## Details of LS4202 (Spring 2020)

 Level: 4 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
LS4202 Biostatistics Dipjyoti Das,
Robert John Chandran

Preamble

• Thermal Physics: Kinetic theory of gases. Derivation of the ideal gas laws based on kinetic theory. The first law of thermodynamics. Applications to ideal gas processes. Carnot cycle. The second law of thermodynamics. The concept of entropy.

• Basics of Electromagnetism: Electrostatics - electric field and potential. Electric flux - analogy with fluid flow. Gauss law and its applications. Magnetism - Amperes law and applications. Faraday's law and electromagnetic induction.

• Special Theory of Relativity: Einstein's postulates. The invariant interval. Lorentz boost (derivation not required). Phenomenological consequences. Redefinition of momentum. The mass energy relation.

• The Nucleus: Nuclear reactions and decay. Basics of nuclear fission and fusion.

Syllabus
A. Scales and variables
B. Descriptive statistics, Exploratory Data Analyses
C. Introduction to Probability
Probability Axioms, Events, Intersections, Probabilistic Models, Conditional Probability, Independence, Conditional Independence, Total Probability Theorem, Bayes Rule.
Population and Sample, Random Variable, Probability Distributions Discrete and Continuous. Bernoulli, Binomial, Poisson, Beta, Geometric, Negative Binomial, Gamma, Weibull, Gaussian, and Lognormal distributions. Working with the Density function, Distribution function, Quantile function, and Random Sample generation.
Mathematical Expectation. Variance and Covariance. Moments of Probability Distributions, Moment-Generating Functions.
D. Sampling Distributions. Definition of a Statistic. Distribution of Sample Mean and Variance. Central Limit Theorem, and its Applications. Mathematical bases of the Chi-squared distribution, Students t-distribution, and F-distribution.
E. Concept of hypothesis testing, Null and Alternative Hypothesis, Statistical Significance, Type 1 and Type 2 Errors, Standard Errors, Confidence Intervals. The Concept of Likelihood. The key Frameworks of Statistical Inference Frequentist, Monte Carlo, Likelihood, and Bayesian Analyses. Model Selection and Multimodel Inference, Information Theoretic Criteria.
F. Linear Statistical Models. Simple and Multiple Linear Regression, Assumptions and Derivation. Least Squares and Likelihood based Estimation. Analysis of Variance (ANOVA), Analysis of Covariance (ANCOVA).
G. Statistical Tests for differences in Mean and Variance among samples. Experimental Design.
H. Cluster Analyses. Distance Metrics. Single Link Algorithm, UPGMA, Hierarchical, K-means Clustering.
I. Generalized Linear Models (GLM). Formulation and Specification. Logistic, Multinomial, and Poisson Regression. Deviance, Overdispersion. Zero-inflated Poisson Regression. Regression with Negative Binomial response.
J. Non-parametric Statistical tests.
K. Introduction to Multivariate statistics. Principal Component Analysis (PCA), Redundancy Analysis (RDA). Ordination using Reciprocal Averaging, Multidimensional Scaling.

References

1. George W. Snedecor and William G. Cochran, Statistical Methods 8th Ed(1989)

2. Robert R. Sokal and F. James Rohlf, Biometry: The Principles and Practices of Statistics in Biological Research (1994)

3. Richard A. Johnson and Dean W. Wichern, Applied Multivariate Statistical Analysis (6th Edition) (2007)

4. Nicholas J. Gotelli and Aaron M. Ellison, A Primer of Ecological Statistics. (2004)

5. Brian S. Everitt, Sabine Landau, Morven Leese and Daniel Stahl, Cluster Analysis (Wiley Series in Probability and Statistics) (2011)

#### Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 2 Not Allowed
2 IP 4 Core
3 IP 6 Not Allowed
4 MR 2 Not Allowed
5 MR 4 Not Allowed
6 MS 8 Core
7 RS 1 Elective
8 RS 2 Elective