🎲 贝叶斯定理Bayes Theorem

使用说明与常见问题How-to & FAQ

「贝叶斯定理」是什么？What is the Bayes Theorem tool?

P(A|B) = P(B|A)P(A) / P(B)。本地处理。可设置「P(A)」、「P(B given A)」、「P(B)」。P(A|B) = P(B|A)P(A) / P(B). Processed locally. Settings: P(A), P(B given A), P(B).

如何使用「贝叶斯定理」？How do I use the Bayes Theorem tool?

在「贝叶斯定理」中，填写「P(A)」、「P(B given A)」、「P(B)」等参数，结果会随输入实时计算并显示在下方。In the Bayes Theorem: Fill in "P(A)", "P(B given A)", "P(B)"; results are recalculated instantly as you type.

P(B) 不知道怎么办？What if I don't know P(B)?

需要先用全概率公式算出来：P(B) = P(B|A)·P(A) + P(B|非A)·P(非A)，再填入。本页按 P(A|B) = P(B|A)·P(A) ÷ P(B) 计算，P(B) 必须大于 0。Work it out first with the law of total probability: P(B) = P(B|A)·P(A) + P(B|not A)·P(not A), then enter it. The page computes P(A|B) = P(B|A)·P(A) ÷ P(B), and P(B) must be above 0.

概率范围？Probability range?

P(A)、P(B|A)、P(B) 均须在 (0,1]。若算出的 P(A|B)>1，页面会警告输入可能不一致。P(A), P(B|A) and P(B) must each be in (0,1]. If P(A|B) comes out above 1, the page warns that the inputs may be inconsistent.

能举个计算实例吗？Can you show a worked example?

例如在「贝叶斯定理」中填 P(A) = 0.01，P(B given A) = 0.9，P(B) = 0.1，结果区显示：P(A|B)：0.09For example, entering P(A) = 0.01, P(B given A) = 0.9, P(B) = 0.1 in the Bayes Theorem gives: P(A|B): 0.09

哪些输入会被检查？Which inputs are validated?

「贝叶斯定理」会检查这些输入——「P(A)」、「P(B given A)」、「P(B)」：必须填写；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Bayes Theorem checks its inputs — "P(A)", "P(B given A)", "P(B)": required; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「贝叶斯定理」的设置：「P(A)」默认 0.01；「P(B given A)」默认 0.9；「P(B)」默认 0.1。每次生成结果都按当前设置处理。Settings in the Bayes Theorem — "P(A)" default 0.01; "P(B given A)" default 0.9; "P(B)" default 0.1. The result always uses the current settings.

计算精度如何？How precise are the results?

「贝叶斯定理」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Bayes Theorem uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「贝叶斯定理」免费吗？需要注册吗？Is the Bayes Theorem free? Do I need an account?

「贝叶斯定理」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Bayes Theorem is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.