This podcast discusses Bayesian Updating, exploring how beliefs change based on new evidence. It uses examples of searching for keys, discovering a pomegranate, and using bags of fruits to understand belief updates. The concept of Bayesian updating and probability is explored, along with the use of Bayes' theorem.
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Quick takeaways
Bayesian beliefs involve considering different hypotheses and updating beliefs based on new evidence.
Bayes' theorem is used to calculate revised beliefs by multiplying the prior belief with the likelihood of the evidence given the theory.
Deep dives
Bayesian Updating and Bayesian Statistics
In this podcast episode, the hosts discuss the concept of Bayesian updating and Bayesian statistics. Bayesian beliefs are described as beliefs in statistics that are expressed as probabilities. The hosts provide an example of asking about the location of keys, where the belief is 90% that they are by the door. They explain that Bayesian belief systems involve considering different hypotheses or prior beliefs, and when evidence is obtained that contradicts one hypothesis, the beliefs should be updated. They introduce Bayes' theorem as a way to update beliefs based on new evidence and explain how the likelihood of a theory producing evidence is calculated.
The Example of Fruit Bags at a Farmers Market
To illustrate Bayesian updating, the hosts present an example of fruit bags at a farmers market. The bags contain pomegranates and lemons. The hosts consider three hypotheses: bags with all pomegranates, bags with a 50-50 mix, and bags with all lemons. When evidence is obtained by pulling out a pomegranate, the hosts eliminate the possibility of all lemons. Using Bayes' theorem, they determine that it is more likely the bag is filled with all pomegranates due to the higher chance of pulling a pomegranate from that bag. They explain how the revised belief is calculated based on the prior belief and the likelihood of the evidence given the theory.
Basics of Bayesian Updating and Probability
The hosts summarize the concept of Bayesian statistics as updating beliefs based on new evidence. They explain that the posterior belief, which is the revised belief after considering new evidence, is calculated by multiplying the prior belief with the likelihood of the evidence given the theory. They emphasize the importance of considering the likelihood of the evidence when updating beliefs. The example of fruit bags is used to demonstrate how new evidence can change the probabilities assigned to different hypotheses. The hosts conclude by highlighting the usefulness of Bayesian statistics in decision-making scenarios, such as when assessing the likelihood of a deal offered by a farmer.
In this minisode, we discuss Bayesian Updating - the process by which one can calculate the most likely hypothesis might be true given one's older / prior belief and all new evidence.
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