### 统计代写|贝叶斯网络代写Bayesian network代考|CS228

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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

## 统计代写|贝叶斯网络代写Bayesian network代考|Extended Bayesian Network Models

Several Bayesian network analysis mechanisms can be found in literature. A few of these are described below, along with the potential scopes of using these in ST data prediction.
Fuzzy Bayesian Network
Fuzzy Bayesian networks (FBNs) are the combination of fuzzy methods and BNs. These can be very useful in the situation when it becomes difficult to express knowledge in BNs because of ambiguity due to lack of data/information and expert knowledge. Fuzzy Bayesian networks (FBNs) are the generalization of classical Bayesian networks where the networks contain variables having fuzzy states. Some most popular FBN approaches include the work by Tang and Liu [24], Ferreira and Borenstein [16], Penz et al. [21], D’Angelo et al. [7] etc. FBNs provide the required mathematical basis for constructing and parameterizing a model in a more explicit manner, and help to solve problems containing uncertainty [15]. However, application of FBNs in prediction of spatial time series is yet to be explored more. There remains enough scope of using FBNs to deal with parameter learning uncertainty [12, 13] which arises due to discretization of continuous spatial time series data during discrete $\mathrm{BN}$ analysis.
Dynamic Bayesian Network
The recent research shows a tendency of applying dynamic Bayesian networks for time series modeling. In a dynamic BN, the links in the networks are considered as the effect of time over the variables. Majority of the works on dynamic BN are found over gene expression data [2]. However the complexity makes even medium size dynamic BN-based models intractable, since the number of variables involved is greater than that in static models. Therefore, opportunity remains in devising variants of dynamic BN that can overcome this issue.

## 统计代写|贝叶斯网络代写Bayesian network代考|Why BN for Spatial Time Series Prediction

for crop irrigation purpose [19]. Gross evaporation from water surfaces in the tropical and temperate climate regions may contribute to a few meters a year, whereas, in humid regions this loss is offset by direct precipitation, and thus, the net surface loss becomes moderate or negligible. Thus, reservoir water level variations are complex outcomes of several of these environmental factors. Similar implications can also be drawn in case of predicting traffic flow data based on the traffic flow conditions in the different parts of the road network. This is because traffic flow condition is influenced by various other factors, like whether the day is weekday or holiday, whether there is a strike or accident at any part of the road network and so on, which must also be taken into account while making the prediction. The same is true for predicting spatial time series data from other domains as well.

With their inherent capability of representing relevant dependencies among the numerous variables in a complex system, the BNs become very much suitable for different applications in spatial time series prediction [4]. BNs can automatically capture probabilistic information from data by utilizing their directed acyclic graphs and thereby leads to efficient inference algorithms for updating probabilities. Nonetheless, there remain a number of other issues, like unavailability of information on influencing factors [8, 11], very large number of variables/nodes in the complex network structure, presence of interrelated concepts on spatial data etc., for which the standard BN models need to be further upgraded for spatial time series prediction. In the following chapters, we cover the details of some recently proposed Bayesian network models, extended with added functionalities to handle diverse contexts of spatial time series prediction.

## 统计代写|贝叶斯网络代写Bayesian network代考|Why BNRC for Spatial Time Series Prediction

One of the key challenges in spatial time series prediction is to appropriately model the complex spatio-temporal dependency among the variables. Probabilistic graphical models, like Bayesian network (BN), Markov random field (MRF) [11], etc. are some effective means of modeling inter-variable relationships. However, one of the common challenges faced by graph-based prediction models/techniques is that the information about all factors influencing the prediction variable is not always available [4]. In some cases the influencing variables/factors are not known. In the other cases, though it is known which variables can have influence on the other variables of interest, the required dataset on influencing variables are not available. If such influencing factors are not accounted for in the graph structure, these may act as the confounding variables $[3,13]$, and can have negative effect on the performance of the prediction model. For example, precipitation is not only dependent on the level of humidity, wind speed, temperature, latitude, altitude etc., but also on several other factors, like atmospheric current, ocean current, and many more, which may be even unknown. Therefore, training of a prediction model in absence of these information always leads to some imperfection in the prediction process. In order to make BNs suitable for such ST prediction in the context of paucity of influencing variables, Das et al. [7] have extended Bayesian network analysis with an functionality of residual correction. This hybrid BN model with residual correction mechanism (BNRC) can be plugged into any discrete BN-based ST prediction frame-work $[5,6]$ for modeling the ST relationships in an effective way so as to improve the prediction accuracy even in the absence of influencing variables.

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。