《machine learning a probabilistic perspective》部分习题解答，持续更新中
Chapter 3
Ex 3.2 Beta-Bernoulli模型的边缘似然函数
由3.3.4节得到，后验预测分布为
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则边际分布为
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Ex 3.3 Beta-Binomial模型的后验预测分布
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n = 1时
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Ex 3.4 Beta updating from censored likelihood
抛掷硬币5次，X为朝上次数。仅仅知道X < 3而不知道X的确切值，求相应后验概率（未归一化）结果为一个混合分布
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Ex 3.12 非共轭先验的Bernoulli分布参数的MAP估计
a
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b
当N很小时，采用a问题的先验可以得到比较好的估计，当N很大时采用Beta分布作为先验可以得到比较好的估计
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[2]:http://latex.codecogs.com/gif.latex?p%28D%29%20%3D%20%5Cfrac%7B%5Calpha_1%28%5Calpha_1%20+%201%29...%28%5Calpha_1%20+%20N_1%20-1%29%5Calpha_0%28%5Calpha_0%20+%201%29...%28%5Calpha_0%20+%20N_0%20-1%29%7D%7B%5Calpha%28%5Calpha%20+%201%29...%28%5Calpha%20+%20N%20-1%29%7D
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[4]:http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5CGamma%28%5Calpha_1%20+%20N_1%29%5CGamma%28%5Calpha_0%20+%20N_0%29%5CGamma%28%5Calpha%29%7D%7B%5CGamma%28%5Calpha_1%29%5CGamma%28%5Calpha_0%29%5CGamma%28%5Calpha%20+%20N%29%7D
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