The Naive Bayes classifier assigns the most probable class $$\hat{c}$$ by choosing the class which has the highest probability for a document $$d$$: $$\hat{c}=argmax_{c\in C}P(c|d)$$. Using Bayesian inference, this is equivalent to finding: $$\hat{c}=argmax_{c\in C}P(d|c)P(c)$$, where $$P(d|c)$$ is the likelihood function and $$P(c)$$ is the prior probability.

Bayesian Inference in Naive Bayes Classifier

Bayesian inference derives the posterior probability based on a prior probability and a likelihood function according to Bayes' theorem. $$P(C|D)=\frac{P(D|C)P(C)}{P(D)}$$ Here, the probability $$P(D|C)$$ is the likelihood function, and $$P(C)$$ is the prior probability.

New York University

Google

Created by Thomas Bayes, who posited that our estimate of the probability of an outcome was determined by two things:
- 1) prior probability of an outcome 
- 2) likelihood of an outcome

Bayesian Inference

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

The likelihood of an outcome represented by the extent to which available evidence points to the outcome.

Likelihood (Bayesian Inference)

Commonly referred to as the prior, it is the prior probability of an outcome occurring, represented by our initial belief about the probability of an outcome.

Prior Probability (Bayesian Inference)

Bayesian networks were developed to understand reasoning under conditions of uncertainty. It is based on Bayes Theorem and is a probabilistic model that represents a set of variables and their conditional dependencies by being able to find the probability of facts being true/false given already defined facts. A Bayesian network is represented by a directed acyclic graph which helps to visualize the probabilistic model for reviewing relationships between random variables and reasonings for causal probabilities given certain facts



Bayesian Networks

Updating your beliefs can be boring or uncomfortable but it very beneficial in the long run. Look for subtle signals in noise and avoid wishful thinking. The world doesn't work the way we want it so ideally we would behave like rational Bayesian updaters.

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