Bayesian data analysis
Bayesian data analysis
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DOI：
10.12746/swrccc.v8i36.773
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发表时间：
2020-10
期刊：
影响因子：
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通讯作者：
Shengping Yang;G. Berdine
中科院分区：
文献类型：
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作者：
Shengping Yang;G. Berdine
为了使贝叶斯规则的解释更直观，我们将从一个例子开始。正如我们所知，诊断测试几乎从来都不是完全准确的。一个好的测试应该既有高灵敏度（也称为真阳性率；在患病情况下测试结果为阳性）又有高特异性（也称为真阴性率；在无病情况下测试结果为阴性）。虽然灵敏度和特异性说明了在已知疾病状态下测试结果的好坏，但它们并没有直接说明在已知测试结果的情况下受试者患病的概率。这是一个可以应用贝叶斯规则的情况。具体来说，设\(P(A)\)为在特定人群中随机选择的受试者患有某种特定疾病的概率（疾病患病率），\(P(B|A)\)为测试的灵敏度，而\(P(A|B)\)，称为阳性预测值，是测试结果为阳性的受试者真正患病的概率，这是我们感兴趣的。请注意，\(P(B)\)是该人群中受试者测试结果为阳性的概率，它等于\(P(A)P(B|A)+P(\neg A)P(B|\neg A)\)，其中\(P(\neg A)=1 - P(A)\)是受试者无病的概率，\(P(B|\neg A)\)是\(1 -\)特异性。众所周知，贝叶斯分析能够将先验信息纳入决策过程。当应用于临床数据分析时，这可能会有所帮助。我想知道贝叶斯方法与频率论方法有何不同。
To make the interpretation of Bayes’s rule more intuitive, we will start with an example. As we know, diagnostic tests are almost never perfectly accurate. A good test is supposed to have both high sensitivity (also called true positive rate; test result positive given disease present) and high specificity (also called true negative rate; test result negative given disease free). While sensitivity and specificity tell how good the test results are given the disease status, they do not directly tell the probability that a subject has the disease, given the test results. This is a situation where the Bayes’s rule can be applied. Specifically, let P(A) be the probability that a randomly chosen subject has a specific disease in a specific population (disease prevalence), and P(B|A) be sensitivity of the test, and P(A|B), called positive predictive value, is the probability that subjects with a positive test result truly have the disease, which is what we are interested in. Note that P(B) is the probability of having a positive test result among subjects in this population, which equals to P(A)P(B|A) + P(A) P(B|A), where P(A) = 1 P(A) is the probability of being disease free among the subjects, and P(B|A) is 1-specificity. Bayesian analysis is known to be able to incorporate prior information into decision making. This can be helpful when applied to clinical data analysis. I am wondering how Bayesian differs from the frequentist’s approach.