This course is an introduction to theoretical statistics for students with a background in probability. A mathematical formalism for inference on experimental data will be developed.
MATH 3235 Introduction to Probability
M. H. De Groot, Probability and Statistics, 3rd edition
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Sample sets
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Parametric statistical inference
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Point estimation
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Confidence intervals
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Estimation Techniques: Method of Moments, Maximum Likelihood Estimation
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Cramer-Rao Inequality; Asymptotic normality of the MLE
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Hypothesis Testing; Likelihood Ratio Tests; Chi-Squared Tests
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Introduction to regression
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Analysis of Variance
Instructors may cover additional topics including but not restricted to:
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Topics in Machine Learning such as classification, logistic regression, and Principal Component Analysis
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Introduction to the statistical software R