"Optional stopping" and "optional sampling" refer to a strategy of peeking while you are sampling and then, based on what you find, exercise the option to quit sampling.

Doob's theorem states that in a fair casino, where your return is a martingale, you cannot increase your expected return if you are given the option to stop betting (= sampling) when you think "it's time to quit".

The names originate from J. L. Doob, Stochastic Processes (Wiley, 1953): page 300, 366.

"Optional stopping" and "optional sampling" refer to a strategy of peeking while you are sampling and then, based on what you find, exercise the option to quit sampling.

Doob's theorem states that in a fair casino, where your return is a martingale, you cannot increase your expected return if you are given the option to stop betting (= sampling) when you think "it's time to quit".

The names originate from J. L. Doob, Stochastic Processes (Wiley, 1953): page 300, 366. Doob uses "optional sampling" for the stochastic process itself, and "optional stopping" for the random variable that represents the stopping time.

"Optional stopping" and "optional sampling" refer to a strategy of peeking while you are sampling and then, based on what you find, exercise the option to quit sampling.

Doob's theorem states that in a fair casino, where your return is a martingale, you cannot increase your expected return if you are given the option to stop betting (= sampling) when you think "it's time to quit".

"Optional stopping" and "optional sampling" refer to a strategy of peeking while you are sampling and then, based on what you find, exercise the option to quit sampling.

Doob's theorem states that in a fair casino, where your return is a martingale, you cannot increase your expected return if you are given the option to stop betting (= sampling) when you think "it's time to quit".

The names originate from J. L. Doob, Stochastic Processes (Wiley, 1953): page 300, 366.