The real-world signal can be considered as a random signal. The random signal processing is a technique to estimate parameters from the random signal. For that purpose, typical probability distributions will introduced. Then, statistical estimators will be discussed. The course will demonstrate how to use the statistical estimators for real-world problems.
This course will provide a comprehensive overview of the probability distributions and the statistical estimators. The derivations of Gaussian and Poisson distributions will be presented. Law of large numbers and central limit theorem will be proven. Maximum likelihood and maximum a priori will be introduced. The course will conclude by discussing how to apply those estimators to the real-world problem.
By the end of this course, students will be able to:
1. Explain and derive Gaussian and Poisson distributions
2. Prove and use the law of large numbers and the central limit theorem
3. Explain and apply the maximum likelihood and the maximum a posteriori estimators
Gaussian distribution, Poisson distribution, the law of large numbers, the central limit theorem, the maximum likelihood estimator, and a posteriori estimator
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
Assignment is checked and reviewed. Then, main points are discussed in detailed. Student are asked to provide the solution of quick expiries during class.
|Course schedule||Required learning|
|Class 1||Introduction of the course||Understand importance|
|Class 2||Definition of probability, mean, variance and moment||Compute mean, variance and moment|
|Class 3||Various types of distributions||Know various types of distribution|
|Class 4||Derivation of Poisson distribution||Derive Poisson distribution|
|Class 5||Moment generating function||Understand moment generating function|
|Class 6||the law of large numbers||Understand the law of large number|
|Class 7||the central limit theorem||Proove the central limit theorem|
|Class 8||application of the central limit theorem||Apply the central limit theorem|
|Class 9||Least square||Understand the least squre|
|Class 10||Conditional probability, posterior, Bayes’ theorem||Understand Conditional probability, posterior, Bayes’ theorem|
|Class 11||Maximum likelihood estimator||Understand Maximum likelihood estimator|
|Class 12||maximum a posteriori estimator||Understand maximum a posteriori estimator|
|Class 13||Natural prior||Understand Natural prior|
|Class 14||stochastic process, filter||Understand stochastic process, filter|
|Class 15||MCMC, Gibbs sampling||Understand MCMC, Gibbs sampling|
Books in Japanese
Assignments, excersises, final exams.
Basics of statistics