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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

Several books on graphical models devote some space specifically to DBNs: among them Korb and Nicholson (2011) in Section 4.5, Koller and Friedman (2009) in Section 6.2.2, Kjærluff and Madsen (2013) in Section $4.4$ and Sucar (2015) in Chapter $9 .$

DBNs are a useful tool in modelling dynamic systems in a more general machine learning setting, and are covered as such in Russell and Norvig (2009) in Section $15.5$ and in Murphy (2012). They have also been extended beyond the basic formulation to model continuous variables and nonhomogeneous Markov processes; for a recent review see Scutari (2020).
Exercises
Exercise 4.1 Consider the networks in Figure 4.1.

1. How many parameters have the networks, and the local distributions associated with the individual nodes, in the top-left, top-right and bottom-left panels?
2. Extend the network in the bottom-left panel to model as second time point $t_{2}$ in addition to $t_{0}$ and $t_{1}$. How many additional parameters does that require?
3. Finally, make the nodes in $t_{2}$ dependent on the nodes in $t_{0}$ in addition to those in $t_{1}$. How many additional parameters does that require?
Exercise 4.2 Consider again the DBN in the bottom-left panel of Figure 4.1.
4. Extend the network to model $t_{2}$ as in point 2 of Exercise 4.1, and create the bn object encoding it. Call the new nodes St2, Tin2 and Tout2.

统计代写|贝叶斯网络代写Bayesian network代考|General Bayesian Networks

In this chapter we will conclude our exploration of BNs, moving to the more general case in which each variable in the data is modelled with the random variable that best suits it rather than limiting ourselves to multinomial and normal distributions. For this purpose, we will use the Stan (Carpenter et al., 2017) MCMC sampler through its interface rstan (Stan Development Team, 2020b).

Suppose that we are interested in estimating the waiting times in the Accidents \& Emergency (A \& E) department of a hospital. Much information is publicly available on the subject, since this is one of the key metrics A \& E departments are evaluated on. For instance, the House of Commons’ and NHS England2 regularly report the relevant statistics on this subject: we will use them as a source of expert knowledge in constructing our $\mathrm{BN}$.

Patients that present themselves to $\mathrm{A} \& \mathrm{E}$ are prioritised based on the severity of their symptoms; this process is called triage. Clearly, some patients arrive in critical condition and need immediate attention; some can wait for a short time before treatment is administered; while others need little or no medical treatment at all. Two important factors that may determine which category patients fall in are the type of incident (I) they were involved in and their age (A), since older people are physically more fragile and recover more slowly. We take these two variables to largely determine the trauma score (s), which is defined by the Smart Incident Command System triage system on a scale from 0 to 12. This is a vastly simplified characterisation, which we choose for the sake of the example: a real triage process takes into account other information such as co-morbidities (diabetes, cancer, etc.) and many other risk factors (obesity, high blood pressure, etc.).

贝叶斯网络代考

DBN 是在更通用的机器学习环境中对动态系统进行建模的有用工具，Russell 和 Norvig (2009) 的第 1 节对此进行了介绍。15.5在墨菲（2012 年）中。它们还扩展到模拟连续变量和非齐次马尔可夫过程的基本公式；有关最近的评论，请参阅 Scutari (2020)。

1. 在左上角、右上角和左下角的面板中有多少个参数以及与各个节点相关联的局部分布？
2. 将左下面板中的网络扩展为第二个时间点的模型吨2此外吨0和吨1. 这需要多少额外的参数？
3. 最后，使节点在吨2依赖于节点吨0除了那些在吨1. 这需要多少额外的参数？
练习 4.2 再次考虑图 4.1 左下角的 DBN。
4. 将网络扩展到模型吨2如练习 4.1 的第 2 点，并创建 bn 对象对其进行编码。调用新节点 St2、Tin2 和 Tout2。

有限元方法代写

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MATLAB代写

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