Application of Bayesian Networks
You are given the following description on COVID-19 and its available tests. There are
two COVID tests available in the EU: at-home rapid antigen test and PCR test. The first
one can be taken at home and it takes around 30 mins to get a result while the PCR test
needs to be carried out at a lab. Researches have found that the rapid antigen test’s
accuracy is affected by whether the subject has COVID symptoms or not. If the subject
has COVID symptoms, the sensitivity and specificity are 85% and 98% respectively.
However, without symptoms, the sensitivity and specificity drop to 59% and 96%.
PCR test on the other hand is considered as a gold-standard test. It is sometimes
prescribed as a second confirmation test. PCR test accuracy is affected by how the
sample is collected. If the sample is collected by trained clinical staff, the sensitivity and
specificity are 99.2% and 99.98%. On the other hand, the accuracies for self
administrated samples drop to 95% and 99% respectively. According to the latest
statistics, the national COVID rate currently in the Iceland is roughly 2% (1.33 million
active COVID case divided by the total population 68 million). It is estimated about one
third of COVID cases are asymptomatic and about 9 in 10 PCR testing samples are
collected by testee themselves.
______________________________________________________________________________
Read the description carefully and design a Bayesian network that is suitable to answer
the following queries:
Question 1: Testee A has been tested positive using an at-home COVID rapid antigen
test. He/She feels pretty normal and bears no obvious COVID symptom. How likely is A
infected with COVID?
Question 2: Testee B, who has no connection to A, has been tested positive using an
at-home COVID rapid antigen test. How likely is B infected with COVID?
Question 3: Should they take a second confirming PCR lab test and why ? If so, should
they take the sample by themselves or by trained staff ?
Specifically, you should:
1. Present your network in a graphical representation and state all the assumptions you
have made.
• briefly describe the steps you have followed to reach the final Bayesian Network;
• how many parameters are required for your Bayesian network ?
2. Answer the above three queries by making probabilistic inferences with your Bayesian
network. You should provide intermediate steps for the inference results.
【题目翻译】贝叶斯网络的应用
COVID-19 及其可用测试将向您提供以下描述。欧盟有两种 COVID测试：国内快速抗原测
试和 PCR测试。第一个可以在家里采取，它需要大约 30分钟才能得到一个结果而 PCR测
试需要在实验室进行。研究发现，快速抗原测试的准确性受受试者是否有 COVID症状的影
响或不是。如果受试者有 COVID 症状，敏感性和特异性为 85%和 98%分别。然而，没有
症状，敏感性和特异性下降到 59%和 96%。
另一方面，PCR 测试被视为黄金标准测试。有时候是这样规定作为第二次确认测试。PCR
测试精度受收集样本。如果样本是由训练有素的临床工作人员收集的，则敏感性特异性为
99.2%和 99.98%。另一方面，自我管理样本的归因分别下降到 95%和 99%。根据最新的
统计数据，目前冰岛的全国 COVID率大约是 2% （133 万活跃 COVID 案例除以总人口
68百万）。据估计，大约三分之一的 COVID病例是无症状的和大约十个 PCR测试样本中，
有 9个由测试者自己收集。
仔细阅读描述，并设计一个贝叶斯网络：
问题 1：测试 A已使用家庭 COVID快速抗原测试检测呈阳性。他/她感觉很正常， 没有明
显的 COVID 症状。A 感染的可能性有多大科维德？
问题 2： 与 A 无关的测试 B 使用家庭 COVID 检测呈阳性快速抗原测试。B 感染
COVID 的可能性有多大？
问题 3：他们应该采取第二次确认 PCR实验室测试，为什么？如果是这样，他们应该采取
样本由自己或训练有素的工作人员？
具体来说，您应该：
1. 以图形表示形式呈现您的网络，并陈述您拥有的所有假设。
• 简要描述您为到达最终的贝叶斯网络而遵循的步骤;
• 您的贝叶斯网络需要多少参数？
2. 通过与您的贝叶斯人进行概率推论来回答上述三个疑问网络。您应该为推理结果提供中
间步骤。
要 求 下 载 的 包 （ hedgehog 和 panda ）
画图示例





























































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