统计代写|贝叶斯分析代写Bayesian Analysis代考|STATS 3023

2022年7月21日

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
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统计代写|贝叶斯分析代写Bayesian Analysis代考|Decisions and Utilities

Although all the nodes in the Armageddon example were treated as uncertain Boolean variables, there are clear differences between them from a “decision theory” perspective. Both the control node (“Explode meteor”) and the mitigant node (“Move people underground”) really represent decisions that we may choose to perform or not. In contrast, the other nodes really are chance nodes. There is also something very important missing from the model, namely explicit utilities. In general any decision (such as exploding the meteor or moving people underground) will have a cost (which we can think of as a negative utility) and every consequence node (such as “loss of life”) will have either a cost or benefit (negative or positive utility). The “correct” model therefore is the one shown in Figure 3.20, where decision nodes are represented as rectangles and utility nodes as diamonds (such a diagrammatic model is called an influence diagram).

In practice if we are choosing which of a set of decisions is optimal we may need to be explicit about the utility of each decision and outcome. Once we do this the optimal risk strategy is the one that involves the set of decisions with the maximum overall utility.

Models that include explicit decision nodes and utility nodes (influence diagrams) can be considered as a special type of BN model, called an influence diagram. Whereas in a normal BN we are interested in seeing how each uncertain node is updated when we observe evidence, in an influence diagram we are also interested in “solving” the problem of determining which decisions optimise the overall utility. Chapter 11 deals with such influence diagrams in depth and describes how AgenaRisk is used to calculate the necessary solutions.

统计代写|贝叶斯分析代写Bayesian Analysis代考|Causal Revelation and Absence of Information

Imagine a conversation between a modeller, interested in predicting whether a borrower can repay a financial debt, and an independent observer quizzing the modeller on their probabilities.

Modeller: My model contains two variables “lose job” causes “cannot pay debt.” If a borrower loses employment they cannot pay the debt back $90 \%$ of the time.

Observer: But by losing income they can still pay debt $10 \%$ of the time. Why is that? This looks odd. How can they still have chance of $10 \%$ of paying debt without a job?
Modeller: Because they could sell their house and can still pay.
Observer: OK, that isn’t in the model, let’s add that to model (model now has two causes for “can pay debt”: lose job and sell house)

Observer: But if the borrower loses their job but doesn’t sell their house what’s the chance of paying the debt?
Modeller: Answer is $5 \%$.
Observer: How could someone still pay? There must be some other reason.
Modeller: Perhaps they could sell their grandmother into slavery?
Observer: OK, sounds a bit extreme but let’s add that to the model. What’s the chance of not paying debt now? Modeller: If borrower loses job, doesn’t sell the house and they don’t sell their grandmother into slavery, then the chance is $1 \%$.
Observer: But why $1 \%$ ?
Modeller: Because they may rob a bank!
Observer: OK, let’s add that to the model
..dialogue continues
At some point the modeller reveals all possible causal mechanisms and achieves a zero probability of the borrower not paying their debt in the presence of all possible causes, thus rendering the model deterministic. This is Godlike omniscience (and is, of course, impossible). Einstein said: “God does not play dice with the universe,” perhaps meaning that-to God-there are no probabilities only certainties.

What can we learn from this dialogue? That our probabilities represent casual mechanisms that are NOT in the model; they represent our lack of information about possible causes. Also, what is or isn’t in the model depends on our cognitive revelation, imagination, experience and availability of information. Hence, different people have different probabilities and build different models.

All probabilities depend on context (model boundary and scope) and at each stage of the conversation the modeller extended the scope realising that other factors may be relevant. Hence, the probabilities changed.

贝叶斯分析代考

统计代写|贝叶斯分析代写Bayesian Analysis代考|Causal Revelation and Absence of Information

Modeller：我的模型包含两个变量“失业”导致“无法偿还债务”。如果借款人失业，他们将无法偿还债务90%的时间。

Modeller：因为他们可以卖掉他们的房子并且仍然可以付款。

Modeller：因为他们可能会抢银行！

有限元方法代写

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MATLAB代写

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