up:: Tags:: #🌱 <% tp.file.cursor(3) %> Links:: <% tp.file.cursor(4) %> # Bayesian Reasoning "Extraordinary claims require extraordinary evidence." —Carl Sagan The great insight of Reverend Thomas Bayes was that the degree of belief in a hypothesis may be quantified as a probability. Bayesian reasoning works off the idea that your credence in a idea should work off the evidence. It should be conditional on the evidence. As new information comes in, the credence of the evidence changes. **The more surprising the a result, the more skeptical we should be of it.** ### Bayes Rule In essence Bayesian reasoning culminates in [[Baye's rule]] which works off of [[Probability#Conditional Probability|conditional probability]] equations but iterates over time with new information. It takes the conditional probability formula as the skeleton: P(Hypothesis|Data) = P(Hypothesis and Data)/P(Data) But since the conjunctive P(Hypothesis and Data) isn't independent we must separate them into P(Hypothesis) X P(Data|Hypothesis). When we plug this back into the conditional probability equation we get: P(Hypothesis|Data) = (P(Hypothesis) X P(Data|Hypothesis))/ P(Data) ### The Base Rate Doesn't Always Equal the Prior Probability This can be for two reasons: 1. The base rate is too general and can't be used on an individual 2. The base rate doesn't reflect the individual 1. It reflects social bias, inequality, prejudice, and discrimination The more specific the prior probability often the more accurate the posterior. ### Why is it rational to not use Bayesian reasoning in the legal system for stereotyping? No, because no one wants to live in a society where the legal system can background check people and calculate their chance of doing a crime with Bayesian reasoning. ### Causality isn't 100% [[Causality isn't 100%]].