### 统计代写|贝叶斯网络代写Bayesian network代考|ECSE4850

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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|Study Area and Dataset

The experimentation is carried out in the watershed and the associated reservoir of the river Mayurakshi in Jharkhand, India. The reservoir is located at the geographical position of $24^{\circ} 6.6^{\prime} \mathrm{N}$ latitude and $87^{\circ} 18.9^{\prime} E$ longitude (refer Tables $4.9$ and $4.10$ ) and the entire watershed covers nearly $1866 \mathrm{sq} . \mathrm{km}$ area (Bottom-Left: $\left[24.09^{\circ} N, 86.84^{\circ} E\right]$, Top-Right: $\left[24.62^{\circ} N, 87.40^{\circ} \mathrm{E}\right]$ ). The region has tropical climate, showing three well defined seasons: (i) summer: (March-June), (ii) rainy: (July-October), and (iii) winter: (November-February).

In order to experiment with SpaBN, the whole watershed region is considered to be distributed over $10 \times 10$ grid with each cell comprising approximately $33 \mathrm{sq} . \mathrm{km}$ area. The details of the datasets are specified below:

• Rainfall: This is a daily rainfall data, interpolated for each of the gridded locations in the watershed for a span of 11 years (from 1st January, 1991 to 31 st December, 2001) The original daily data is available for four rain gauge stations (Jama $\left(24.35^{\circ} N, 87.15^{\circ} E\right)$, Dumka $\left(24.28^{\circ} N, 87.24^{\circ} E\right)$, Sariyahat $\left(24.58^{\circ} N, 87.01^{\circ} E\right)$,

and Jharmundi $\left(24.40^{\circ} \mathrm{N}, 87.05^{\circ} \mathrm{E}\right)$ ). Additionally, $0.5^{\circ} \times 0.5^{\circ}$ gridded rainfall data (refer Table 4.9) from Indian Meteorological Department (IMD) was also used for interpolation.

• Temperature: This is a daily data of temperature, interpolated for each of the gridded locations, using original high resolution $1^{\circ} \times 1^{\circ}$ gridded temperature data (refer Table 4.9) from IMD.
• Reservoir live/storage capacity: This data is collected from the office of Irrigation and Waterways Dept. Govt. of West Bengal, Kolkata, India, for the same duration (from 1st January, 1991 to 31 st December, 2001) [refer Table 4.10].
• Topographical data: This includes slope map, soil map, and spatial distribution of land use land cover (LULC) (Fig.4.7) over the whole watershed. The original data of soil map and elevation map are available with National Bureau of Soil Survey and Land Use Planning, Govt of India. The LULC data is collected from Bhuvan portal [18]. It is evident from the maps that the watershed contains diverse LULC and soil categories. Almost $66 \%$ of the total area is agricultural crop land, and about $74 \%$ of the region is full of fine loamy soil.

