Апостериорная вероятность

Апостерио́рная вероя́тность — условная вероятность случайного события при условии того, что известны апостериорные данные, то есть полученные после опыта.

Пример

Рассмотрим приём сигнала $s(t,\lambda )$ на фоне аддитивного гауссовского белого шума $n(t)$ . В этом случае принимаемое колебание $\xi (t)$ будет равно:

\xi (t)=s(t,\lambda )+n(t)

где $\lambda$ — неизвестный непрерывный параметр сигнала $s(t,\lambda )$ , который в общем случае является векторным.

Предположим, что колебание принимается в дискретные моменты времени $t_{1}$ , … , $t_{n}$ . Тогда информация о неизвестном параметре $\lambda$ будет содержаться в дискретной последовательности случайных величинах $\xi (t_{1})$ , … , $\xi (t_{n})$ , а именно в апостериорной вероятности $P_{p}$ $_{s}(\lambda )$ :

P_{p}

_{s}(\lambda )=P(\lambda |\xi (t_{1}),...,\xi (t_{n}))

См. также

Литература

Тихонов В. И. Оптимальный приём сигналов. — М.: Радио и связь, 1983. — 320с. Рецензенты: доктор технических наук, профессор — И. Н. Амиантов, доктор технических. наук проф. Б. Н. Митящев

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