# Office of Academic AffairsIndian Institute of Science Education and Research Bhopal

Earth and Environmental Sciences

EES 647: Data Analyses and Statistics for Geosciences (4)

Learning Objectives:

This course will introduce the various data analysis tools, discuss the mathematical background behind these tools, and illustrate the choice and application of these tools in the analyses of geoscience data. This course will help develop critical thinking skills, particularly in the use of quantitative data across different temporal and spatial scales.

Course Contents:

Statistics and Data Analyses:
Description of data, directional data - circular data, spherical data; Vector and matrix notation, probability theory, probability distributions – common discrete and continuous distributions; Statistical concepts and paradigms, samples versus the population; Normality and error analysis, exploratory data analysis, estimation, bias, causes of variance.

Estimation and Hypothesis Testing on Means and other Statistics:
Introduction, independence of observations; Central limit theorem; Sampling distributions,                t-distribution, confidence interval estimate on a mean, confidence interval on the difference between means, hypothesis testing on means, Bayesian hypothesis testing; Nonparametric hypothesis testing, Bootstrap hypothesis testing on means; Testing multiple means via analysis of variance, multiple comparisons of means, nonparametric ANOVA; Paired data; Kolmogorov-Smirnov goodness-of-fit test.

Statistical Modelling:
Introduction; Steps in statistical modelling, model assumptions, designed experiments, replication.

Regression:
Correlation and covariance, simple linear regression, multiple regression, other regression procedures; Nonlinear models.

Multivariate Analyses:
Multivariate graphics; Principal component analyses; Factor analyses; Cluster analyses; Discriminant analyses.

Design of Experiments:
Sampling designs; Design of experiments; Field studies and design; Missing data.

Time Series:
Time Domain; Frequency Domain; Wavelets; Auto regressive model (AR1) and persistence.

Spatial Statistics:
Three-dimensional data visualization; Spatial association, the effect of trend; Semi-variogram models, Kriging, space-time models.