07 Belief Updating & Bayes’ Rule

Pennycook & Thompson (2022) Base-Rate Neglect

Bayesian reasoning

Updating beliefs using probabilities and evidence

Bayes' theorem

Calculates the probability of a hypothesis given evidence: P(H|D) = P(D|H) × P(H) / P(D)

Prior probability

Probability of a hypothesis before new evidence

Posterior probability

Probability of a hypothesis after new evidence

Conditional probability

Probability of an event given another event

P(D|H)

Probability of evidence if the hypothesis is true

P(H|D)

Probability of a hypothesis given the evidence

Base rate

Initial probability of an outcome

Base-rate neglect

Underweighting prior probabilities when judging an outcome

Representativeness heuristic

Judging probability by similarity to a stereotype

Test sensitivity

Probability of a positive test when the condition is present

Test specificity

Probability of a negative test when the condition is absent

False positive

Positive test result when the condition is absent

Likelihood ratio

How strongly evidence supports one hypothesis over another

Likelihood ratio neglect

Underweighting how diagnostic evidence is

Natural frequencies

Probabilities expressed as counts, e.g. 8 out of 100

Dual-process theory

Type 1: fast, automatic thinking; Type 2: slow, reflective thinking

Individuating information

Specific information about an individual case

Base-rate conflict

When base rates and individual information suggest different conclusions

Conflict detection

Recognising that intuitive judgments conflict with statistical information

Base-rate integration

Combining prior probabilities with individual evidence

Natural frequency effect

Using counts instead of percentages can improve Bayesian reasoning

Bayesian updating

Revising a prior probability using new evidence