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"Probability" allows us to predict unknown outcomes based on known parameters, then "likelihood" allows us to determine unknown parameters based on known outcomes.
The concept differs from that of a probability in that a probability refers to the occurrence of future events, while a likelihood refers to past events with known outcomes.
Many thanks to Niu.
概率:基于现有的总体参数来估测未知事件发生的可能性;
似然:基于现有的事件(数据)来获得对总体参数的估计。
在随机变量的概率分布中,参数被视为恒定值,统计数据为未知变量;在似然函数中,统计数据被视为恒定值,而待估参数则是变量。(类似于频率论者和贝叶斯论者的区别)
为确定参数的最大似然估计值,就要理解似然函数,此函数为待估计的参数提供所有可能的观测值(样本统计数据)。最大似然估计值是这些观测值中的一个??
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