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

On analyzing the tables and the Fig. 4.10, we can infer the following about SpaBNbased prediction model:
(i) It is evident from the Tables $4.13,4.14,4.15$ and $4.16$ that the SpaBNbased approach produces the highest NSE value compared to statistical ARIMA, standard BN, and ANN models. Further, in almost all the cases, the value of NSE is approximately 1 . This indicates a highly accurate prediction made by SpaBN. Contrarily, the NSE values associated with the other prediction models, including standard BN, deviate quite significantly from 1. This demonstrates the preeminence of SpaBN-based prediction over the others, in carrying out spatial time series prediction.
(ii) It can also be noted that the values of NRMSD, computed for all the prediction years, are considerably low $(0.07-0.16)$ in case of SpaBN. This indicates the superiority of SpaBN[6] compared to the other techniques (refer Tables $4.13$, $4.14,4.15$ and 4.16). This also reveals the effectiveness of incorporating spatial information which eventually improves the accuracy for SpaBN-based prediction.
(iii) Besides, from the $\mathrm{D}_{v}$ and SEP values in Tables $4.13,4.14,4.15$ and $4.16$, it can be observed that SpaBN is more than $55 \%$ better than the statistical forecasting models, and almost $25 \%$ better than the ANN-based prediction technique on average. Further, with respect to the standard BNs that handles no spatial information, the performance of SpaBN-based approach is improved about $13 \%$.
(iv) From the Tables $4.13,4.14,4.15$ and $4.16$, we can also find that in most of the cases, the SpaBN provides a high $R^{2}$ value $\sim 1$, whereas the $R^{2}$ value for the ARIMA models, ANN, and standard BN are $\sim 0.0,0.3$, and $0.6$, respectively. In general, the $R^{2}$ values range between 0 and 1 , and these are indicators of fitness of the prediction methods. The higher the value of $R^{2}$, the better the model fits for prediction. Therefore, the high $R^{2}$ value corresponding to SpaBN demonstrates that the model is desirably fit for the hydrological time series prediction.
(v) The comparative study of the model forecasts and the actual/observed daily reservoir live capacities for all the prediction years 1998-2001 are shown in the Fig. 4.10. It is evident from the figure that the predicted time series of SpaBN-based prediction model is matching well with the actual/observed value of live capacity in all the cases, indicating effectiveness of the model. From the Fig. 4.10, it can be also observed that, whenever there is over estimation or under-estimation generated from standard BN, the SpaBN has a notable tendency to improve this by making it as near to the observed value as possible [6]. Consideration of additional predictors like evapotranspiration, evaporation etc. from the reservoir water surface and watershed may further improve the model performance.

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

The idea of incorporating domain semantics in Bayesian network is not very new. Different variants of semantic Bayesian networks $[2,9,12,15,20]$ have shown their effectiveness in several application areas. However, Bayesian networks with embedded semantics from spatial domain is still a little explored topic.
The semantic Bayesian network (SeBN) [9] proposed by Kim et al. is intended for conversational agent to infer the detailed intentions of the user. The SeBN itself maintains probabilistic as well as semantic relationships and the inference generation is followed from a thresholding process that helps in selecting target value appropriate for the user query. The sBN is another variant of semantic Bayesian network proposed by Zhou et al. [20] for constructing web mashup network. sBN is utilized here to process the information from semantic web. In order to describe the information on the graph structure and facilitate processing of semantic graph structure-based attributes, the authors use a semantic subgraph template defined using SPARQL query. There also exist some research works exploiting semantics while generating inference using Bayesian network. The works by Butz et al. $[2,12]$ are worth mentioning in this context. In [2], the authors propose a join tree probability propagation architecture for conducting the semantically enhanced inference generation from BN. The architecture is defined in such a way that each node in the join tree maintains a local BN preserving all conditional independencies of the original Bayesian network. In the work of Madsen and Butz [12], the authors use a lazy Propagation model for capturing semantics of potentials created during belief updating process. The model employs a combination of Shenoy-Shafer propagation [13] and variable elimination scheme to help in computing messages and marginals.

Recently, Das and Ghosh [5] have proposed a new variant of semantic Bayesian network, termed as semBnet, which is also applicable for spatial time series prediction [5]. This can be considered as the first work that uses semantically enhanced BN model for multivariate time series prediction in spatial domain. The overall working principle of semBnet is grounded on semantic hierarchy, a hierarchical representation of domain knowledge from which semBnet is able to extract the semantic similarity between various spatial concepts and can utilize the same in the Bayesian analysis process.

## 统计代写|贝叶斯网络代写Bayesian network代考|Study Area and Dataset

• 降雨量：这是一个每日降雨量数据，在 11 年（从 1991 年 1 月 1 日至 2001 年 12 月 31 日）内为流域中的每个网格位置插值（从 1991 年 1 月 1 日到 2001 年 12 月 31 日）原始每日数据可用于四个雨量站（贾马(24.35∘ñ,87.15∘和), 杜姆卡(24.28∘ñ,87.24∘和), 萨里亚哈特(24.58∘ñ,87.01∘和),

