  • Almost always focused on means and (co-)variances

• What are the differences between statistics and machine learning?

  Statistics vs machine learning
  

  • Causal modeling - Descriptive modeling
    

  • Focus on inference (H0 vs HA) - focus on prediction accuracy
  • Interpretation of model parameters - Meaning of parameters ignored

  • Smaller data sets - large data sets
  • need for statistical power
  • Concerned about chance model - Concerned about prediction accuracy

• What is the basic tactic for machine learning?

  • The data is split in a training set, on which the model is created, and a training set, used to test the model's accuracy
    
  • this concept is called cross validation, there are different kinds of cross validation.

• What are the two rules of calculating with the expected value?

  • if Y = bX then E(Y) = E(b*X) = b*E(X)
  • If Y = X + a then E(Y) = E(X + a) = E(X) + a.
    

• What are the rules for simplifying calculations with the expected values when x is squared or a different function?

  No rules for other transformations, e.g., E(X^2) or E[g(X)], exist.