1.2 Types of models

• Descriptive models: Describe or illustrate characteristics of data.
• Inferential models: Make some statement of truth regarding a predefined conjecture or idea.
  • Inferential techniques typically produce some type of probabilistic output, such as a p-value, confidence interval, or posterior probability.
  • Usually delayed feedback between inference and actual result.
• Predictive models: Produce the most accurate possible prediction for new data. Estimation (“How much?”) rather than inference (“Will it?”).
  • Mechanistic models are derived using first principles to produce a model equation that is dependent on assumptions.
    • Depend on the assumptions that define their model equations.
    • Unlike inferential models, it is easy to make data-driven statements about how well the model performs based on how well it predicts the existing data
  • Empirically driven models have more vague assumptions, and are derived directly from the data.
    • No theoretical or probabilistic assumptions are made about the equations or the variables
    • The primary method of evaluating the appropriateness of the model is to assess its accuracy using existing data

_{1. Broader discussions of these distinctions can be found in Breiman (2001b) and Shmueli (2010)}