### 统计代写|贝叶斯网络代写Bayesian network代考|CSC403

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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|Hydrological Time Series Prediction

In this case study, the BNRC-based prediction model is evaluated with respect to a real-life hydrological dataset (refer Table 3.8) to predict water level in $M a y u=$ rakshi reservoir, India (central co-ordinate: $24^{\circ} 6.6^{\prime} N, 87^{\circ} 18.9^{\prime} E$ ) for future five years (2008-2012), based on the historical daily water level data from the year 1991 to 2007. Reservoir water level variations are complex outcomes of many of the environmental factors. It depends not only on the stream flow volume but also on other parameters, like flow velocity, stream flow path, climatological factors (rainfall/precipitation rate, temperature etc.) and so on. However, in the present case study, the datasets on those influencing factors are not at all available, especially for the duration 2002-2011. The experimental results prove the BNRC-based prediction model to be highly effective to tackle such situation. A more detailed description of this case study can be found in the main paper [7].

In this study, Mayurakshi reservoir (catchment area of $1860 \mathrm{sq} . \mathrm{km}$ ) in Jharkhand, India, is considered as the case study area (Table 3.8). The climate of the study area is tropical and it experiences three well defined seasons: (i) hot weather from March to June, (ii) rainy season from July to October, and (iii) winter season from November to February. The average annual rainfall in the study area is nearly $1400 \mathrm{~mm}$. The reservoir has a live storage of $559.49 \mathrm{Mm}^{3}$ at full reservoir level (FRL) i.e $121.31 \mathrm{~m}$ above mean sea level (amsl) and dead storage of $49.86 \mathrm{Mm}^{3}$ at dead storage level of $106.38 \mathrm{~m}$ as per the capacity survey conducted during the year 2001 [16]. The total culturable command area (CCA) is nearly $2.27$ lakh ha. The water spread area of the Mayurakshi reservoir at full reservoir level (FRL) is around $68 \mathrm{~km}^{2}$. The daily water level data of this reservoir for a span of 22 years (1st January, 1991 to 31 st December 2012) has been collected from the office of the Irrigation and Waterways Department, Kolkata, India.

## 统计代写|贝叶斯网络代写Bayesian network代考|Existing Variants of Spatial Bayesian Network

A spatial Bayesian network can be treated as a variant of standard or classical Bayesian network which possesses intrinsic ability to capture spatial influenceover the variables considered in the network (as already introduced in Chap. 2). In order to deal with the different aspects of spatial/spatio-temporal analysis, recently several variants of spatial Bayesian networks have been proposed in literature. For example, Liebig et al. [8] have applied spatial Bayesian network for modeling condi tional dependencies between two or more locations with the help of trajectory data. Walker et al. [15] have proposed two spatial Bayesian network structure learning algorithms which have demonstrated the advantage of incorporating spatial relationships while comparing with traditional structure learning algorithms. In the work [15], the spatial Bayesian learning approaches are meant for handling thematic data in geographic information retrieval system which required significant amount of time for calculating the spatial relationships in large GIS datadatasets. However, none of these works is meant for predicting spatial time series data, and there remains huge scope in spatially extending BN for dealing with various other aspects in ST prediction, especially for spatial time series data.

One of such recently developed spatial Bayesian network model is the SpaBN, which is proposed in the work of Das et al. [6] and is presented in the context of spatial time series prediction. In this chapter, we pay the key attention on SpaBN and attempt to provide a thorough description of its working principle along with relevant case studies on spatial time series data.

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

The SpaBN is an enhanced version of Bayesian network which is recently proposed in [6] to address the issue of very large number of influencing factors in a spatial time series prediction scenario. Unlike a standard or classical Bayesian network, SpaBN structure contains composite nodes along with the usual standard nodes in its directed acyclic graph (DAG). An example network structure (or DAG) in this regard is depicted in Fig. 4.1, where we denote the composite nodes by double lined circles. Typically, a composite node is a composition of several standard/classical nodes corresponding to the same but spatially distributed variable [6]. For instance, composite node $V_{4}$, as shown in Fig. 4.1, is composed of eight standard nodes, namely $V_{4}^{1}, V_{4}^{2}, V_{4}^{3}, \ldots . V_{4}^{8}$, where $V_{4}^{i}$ represents the variable $V_{4}$ at the $i$ th spatial region (or location). The key objective of introducing composite node in the network is to diminish the learning time and space complexity of the spatial Bayesian network model. If, in place of each single composite node, the constituting standard/classical nodes were used separately, then it would include one or more edges for each such node (Fig. 4.1) leading to exponentially very high time and space requirement [7]. Replacement of the standard nodes with equivalent composite node aids in drastically reducing the structural as well as algorithmic complexity of SpaBN. Considering the example scenario in the Fig. $1.2$ in Chap. 1, the SpaBN structure over the spatially distributed variables $T, H$, and $R$, can be represented as in Fig. $4.2$.

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

SpaBN 是最近在 [6] 中提出的贝叶斯网络的增强版本，用于解决空间时间序列预测场景中影响因素非常多的问题。与标准或经典贝叶斯网络不同，SpaBN 结构在其有向无环图 (DAG) 中包含复合节点以及通常的标准节点。图 4.1 描绘了这方面的一个示例网络结构（或 DAG），其中我们用双线圆圈表示复合节点。通常，复合节点是几个标准/经典节点的组合，对应于相同但空间分布的变量[6]。例如，复合节点在4，如图 4.1 所示，由 8 个标准节点组成，即在41,在42,在43,….在48， 在哪里在4一世表示变量在4在一世空间区域（或位置）。在网络中引入复合节点的主要目的是降低空间贝叶斯网络模型的学习时间和空间复杂度。如果单独使用构成标准/经典节点来代替每个单个复合节点，则每个此类节点将包含一条或多条边（图 4.1），从而导致对时间和空间的需求呈指数级增长 [7]。用等效的复合节点替换标准节点有助于大大降低 SpaBN 的结构和算法复杂性。考虑图中的示例场景。1.2在第一章。1、空间分布变量上的SpaBN结构吨,H， 和R, 可以表示为如图.4.2.

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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。