## Probability and StatisticsBack

Numbering Code |
U-ENG29 39028 LJ55 U-ENG29 39028 LJ10 |
Year/Term | 2021 ・ First semester | |
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Number of Credits | 2 | Course Type | Lecture | |

Target Year | Target Student | |||

Language | Japanese | Day/Period | Wed.2 | |

Instructor name | Shimodaira, Hidetoshi (Graduate School of Informatics Professor) | |||

Outline and Purpose of the Course | This course involves the basics of probability and statistics. The probability theory is illustrated through random number generation. Theory and applications of statistical inference, such as Bayesian inference and maximum likelihood method, are then discussed. | |||

Course Goals | To understand the basics of probability and statistics from the viewpoints of mathematics, algorithm, and applications. | |||

Schedule and Contents |
Monte Carlo methods,6times,Random number generation from probability distribution: inverse transform sampling, rejection sampling, Markov chain Monte Carlo (Metropolis-Hastings sampler，Gibbs sampler). Simulation of the model of ferromagnetism. The basics of probability (probability distribution, density function, the law of large numbers, the central limit theorem). Bayesian inference,4times,Statistical inference with Bayes method. Image restoration via Bayesian inference with Markov chain Monte Carlo. Classification via Bayesian discriminant analysis with an application to spam mail filter. The error rate of Bayes classifier. The methods of least squares and maximum likelihood,5times,Theory of statistical inference including the following topics. Multiple regression analysis with least squares and weighted least squares. Logistic regression analysis via maximum likelihood method. The asymptotic distribution of the maximum likelihood estimator (MLE). Hypothesis testing and model selection. Additional topics including multivariate analysis (principal component analysis, canonical correlation analysis). |
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Evaluation Methods and Policy | Grading is based on papers and final exam. | |||

Course Requirements | None | |||

Study outside of Class (preparation and review) | In addition to attending class, work at home including real data analysis is required. | |||

Textbooks | Textbooks/References | Handouts may be distributed in class. | ||

References, etc. |
C. M. Bishop: Pattern Recognition and Machine Learning, Springer. isbn{}{9780387310732} T. Hastie, R. Tibshirani, and J. Friedman: The Elements of Statistical Learning, Springer. isbn{}{0387952845} isbn{}{9780387848570} isbn{}{9780387848587} |
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