hls__Pattern recognition and machine learning_2006_Bishop

One role for the distributions discussed in this chapter is to model the probability distribution p(x) of a random variable x, given a finite set x1, . . . , xN of observations.
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• [[density estimation]] 定义

sufficient statistic
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• [[充分统计量]]

discrete random variables
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• 离散随机变量

parametric distribution
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• 参数分布

criterion
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• 标准

in a Bayesian treatment we introduce prior distributions over the parameters and then use Bayes’ theorem to compute the corresponding posterior distribution given the observed data.
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• [[贝叶斯方法]] 流程

conjugate prior
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• 共轭先验

One limitation of the parametric approach is that it assumes a specific functional form for the distribution, which may turn out to be inappropriate for a particular application.
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• 参数化方法的一个限制是需要先假设分布的特定函数形式

calculus
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• [[微积分]]

In fact, we might wonder whether it is a general property of Bayesian learning that, as we observe more and more data, the uncertainty represented by the posterior distribution will steadily decrease.
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They can be used, for example, in real-time learning scenarios where a steady stream of data is arriving, and predictions must be made before all of the data is seen. Because they do not require the whole data set to be stored or loaded into memory, sequential methods are also useful for large data sets. Maximum likelihood methods can also be cast into a sequential framework.
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• [[Bayesian Online Learning]]