Prior
High school
Consider an unknown quantity, such as the chance that a coin lands heads. The prior is a description of what you believe about the quantity before you see the data, given by a probability for each possible value. In the case of the coin, you may have a prior belief that the coin is fair: It lands on heads 50% of the time.
Undergraduate (Bayesian inference)
Consider a statistical model $p(x \mid \theta)$ of data $x$ for each value of a parameter $\theta$. A prior is a probability distribution $p(\theta)$ on the parameter that is chosen before the data are observed.
Properties
- “A priori” is Latin for “from the earlier,” and “a posteriori” is Latin for “from the later.”
- In a Kalman filter, the a priori estimate is the prediction before the measurement update, and the a posteriori estimate is the estimate after it.