贝叶斯定理先验概率
贝叶斯定理 (Bayes
Theorem)
Bayes theorem, given by Reverend Thomas Bayes and thus named after him, is a method to
find the probability of an event whose occurrence is dependent on some other
event’s occurrence. In simple words, using the Bayes theorem, we can find
the conditional probability of any event.
托马斯·贝叶斯牧师给出的贝叶斯定理 ( Bayes
theorem)以他的名字命名，是一种找到事件的发生率取决于其他事件的发生率的方法。 简单来说，使用贝叶斯定理 ，我们可以找到任何事件的条件概率。
The Bayes Theorem, also known as Bayes law or Bayes equation is
a mathematical equation which is given as follows:
贝叶斯定理 ，也称为贝叶斯定律或贝叶斯方程，是一个数学方程，其给出如下：
Where A and B are events and P(B) ≠ 0.
其中A和B是事件， P(B)≠0 。
Here,
这里，
P(A|B): conditional probability of occurrence of event A when
event B has already occurred.
P(A | B)： 事件B已经发生时事件 A发生的条件概率。
P(B|A): conditional probability of occurrence of event B when
event A has already occurred.
P(B | A)： 事件A已经发生时事件 B发生的条件概率。
P(A): Probability of occurrence of event A alone without any
dependence on other events.
P(A)：单独发生事件A的概率，而不依赖于其他事件。
P(B): Probability of occurrence of event B alone without any
dependence on other events.
P(B)：单独发生事件B的概率而不依赖于其他事件。
贝叶斯定理的推导 (Derivation
of Bayes Theorem)
Similarly,
同样，
Putting the value of P (A^B) in equation (1), we get
将P(A ^ B)的值放在等式(1)中，我们得到
Which is our required Bayes equation.
这是我们所需的贝叶斯方程。
It should be noted that in the Bayesian equation, we need not find the
probability of both the events occurring simultaneously, i.e. P(A^B). We
can simply calculate the conditional probability of an event if we know the
conditional probability of the event on which it is dependent and the individual
probabilities of both the events without any dependency on each other.
应该注意的是，在贝叶斯方程中，我们不需要找到两个事件同时发生的概率，即P(A ^ B) 。
如果我们知道事件所依赖的事件的条件概率以及两个事件彼此之间没有任何依赖关系的概率，那么我们可以简单地计算事件的条件概率。
Bayes Theorem is applicable only in those experiments where we have only two
events. It is not applicable to the cases where the number of events is more
than two.
贝叶斯定理仅适用于只有两个事件的那些实验。 它不适用于事件数大于两个的情况。
Nowadays, Bayes Theorem is used in many areas, and we can find its
applications in various fields. For example, in chemical engineering, Bayes
theorem is used to predict the drug concentrations in a body, it is also used to
anticipate the viability of generated H2 by the electrocatalyst made for
hydrogen evolution process. It is also used to find the estimates that how
likely a person is prone to cancer depending upon his/her age. Apart from these
examples, the Bayes rule is widely used and this theorem has proved to be a very
efficient method to find the conditional probabilities.
如今，贝叶斯定理已在许多领域使用，我们可以在各个领域找到其应用。
例如，在化学工程中，贝叶斯定理用于预测人体中的药物浓度，还用于预测用于制氢过程的电催化剂产生的H2的活力。
它也可以用来根据一个人的年龄来估算一个人患癌症的可能性。 除了这些示例之外，贝叶斯规则得到了广泛使用，并且该定理已被证明是找到条件概率的一种非常有效的方法。