# Questions tagged [bayes-theorem]

For questions related to Bayes' theorem (or rule) used in the AI context.

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### How can i cast this problem as an POMDP or an belief space MDP?

I am currently attempting to formulate my problem as either a Partially Observable Markov Decision Process (POMDP) or a Belief space MDP. My end goal is to gain insights into the proposed methods ...
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### Doesn't every single machine learning classifier use conditional probability/Bayes in its underlying assumptions?

I'm reading about how Conditional Probability/ Bayes Theorem is used in Naive Bayes in Intro to Statistical Learning, but it seems like it isn't that "groundbreaking" as it is described? If ...
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### Understanding how to calculate $P(x|c_k)$ for the Bernoulli naïve Bayes classifier

I'm looking at the Bernoulli naïve Bayes classifier on Wikipedia and I understand Bayes theorem along with Gaussian naïve Bayes. However, when looking at how $P(x|c_k)$ is calculated, I don't ...
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### What is Bayes' theorem?

What is Bayes' theorem? How does it relate to conditional probabilities?
The naïve Bayes' generative algorithm is often represented by the following formula: $$\text{argmax}_{y} p(y|x) = \text{argmax}_y \frac{p(x|y)p(y)}{p(x)} \approx \text{argmax}_y p(x|y)p(y)$$ Why do we ...