Lecture

Generalized Bayes Theorem: Vaccines and Population Probability

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In course

CS-101: Advanced information, computation, communication I

Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics as diverse as mathematical reasoning, combinatorics, disc ...

Description

This lecture discusses the Generalized Bayes Theorem through an example involving three vaccines against a disease, each with different probabilities of protection. The vaccines are administered to a fraction of the population, and the lecture explores the probability of a person being protected if they catch the disease. The presentation covers the concept of mutually exclusive events and calculates conditional probabilities based on the given scenarios.

Instructor

Karl Aberer

Karl Aberer received his PhD in mathematics in 1991 from the ETH Zürich. From 1991 to 1992 he was postdoctoral fellow at the International Computer Science Institute (ICSI) at the University of California, Berkeley. In 1992, he joined the Integrated Publication and Information Systems institute (IPSI) of GMD in Germany, where he was leading the research division Open Adaptive Information Management Systems. In 2000 he joined EPFL as full professor. Since 2005 he is the director of the Swiss National Research Center for Mobile Information and Communication Systems ( NCCR-MICS, www.mics.ch ). He is member of the editorial boards of VLDB Journal, ACM Transaction on Autonomous and Adaptive Systems and World Wide Web Journal. He has been consulting for the Swiss government in research and science policy as a member of the Swiss Research and Technology Council ( SWTR ) from 2003 - 2011.

Official source

Related concepts (32)

Conditional probability distribution

In probability theory and statistics, given two jointly distributed random variables and , the conditional probability distribution of given is the probability distribution of when is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value of as a parameter. When both and are categorical variables, a conditional probability table is typically used to represent the conditional probability.

MRNA vaccine

An mRNA vaccine is a type of vaccine that uses a copy of a molecule called messenger RNA (mRNA) to produce an immune response. The vaccine delivers molecules of antigen-encoding mRNA into immune cells, which use the designed mRNA as a blueprint to build foreign protein that would normally be produced by a pathogen (such as a virus) or by a cancer cell. These protein molecules stimulate an adaptive immune response that teaches the body to identify and destroy the corresponding pathogen or cancer cells.

Attenuated vaccine

An attenuated vaccine (or a live attenuated vaccine, LAV) is a vaccine created by reducing the virulence of a pathogen, but still keeping it viable (or "live"). Attenuation takes an infectious agent and alters it so that it becomes harmless or less virulent. These vaccines contrast to those produced by "killing" the virus (inactivated vaccine). Attenuated vaccines stimulate a strong and effective immune response that is long-lasting. In comparison to inactivated vaccines, attenuated vaccines produce a stronger and more durable immune response with a quick immunity onset.

Polio vaccine

Polio vaccines are vaccines used to prevent poliomyelitis (polio). Two types are used: an inactivated poliovirus given by injection (IPV) and a weakened poliovirus given by mouth (OPV). The World Health Organization (WHO) recommends all children be fully vaccinated against polio. The two vaccines have eliminated polio from most of the world, and reduced the number of cases reported each year from an estimated 350,000 in 1988 to 33 in 2018. The inactivated polio vaccines are very safe.

Conditional independence

In probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of a hypothesis. Conditional independence is usually formulated in terms of conditional probability, as a special case where the probability of the hypothesis given the uninformative observation is equal to the probability without. If is the hypothesis, and and are observations, conditional independence can be stated as an equality: where is the probability of given both and .

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