• 温度：这是每日的温度数据，使用原始高分辨率对每个网格位置进行插值1∘×1∘来自 IMD 的网格温度数据（参见表 4.9）。
• 水库活/蓄水能力：该数据是从灌溉和水道部政府办公室收集的。印度加尔各答的西孟加拉邦，同样的时间（从 1991 年 1 月 1 日到 2001 年 12 月 31 日）[参见表 4.10]。
• 地形数据：包括坡度图、土壤图和整个流域土地利用土地覆被（LULC）的空间分布（图 4.7）。土壤图和海拔图的原始数据可从印度政府国家土壤调查和土地利用规划局获得。LULC 数据是从 Bhuvan 门户网站 [18] 收集的。从地图上可以明显看出，流域包含不同的 LULC 和土壤类别。几乎66%总面积的一半是农田，大约74%该地区充满了细壤土。

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

(i) 从表格中可以看出4.13,4.14,4.15和4.16与统计 ARIMA、标准 BN 和 ANN 模型相比，基于 SpaBN 的方法产生最高的 NSE 值。此外，几乎在所有情况下，NSE 的值都约为 1。这表明 SpaBN 做出了高度准确的预测。相反，与包括标准 BN 在内的其他预测模型相关的 NSE 值与 1 有很大的偏差。这证明了基于 SpaBN 的预测在执行空间时间序列预测时优于其他预测模型。
(ii) 还可以注意到，针对所有预测年份计算的 NRMSD 值相当低(0.07−0.16)在 SpaBN 的情况下。这表明 SpaBN[6] 与其他技术相比具有优势（参见表4.13, 4.14,4.15和 4.16)。这也揭示了结合空间信息的有效性，最终提高了基于 SpaBN 的预测的准确性。
(iii) 此外，从D在和表中的 SEP 值4.13,4.14,4.15和4.16, 可以看出 SpaBN 大于55%比统计预测模型好，而且几乎25%平均而言，优于基于 ANN 的预测技术。此外，对于不处理空间信息的标准 BN，基于 SpaBN 的方法的性能提高了大约13%.
(iv) 从表格4.13,4.14,4.15和4.16，我们还可以发现，在大多数情况下，SpaBN 提供了很高的R2价值∼1，而R2ARIMA 模型、ANN 和标准 BN 的值是∼0.0,0.3， 和0.6， 分别。一般来说，R2值范围在 0 和 1 之间，这些是预测方法的适应度指标。的价值越高R2，模型越适合预测。因此，高R2对应于 SpaBN 的值表明该模型非常适合水文时间序列预测。
(v) 1998-2001 年所有预测年份的模型预测与实际/观测的水库日活容量对比研究见图 4.10。从图中可以明显看出，基于 SpaBN 的预测模型的预测时间序列在所有情况下都与实际/观察到的活量值很好地匹配，表明了模型的有效性。从图 4.10 还可以观察到，每当标准 BN 产生高估或低估时，SpaBN 具有通过使其尽可能接近观察值来改善这一点的显着趋势 [6] . 考虑来自水库水面和流域的其他预测因子，如蒸发量、蒸发量等，可以进一步提高模型性能。

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

Kim等人提出的语义贝叶斯网络（SeBN）[9]。旨在让会话代理推断用户的详细意图。SeBN 本身维护概率关系和语义关系，并且推理生成是从有助于选择适合用户查询的目标值的阈值处理之后进行的。sBN 是 Zhou 等人提出的语义贝叶斯网络的另一种变体。[20] 用于构建 web mashup 网络。这里使用 sBN 来处理来自语义网络的信息。为了描述关于图结构的信息并促进基于语义图结构的属性的处理，作者使用了使用 SPARQL 查询定义的语义子图模板。也有一些研究工作在利用贝叶斯网络生成推理的同时利用语义。Butz 等人的作品。[2,12]在这方面值得一提。在 [2] 中，作者提出了一种连接树概率传播架构，用于从 BN 进行语义增强的推理生成。该架构以这样一种方式定义，即连接树中的每个节点都维护一个本地 BN，保留原始贝叶斯网络的所有条件独立性。在 Madsen 和 Butz [12] 的工作中，作者使用惰性传播模型来捕获在信念更新过程中创建的势的语义。该模型采用 Shenoy-Shafer 传播 [13] 和变量消除方案的组合来帮助计算消息和边缘。

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