### 统计代写|贝叶斯网络代写Bayesian network代考|CSC216

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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|B N R C-Based Prediction

Once all the tuned inferred values are produced, these are further processed to finally generate the predicted value of the variable. Among all the tuned inferred values of the prediction variable, the predicted value becomes the one which is associated with the highest probability estimates $P\left({ }^{*}\right)$ during inference generation. Therefore, if pre $d_{V_{j}}$ is the predicted value of the variable $V_{j}$, then pred $V_{V_{j}}=$ tuned_infer $_{V_{j}}^{(t+1)}$ such that $P\left(\operatorname{infer}{V} \mid e\right)=\max \left{P\left(V{j} \mid e\right)\right}$, where $e$ indicates the given combination of values for the set of evidence variables. Now, since the overall analysis is performed considering discretized value of the variables, the predicted value pred ${ }{V j}$ may also be obtained in the form of range of values $\left[L B{j}, U B_{j}\right]$. In order to get a single value for the prediction variable, the mid value of the range may be considered. Therefore, finally, pre $_{V_{j}}=\left(L B_{j}+U B_{j}\right) / 2$.

In the following part of the chapter, we attempt to present two separate case studies to validate the effectiveness of BNRC model in the context of spatial time series prediction under paucity of domain variables.

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

The architecture of the BNRC-based prediction system corresponding to the present case study is depicted in Fig. 3.8. The evaluation of the model is carried out in comparison with a number of benchmark time series prediction techniques, namely Automated Auto-regressive Integrated Moving Average (A-ARIMA), Vector Auto-regressive Moving Average (VARMA), Generalized Auto-regressive Heteroskedasticity (GARCH) model, neural network with feed forward back propagation (FFBP) [10], Recurrent Neural Network (RNN), Non-linear Auto-Regressive Neural Network (NARNET), Support Vector Machine (SVM), and the state-of-the-art space-time model based on

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

The performance of the BNRC and the other prediction techniques are measured in terms of four statistical measures, namely NRMSD, MAE, MAPE and $R^{2}$. The detailed mathematical formulations for these metrics are given below. In each case, $O_{\max }$ is the maximum observed (actual) value of the prediction variable, $O_{\min }$ is the minimum observed value of the prediction variable, $V_{o_{\mathrm{r}}}$ is the actual value corresponding to the $i$-th observation of the variable, $V_{p i}$ is the predicted value corresponding to the $i$-th observation of the variable, $\bar{V}{o}$ is the mean of observed/actual values of the prediction variable, $\overline{V{p}}$ is the mean of predicted values of the variable, and $N$ is the total number of observations.: The performance of the BNRC and the other prediction techniques are measured in terms of four statistical measures, namely NRMSD, MAE, MAPE and $R^{2}$. The detailed mathematical formulations for these metrics are given below. In each case, $O_{\max }$ is the maximum observed (actual) value of the prediction variable, $O_{\min }$ is the minimum observed value of the prediction variable, $V_{o_{\mathrm{r}}}$ is the actual value corresponding to the $i$-th observation of the variable, $V_{p i}$ is the predicted value corresponding to the $i$-th observation of the variable, $\bar{V}{o}$ is the mean of observed/actual values of the prediction variable, $\overline{V{p}}$ is the mean of predicted values of the variable, and $N$ is the total number of observations.:

$$N R M S D=\frac{1}{\left(O_{\max }-O_{\min }\right)} \sqrt{\frac{1}{N} \sum_{i=1}^{N}\left(V_{o_{i}}-V_{p_{i}}\right)^{2}}$$
NRMSD is also called Normalized Root Mean Square Error (NRMSE), and is often expressed in percentage ( $\%$ ). The best-fit between observed (actual) and predicted value under ideal conditions yields NRMSD $=0$.
$$R^{2}=\frac{\left[\sum_{i=1}^{N}\left(V_{o_{i}}-\overline{V_{o}}\right)\left(V_{p_{i}}-\overline{V_{p}}\right)\right]^{2}}{\sum_{i=1}^{N}\left(V_{o_{i}}-\overline{V_{o}}\right)^{2} \cdot \sum_{i=1}^{N}\left(V_{p_{i}}-\overline{V_{p}}\right)^{2}}$$
An $R^{2}$ value of 1 indicates a perfect fit between the observed and predicted value.
$$M A E=\frac{1}{N} \sum_{i=1}^{N}\left|V_{o_{i}}-V_{p_{i}}\right|$$
The best-fit between observed and predicted value under ideal conditions yields MAE $=0$.
$$M A P E=\frac{\left|\overline{V_{o}}-\overline{V_{p}}\right|}{\left|\overline{V_{o}}\right|} \times 100$$
The best-fit between observed (actual) and predicted value yields MAPE $=0$.
The comparative results of predicting Temperature $(\mathcal{T})$, Humidity $(\mathcal{H})$, and Precipitation rate $(\mathcal{R})$ are summarized in the Table $3.5$, Table $3.6$, and Table $3.7$, respectively.

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

BNRC 和其他预测技术的性能是根据四个统计指标来衡量的，即 NRMSD、MAE、MAPE 和R2. 下面给出了这些指标的详细数学公式。在每种情况下，○最大限度是预测变量的最大观察（实际）值，○分钟是预测变量的最小观测值，在○r是对应的实际值一世-对变量的第一次观察，在p一世是对应的预测值一世-对变量的第一次观察，在¯○是预测变量的观察值/实际值的平均值，在p¯是变量预测值的平均值，并且ñ是观察的总数。：BNRC 和其他预测技术的性能是根据四个统计指标来衡量的，即 NRMSD、MAE、MAPE 和R2. 下面给出了这些指标的详细数学公式。在每种情况下，○最大限度是预测变量的最大观察（实际）值，○分钟是预测变量的最小观测值，在○r是对应的实际值一世-对变量的第一次观察，在p一世是对应的预测值一世-对变量的第一次观察，在¯○是预测变量的观察值/实际值的平均值，在p¯是变量预测值的平均值，并且ñ是观察的总数。：

ñR米小号D=1(○最大限度−○分钟)1ñ∑一世=1ñ(在○一世−在p一世)2
NRMSD 也称为归一化均方根误差 (NRMSE)，通常以百分比 (%）。理想条件下观察值（实际值）和预测值之间的最佳拟合产生 NRMSD=0.

R2=[∑一世=1ñ(在○一世−在○¯)(在p一世−在p¯)]2∑一世=1ñ(在○一世−在○¯)2⋅∑一世=1ñ(在p一世−在p¯)2

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## MATLAB代写

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