### Definition(s)

#### Bayesian Probability (Subjective Probability)

Interpretation or estimate of probability as a personal judgment or ―degree of belief‖ about how likely a particular event is to occur, based on the state of knowledge and available evidence

Sample Usage: Analysts use their knowledge of terrorist strategies, objectives, and capabilities in combination with evidence from operations to estimate a subjective probability of 10 percent for an attack to occur within the next five years. An analyst may use Bayesian probability to estimate likelihood based on a degree of belief.

Annotation:

1. Like all probabilities, subjective probability is conventionally expressed on a scale from zero to one where zero indicates the event is impossible and one indicates the event has or certainly will occur.
2. Within the subjective probability interpretation, it is possible to estimate probabilities of events (using experts or models) that have not previously occurred or that have only rarely occurred, such as acts of terrorism. However, because subjective probabilities incorporate historical or trial data when available, the subjective probability will approximate the frequentist probability as data becomes more plentiful.
3. Subjective probability is currently one of the most common uses of probability among statisticians and the risk analysis community.
4. Bayesian probability is colloquially used as a synonym for subjective probability. In statistical usage, Bayesian probabilistic inference is an approach to statistical inference that employs Bayes’ theorem to revise prior information using evidence.

Source: DHS Risk Lexicon, U.S. Department of Homeland Security, 2010 Edition. September 2010 Regulatory Guidance