Basic Concepts:
Histogram – univariate and bivariate, estimation of basic statistical parameters, viz., mean, standard deviation, variance, covariance.
Probability Theory:
Introduction to probability theory, kinds of probability – classical or apriority probability, A posteriori or Frequency probability, probability models, an inside to set theory, sample space and events, conditional, joint probability and independence.
Special Parametric Families of Univariate and Multivariate Distributions:
Introduction and summary, Discrete and continuous distributions – binomial, poisson, exponential, Gaussian/Normal distribution functions, joint and continuous distributions, bivariate and multivariate normal distribution.
Estimation Theory:
Introduction and summary, methods of finding estimators, properties of point estimators, unbiased estimation, location or scale invariance, Bayes estimators – posterior distribution, loss function approach, min-max estimators, maximum likelihood estimators.
Stratification and Sampling:
Introduction, sampling, sample mean, sampling from normal distribution, stratification and sampling.
Testing of Hypothesis:
Introduction and summary, simple hypothesis testing, composite hypothesis, tests of hypotheses – sampling from normal distribution, chi-square tests, tests of hypotheses and confidence intervals, sequential test of hypotheses.
Geo-statistics for Spatial Analysis and Modeling:
Cluster analysis concepts and techniques, Spatial autocorrelation, Multivariate Correlation, Linear regression, Multiple regressions. Statistical SurfacesInterpolation, Variogram, Kriging. Geostatistical models, stochastic models, probabilistic models, Deterministic models.
Time Series and Forecasting:
Introduction, variation in time series, trend analysis, time series analysis in forecasting.
Introduction to Spatial data analysis in R:
Introduction to R, Data exploration in Bivariate plots in R, finding relationship in R, making maps in R, making point data in R, using R as A GIS, representing Densities in R, Spatial Attribute analysis with R, Function and loops in R. Introduction to MATLAB Programming.