From bd7093d85071a6da5b7c2cfd7b9e5db8d8458f2f Mon Sep 17 00:00:00 2001
From: rudra20-6
+#### Mathematical Formulation
+Bayes' Theorem can be derived from the joint probability of events A and B:
+
-where *P(A|B)* is referred to as the posterior; *P(B|A)* is known as the likelihood, *P(A)* is the prior and *P(B)* is generally the evidence and is used as a scaling factor. Therefore, it is handy to remember Bayes Rule as:
+where:
+- $P(A|B)$ is the posterior probability
+- $P(B|A)$ is the likelihood
+- $P(A)$ is the prior probability
+- $P(B)$ is the evidence (scaling factor)
-
+#### Simplified Form
+For practical applications, we often use this form:
+
-These terms will be discussed a little later.
+### Key Components
+1. **Prior Probability** ($P(A)$)
+ - Initial belief before seeing new evidence
+ - Based on previous knowledge or experience
+
+2. **Likelihood** ($P(B|A)$)
+ - Probability of observing the evidence given the hypothesis
+ - Measures how well the evidence supports the hypothesis
+
+3. **Posterior Probability** ($P(A|B)$)
+ - Updated belief after considering new evidence
+ - Used for making final decisions
+
+4. **Evidence** ($P(B)$)
+ - Total probability of observing the evidence
+ - Acts as a normalizing constant
From 4e0fc4edadae0e097830165aed3c71230ead7be3 Mon Sep 17 00:00:00 2001
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