Кто читает:: Кафедра фундаментальной математики (Факультет информатики, математики и компьютерных наук (Нижний Новгород))

Статус:: Курс обязательный

Когда читается:: 1-й курс, 2 модуль

Abstract

This class emphasizes both theoretical and applied aspects of data analysis methods. Weekly lab exercises are from applications in biology. The course will cover topics from survey design, regression models, analysis of variance, non-parametric methods, general and generalized linear models, drawing on a range of practical examples. It will also provide an introduction to statistical computing in R.

Learning Objectives

The objective of this course is to provide students with probabilistic and statistical methods to analyze data in the field of biology.

Expected Learning Outcomes

Able to fit a logistic regression model on a given dataset
Be familiar with a very broad class of non – parametric techniques (polynomial regression, regression splines, smoothing splines, kernel – methods, generalized additive models). Additionally, they should be able to derive simplest properties of kernel estimators. Finally, they should be able to study properties of these estimators using Monte – Carlo techniques and apply these estimators on real datasets using the computing language R.
Be able to write a statistical analysis report
Be able to calculate confidence intervals
Able to model nonlinear relationships between variables
Skill of using logistic regression
Be able to understand and estimate the simple and multiple linear regression models, test the specification of the estimated models, interpret the estimation results, and make the predictions;
Apply linear regression models in practice: identify situation where linear regression is appropriate; build and fit linear regression models with software; interpret estimates and diagnostic statistics; produce exploratory graphs
Able to interpret the logistic regression’s coefficients
Perform basic and more advanced statistical analysis via python
Students choose appropriate estimation methods for regression models with discrete dependent variables of different types

Course Contents

Fundamentals of Mathematical Statistics
General Linear Model
Generalized Linear Models
General Additive Models
Elements of Multidimensional Analysis

Assessment Elements

Practical work "Major genetic information databases"
Practical work "Linear and Logistic Regression"
Practical work "Feature Engineering"

Interim Assessment

2025/2026 2nd module
0.3 * Practical work "Linear and Logistic Regression" + 0.3 * Practical work "Feature Engineering" + 0.4 * Practical work "Major genetic information databases"

Bibliography

Recommended Core Bibliography

A practical guide to scientific data analysis, Livingstone, D., 2010
Data analysis : a model comparison approach, Judd, C. M., 2009
Interactive visual data analysis, Tominski, C., 2020
Naldi, G., & Nieus, T. (2018). Mathematical and Theoretical Neuroscience : Cell, Network and Data Analysis. Cham, Switzerland: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1737030
Pandas for everyone : Python data analysis, Chen, D. Y., 2023
Pardalos, P. M., Coleman, T. F., & Xanthopoulos, P. (2012). Optimization and Data Analysis in Biomedical Informatics. New York, NY: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=537522

Recommended Additional Bibliography

Ahmed, S. E. (2017). Big and Complex Data Analysis : Methodologies and Applications. Cham, Switzerland: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1383914
Core data analysis : summarization, correlation, and visualization, Mirkin, B., 2019
Data analysis and graphics using R : an example-based approach, Maindonald, J., 2010
Handbook of data analysis, , 2009
Introduction to Statistics and Data Analysis, With Exercises, Solutions and Applications in R, Christian Heumann, Michael Schomaker, Shalabh, Springer Nature Switzerland AG 2022, 978-3-031-11833-3, published: 30 January 2023

Authors

Stankevich Nataliia Vladimirovna
Bagaev Andrei Vladimirovich

Магистерская программа «Математика»

Адрес:

Data Analysis in Biological Disciplines

Course Syllabus