Probability vs Statistics for CS

[Poopsilon]

So I have the option of either taking a year long sequence in probability theory or a year long sequence in mathematical statistics. Both require real analysis so both will be at the 'measure theoretic' level. I'm interested in these classes as they relate to computer science and specifically AI: data mining, NLP, gaming etc. Which sequence would you all suggest as more important for these applications? Thanks.

Probability Theory:
-Probability measures; Borel fields; conditional probabilities, sums of independent random variables; limit theorems; zero-one laws; stochastic processes

Mathematical Statistics:
-Statistical models, sufficiency, efficiency, optimal estimation, least squares and maximum likelihood, large sample theory Hypothesis testing and confidence intervals, one-sample and two-sample problems. Bayes theory, statistical decision theory, linear models and regression. Nonparametrics: tests, regression, density estimation, bootstrap and jackknife.

 

[Future Bruno]

It really depends on what your specific interests are within Computer Science and AI. If you're interested in data mining, NLP and gaming, then the probability theory sequence may be more beneficial as it will provide you with a strong foundation in probability and stochastic processes, which are foundational for many machine learning algorithms. Mathematical statistics will give you a solid background in statistical models and methods, which could be useful if you plan to work with large datasets.