In the context of Bayes' theorem and diagnostic testing, the likelihood ratio measures how much more likely a positive test is in diseased individuals than in the general population. It is given by the formula $$P(T|D) / P(T)$$, where $$D$$ denotes the disease and $$T$$ stands for the test. Using this ratio, Bayes' theorem can be rewritten as: $$\text{Updated probability of } D = P(D|T) = \text{Likelihood ratio} \times \text{Prior probability of } D$$.

Likelihood Ratio

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

University of Michigan - Ann Arbor

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

Goldstein, E. B. (2014). Cognitive psychology: Connecting mind, research and everyday experience. Nelson Education.


Cognitive psychology: Connecting mind, research and everyday experience

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.

Update your Beliefs

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.

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