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Lecture# Detection & Estimation

Description

This lecture covers the fundamentals of detection and estimation theory, focusing on mean-squared error, hypothesis testing, and discrete observations. Topics include Gaussian distribution, hypothesis testing, and detection methods for discrete signals.

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In course

Instructors (2)

COM-406: Foundations of Data Science

We discuss a set of topics that are important for the understanding of modern data science but that are typically not taught in an introductory ML course. In particular we discuss fundamental ideas an

Related concepts (104)

Smallpox

Smallpox was an infectious disease caused by variola virus (often called smallpox virus) which belongs to the genus Orthopoxvirus. The last naturally occurring case was diagnosed in October 1977, and the World Health Organization (WHO) certified the global eradication of the disease in 1980, making smallpox the only human disease to be eradicated. The initial symptoms of the disease included fever and vomiting. This was followed by formation of ulcers in the mouth and a skin rash.

Poxviridae

Poxviridae is a family of double-stranded DNA viruses. Vertebrates and arthropods serve as natural hosts. There are currently 83 species in this family, divided among 22 genera, which are divided into two subfamilies. Diseases associated with this family include smallpox. Four genera of poxviruses may infect humans: Orthopoxvirus, Parapoxvirus, Yatapoxvirus, Molluscipoxvirus. Orthopoxvirus: smallpox virus (variola), vaccinia virus, cowpox virus, monkeypox virus; Parapoxvirus: orf virus, pseudocowpox, bovine papular stomatitis virus; Yatapoxvirus: tanapox virus, yaba monkey tumor virus; Molluscipoxvirus: molluscum contagiosum virus (MCV).

Chickenpox

Chickenpox, or chicken pox, also known as varicella, is a highly contagious, vaccine-preventable disease caused by the initial infection with varicella zoster virus (VZV), a member of the herpesvirus family. The disease results in a characteristic skin rash that forms small, itchy blisters, which eventually scab over. It usually starts on the chest, back, and face. It then spreads to the rest of the body. The rash and other symptoms, such as fever, tiredness, and headaches, usually last five to seven days.

Mean squared error

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate.

Statistical hypothesis testing

A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see .

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