Foundations I

Statistics is a mathematical discipline developing tools for describing uncertainty. Based on these descriptions, statistics also provides tools for inferring unobserved properties.

Selecting the best element from a set of possible elements based on some criterion.

Descriptive statistics

• Describe available data quantitatively

Inferential Statistics

• Draw conclusions about a population from sampled data

  • Frequentist inference: Probabilities are interpreted as frequencies of occurrence of sample data in the whole data population.

    • Parameter estimation: Is used to infer parameters of a population based on samples of that population.

    • Data prediction is used to infer properties of random variables based on samples.

  • Bayesian inference, probabilities are interpreted as quantifications of reasonable belief based on prior knowledge and based on evidence.

• execution time

• memory usage

• optimality

• disk space

• accuracy and precision

• power consumption

• Other resources

• completeness