Mathematical statistics for biologists
The aim of the course is to provide an in-depth knowledge of the basic methods of classical statistics and their application to biomedical data analysis. Statistical learning is a crucial tool for anyone who wants to make sense of their data and extract useful patterns from an array of information. This field of science combines both classical statistics and modern machine learning methods to create models that describe complex relationships between data, as well as to draw the necessary conclusions about the nature of this interaction.
Statistical learning, basic definitions. Null and alternative hypotheses. Statistical significance, effect size.
Overview of the main tools for performing statistical training. Programming languages R and Python as the most flexible and powerful options.
Parametric and nonparametric methods for comparing means between 2 groups. Welch's method. Student's method. Checking normality and homoscedasticity of data.
Basic principles of the method. Features of application. Checking the basic assumptions of the method. Correction for multiple comparisons.
Features of the application of two-factor analysis of variance. Multivariate analysis of variance. Analysis of variance with repeated measurements.
Correlation and covariance. Correlation as the magnitude of the effect. The main types of correlations. Partial correlation.
Features of the chi-square method. Calculation of the expected frequency of the phenomenon. Fisher's exact method.
Basic principles of linear regression methods. Method of least squares. Gradient descent method for determining coefficients.
Definition of regularization. Lasso regularization. Ridge regularization. Elastic grid.
Sigmoid function. Linear combination of predictors. Odds ratio and interpretation of regression coefficients.