Statistics

Statistics#

In our quest to understand the physical and biological processes within the ocean, we often observe the environment, form hypotheses, formulate experiments to collect observations and test the hypotheses. As we cannot sample the “whole” ocean, and the data recorded by our instruments go through multiple stages in which information is lost and uncertainty is introduced, we have to account for these factors in our statistical analysis. In this primer we introduce/review fundamental statistical concepts paired with examples in ocean acoustics. We discuss topics such as probability distributions, statistical testing, parameter estimation, and provide examples of their application to simulated and real datasets. The goal is for readers to understand the underlying assumptions and be capable to apply the methods to problems which do no follow a textbook definition.

Random Variables#

  • Random experiment

  • Empirical distribution

  • Empirical probability

Sound Level Distribution#

Parametric Distributions#

  • Normal distribution

  • Skew-normal distribution

  • Cauchy distribution

  • Logistic distribution

  • Laplace distribution

  • Gamma distribution

  • Exercise: fitting a distribution by modifying parameters

Parameter Estimation (high level)#

  • Maximum Likelihood

Testing#

  • Statistical Hypothesis

  • Test Statistic

  • Significance Level, Power

  • Likelihood Ratio Test

Contents