问题描述
假设我有一组hypotesys H = {h1,h2}互斥.对于它们,P(h1)= 0.2,p(h3)= 0.3(先验分布).假设我们也知道
Suppose I have a set of hypotesys H = {h1, h2} mutual exclusive. For them P(h1) = 0.2 and p(h3) = 0.3 (prior distribution).Suppose we know also that
P(Y = 0 | h1)= 0.2P(Y = 0 | h2)= 0.4
P(Y=0 | h1) = 0.2P(Y=0 | h2) = 0.4
其中,Y是可以具有两个值{1,0}的属性(目标).最后假设您观察到事件Y = 0.
where Y is an attribute (target) that can have two values {1,0}.Suppose finally that you observe the event Y = 0.
MAP(最大后验)hipotesys是哪个?
Which one is the MAP (Maximum a posteriori) hipotesys?
- 地图是h1
- MAP为h2
- 没有足够的元素来查找MAP
- MAP h1 = MAP h2
- 没有一个以上可能的答案
推荐答案
应该在math.stackexchange.com或stats.stackexchange.com上问(现在可能已经迁移了)这样的问题.
Such question should be asked (and now probably migrated) on the math.stackexchange.com or stats.stackexchange.com .
您的问题是贝叶斯定理的基本应用
Your question is basic application of the Bayes Theorem
P(Y=0|h1)P(h1) 0.2*0.2 0.04
P(h1|Y=0) = ------------- = ------- = ------
P(Y=0) P(Y=0) P(Y=0)
P(Y=0|h2)P(h2) 0.3*0.4 0.12
P(h2|Y=0) = -------------- = ------- = ------
P(Y=0) P(Y=0) P(Y=0)
因此h2
是更可能的假设,如P(Y=0)>0
So the h2
is the more probable hypothesis, as P(Y=0)>0
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