# 统计代写|贝叶斯分析代写Bayesian Analysis代考|STATS3023

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Value of Information Analysis

Often, when making a decision, decision makers face the vexing question of whether to pay for better information about key uncertain variables that they suspect might heavily influence the viability of the outcome. For instance, bcforc launching a ncw product, a markcting managcr might want to conduct a survey of potential customers to determine likely customer demand, or an investor might be motivated to estimate economic growth before recommending investment portfolio options to clients. A medical researcher might wish to make decisions about medical interventions and quantify the effects of different clinical medical strategies over populations of patients. The question, therefore, for the decision maker is: How much should they invest in obtaining answers to these questions before making their decision?

One way of answering these kinds of questions involves using value of information (VOI) analysis. VOI analysis aims to identify the maximum value the decision maker should be willing to pay for perfect information about one or more chance nodes in the BN model.

To motivate the formal definitions involved in VOI (which are provided in Box $11.2$ ), we consider the following problem.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Sensitivity Analysis

Sensitivity analysis can be used for a number of purposes:

• As an extremely useful way to check the validity of an expert built model, whereby it is possible to see diagrammatically which nodes have the greatest impact on any selected (target) node.

As a means of determining how sensitive the results of a decision analysis are to changes in related observable variables. Thus, it can be used as an adjunct and supporting step after decision analysis or value of information analysis.
In the discrete case, assessing sensitivity involves identifying a target node, $\mathrm{T}$, the node we are interested in assessing the sensitivity of, and the set of source nodes, $\bar{X}$, we want to assess in terms of their joint or single effects on T. Box $11.4$ describes sensitivity analysis formally, but AgenaRisk automatically provides these computations.

Consider the Asia model example in Chapter 9 . It would clearly be interesting to know, based on the overall $\mathrm{BN}$ definition, which nodes have the greatest impact on the node “Lung Cancer.” In theory, we could find this out manually by running through various scenarios of the model setting different combinations of true and false to all the other nodes and observing the different resulting values for “Lung Cancer” being yes. Fortunately, AgenaRisk does this automatically by allowing us to select a target node and any number of other nodes (i.e., sensitivity nodes).
So, setting “Lung Cancer” as the target node, we can automatically obtain the tornado graph in Figure $11.13 .$

From a purely visual perspective, you can think of the length of the bars corresponding to each sensitivity node in the tornado graph as being a measure of the impact of that node on the target node. Thus, the node “Positive x-ray” has by far the most impact on lung cancer.

The formal interpretation is that the probability of lung cancer given the result of positive $\mathrm{x}$-ray goes from $0.001$ (when positive $\mathrm{x}$-ray is no) to $0.49$ (when positive $x$-ray is yes). This range (from $0.001$ to $0.49$ ) is exactly the bar that is plotted for the tornado graph. The vertical bar on the graph is the marginal probability for lung cancer being yes $(0.055)$.

## 统计代写|贝叶斯分析代写贝叶斯分析代考|高级混合影响图

，它模拟了期望效用和期望效用方差之间的权衡。因此，预期效用方差的增加会被平均效用的增加所抵消。这个函数是什么呢?如果我们检验Wildcatter模型$\mathrm{BN}$并检验最终效用节点的边际概率分布，我们会发现期望效用$\mu$是5，方差$\sigma^2$是$5.525$。假设这些值之间的比率是$1000: 1$，我们可以通过将方差除以1000来“规范化”它们之间的权衡。这样，方差1000的变化等价于期望1的变化。接下来，我们可能想要表示决策者的风险厌恶程度，并应用风险厌恶因素——该值越高，表示他们对高方差的厌恶程度越高。我们将其表示为$\lambda$ .

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