When you toss a coin, you do not know it will be positive or negative, but you know exactly what positive and negative probability is 50%.
Probability of magic is that it actually found certainty from uncertainty.
This article does not textbook, but illustrate my point and thinking, if false, welcomed the discussion or correction.
Some interesting points:
N kinds of things that have a possibility of happening, we can not be sure what will happen, because we can not control the results of the mechanism of occurrence of many factors affecting the result is not within our power range, these factors affect the results or we do not know or too complex beyond our brains or the PC processing power. For example: We're not sure to get heads or tails coin toss, because our capacity is not sufficient to use some physics equations to solve this result. Another example: you can not determine your final exam 88 points, because the topic, you are not scoring.
For what did not happen, we can not grasp or all of its parameters can not be calculated. For what had occurred, things have already happened, the result has been set, will grasp because of incomplete information and so-called probability.
That happened in the past despite the fact that is certain, but because of our ignorance, it became random.
We dug up a piece of debris porcelain somewhere, it might be a chamber pot Confucius, may be the emperor's tableware, it could be the next Pharaoh's broken teapot from his home to the dumpster and was buried in this place.
Therefore: in essence, it is the probability of ignorance, not that the thing itself is random.
This is important, do not mistake probability should be objective facts. If you have the perspective of God, then everything is doomed, no matter the probability is 100%, there is no so-called probability of say.
Therefore, probability theory is built on people with limited cognition, not a true fact. That is when Confucius saw, it looks like his chamber pot ah, he thinks this is a 70% probability of a chamber pot, the emperor saw the piece of debris, it just filled the hearts of the next country, where's cutlery, look at him tableware to the probability is 1/3, however, Wang has long been seen through everything, piece of debris had cut his hand so he remembers vividly clear teapot probability of 100%. Everyone knows the information determines the probability that he once knew.
Like werewolves kill, assuming the game is 7 + personal God, No. 1 and No. 2 players is a werewolf, finished his license when it is already doomed who is a werewolf. For God and No. 2, there is no probability at all, or 1,2 werewolf is the probability is 100%. As for the civilian population, in addition to his own, he could not find reason to think who is the werewolf, and so had to use the classical probability might assume that everyone else is the probability that a werewolf is 1/6, as the game progresses, the prophecy home to have more information, he revised his probability and civilians according to their own grasp of probability information correction, so for everyone who is a werewolf it has a different probability.
He noted that the above story, not difficult to find, it is assumed that only fragments of a chamber pot, tableware, teapot three possible that a start should be a probability 1/3 each. From Confucius to Pharaoh, they use the information at their disposal on the probability of correction is what the debris of. This leads to the concept of prior probability and posterior probability of.
Priori probability (Prior probability) and a posteriori (Posterior probability)
Has not happened, the size requirements of the likelihood of this happening is the a priori probability
things have happened, requested the reason this happened is caused by the size of the possibility of a factor is the posterior probability.
First look at the definition from the wiki:
Similarly, the prior probability of a random event or an uncertain proposition is the unconditional probability that is assigned before any relevant evidence is taken into account.
In Bayesian statistics, the posterior probability of a random event or an uncertain proposition is the conditional probability that is assigned after the relevant evidence or background is taken into account. Similarly, the posterior probability distribution is the probability distribution of an unknown quantity, treated as a random variable, conditional on the evidence obtained from an experiment or survey. “Posterior”, in this context, means after taking into account the relevant evidence related to the particular case being examined.
要注意的是这是在贝叶斯统计中。不是公理化的概率定义。
Look on the interpretation to read
The wall cracked recommended Chen Xiru academician of "Probability theory and mathematical statistics" , which is a large column of probability theory myths get = "_ blank" rel = "external noopener noreferrer"> watercress, know almost book reviews and recommendations. Chen Lao reason why this book is so surrounded that it delegate to fish, rather than delegate to fish, you read just know.
For a simple example: a red ball pocket has three, two white balls, touch taken without replacement, requirements:
probability ⑴ red ball first touch (referred to as A); a
second ⑵ probability touch red ball (referred to as B),;
⑶ known second red ball touched, the first touch is seeking probability red ball.
Solution:
P (A) = 3/5, there has not touched the ball, he asked probability, this is the pretest probability ⑴;
⑵ P (B) = P (A) P (B | A) + P (A inverse ) P (B | A reverse) =. 3 /. 5
⑶ P (A | B) = P (A) P (B | A) / P (B) =. 1/2, which is the posterior probability, the first and touch the ball a second time this thing have happened, but we do not know, like the first time we are touched again and again put it back with his eyes closed, and have given rise to the probability theory. The first thing to ask not happen (or that happened, but relative to the case have not occurred, we did not grasp any more information) we think the probability is 3/5, the third question, we know that a second touch red ball about it, or that evidence, in order to fix this probability, just as detective novels.
Priori probability and a posteriori probability Recommended reading:
Mathematical Statistics in two schools - schools frequency and Bayes School (1990 journals, it is not easy to find)
Murder Caused by a joke:
病人：我听说这个手术成功概率为1%，我是不是该放弃治疗？
医生：你放心，我敢保证这次手术100%会成功。
病人：真的？为什么？
医生：因为我已经失败了99次了。
这是很多人都会犯的“常识”错误，也是经常让人迷惑的地方。可能在这个笑话里，大家没什么深刻感受，那换个例子，比如：A已经抛了100次硬币，每次都是正面，那么下一次反面的几率是不是更大？即使是统计学专业的学生也经常迷糊（比如统计学渣的我），我就一直纳闷，按照大数定律（知乎的解释），如果抛硬币的次数足够多，他就应该是正反各1/2的分布啊，A都抛了100次正面了，下一次就该是反面几率更大了啊。可是每次抛硬币应该是相互独立的，也就是说之前抛无数次也不该影响下一次的概率，即1/2。这个问题的争论，请参考先验概率与后验概率的区别（老迷惑了）。
我比较认可比较的解释是其评论中的一段话，当然，前提是你得清楚频率（ 千万别把频率直接等同于概率），概率的古典定义和统计定义以及公理化定义。
关于概率论，一直有许多搞不懂的问题，迷迷糊糊混过四年。在学习HMM和CRF高楼大厦时，发现地基已碎，一边百度基础概念一边学，更是痛苦万分。在搜寻问题时产生更多的问题，终于在重新读了概率论前几章后，算是豁然开朗了很多，所以打算重读概率论，夯实基础，我应该会开个重读概率论的分类，有很多事要做，就并行处理吧，不知道会不会半途而废，也不知道半途而废的概率是多少（当然，我可以凭经验先给出一个主观先验概率，在以后的过程中再慢慢修正得到后验概率，直到概率为0或1），但是有些疑惑终究会推着我去探寻。
推荐阅读：
参考资料
- 先验概率与后验概率的区别（老迷惑了）
- Prior probability and posterior probability and Bayes' formula
- "Probability and Statistics" - Chen Xiru
- Mathematical Statistics in two schools - schools frequency and Bayes School
- "Probability and Statistics" - Sheng Zhou, Xie Qian, Pan Chengyi edited version-4.