Evidence is an observed fact or data value that changes the probability assigned to a hypothesis or event. Bayesian reasoning uses evidence to update a prior belief into a posterior belief, often by reasoning backward from effects to causes. section 13.0 section 13.3
Evidence participates in a probabilistic model in several connected ways:
- A prior expresses belief before additional evidence is observed. section 13.1
- A likelihood function models how probable an observation is under each possible cause. section 13.6
- A posterior filters possibilities inconsistent with the evidence and renormalizes the remaining beliefs. section 13.3
An accurate test can still provide weak evidence
Frob Syndrome affects 1 in 30,000 people. A cheap test is 99.5% sensitive and specific, yet a positive result produces odds of 199 to 29,999—about 0.7% probability—because false positives among healthy people overwhelm true positives. section 13.4
Table 13.1 A survey of 10,000 respondents organized in a marginal table
| Cold: YES |
Cold: NO |
Total |
|
|---|---|---|---|
| Sneezed: YES |
860 |
270 |
1,130 |
| Sneezed: NO |
140 |
8,730 |
8,870 |
| Total |
1,000 |
9,000 |
10,000 |
Use the marginal survey table to trace how observed sneezing changes belief about having a cold. section 13.1
