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# 数学代写|统计机器学习作业代写Statistical Machine Learning代考|Genomic-Enabled Prediction Bayesian Lasso Model

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## 数学代写|统计机器学习作业代写Statistical Machine Learning代考|Genomic-Enabled Prediction Bayesian Lasso Model

Note that the prior distribution for the beta coefficients and the prior variance of this distribution in BayesB and BayesC can be equivalently expressed as a mixture of a scaled inverse Chi-squared distribution with parameters $v_{\beta}$ and $S_{\beta}$, and a degenerate distribution at zero, that is, $\beta_{j} \sim N\left(0, \sigma_{\beta}^{2}\right)$ and $\sigma_{\beta}^{2} \sim \pi_{p} \chi^{-2}\left(v_{\beta}, S_{\beta}\right)+$ $\left(1-\pi_{p}\right) \mathrm{DG}(0)$. So, based on this result and the connections between the models described before, the main difference between all these models is the manner in which the prior variance of the predictor variable is modelled.

To illustrate how to use the models described before, here we consider the prediction of grain yield (tons/ha) based on marker information. The data set used consists of 30 lines in four environments with one and two repetitions and the genotyped information contains 500 markers for each line. The numbers of lines with one (two) repetition are $6(24), 2(28), 0(30)$, and $3(27)$ in Environments 1,2 , 3 , and 4 , respectively, resulting in 229 observations. The performance prediction of all these models was evaluated with 10 random partitions in a cross-validation strategy, where $80 \%$ of the complete data set was used to fit the model and the rest to evaluate the model in terms of the mean squared error of prediction (MSE).

The results for all models (shown in Table 6.1) were obtained by iterating 10,000 times the corresponding Gibbs sampler and discarding the first 1000 of them, using the default hyperparameter values implemented in BGLR. This indicates that the behavior of all the models is similar, except the BayesC, where the MSE is slightly greater than the rest.
The $\mathrm{R}$ code to obtain the results in Table $6.1$ is given in Appendix 3 .
What happens when using other hyperparameter values? Although the ones used here (proposed by Pérez et al. 2010) did not always produce the best prediction performance (Lehermeier et al. 2013) and there are other ways to propose the hyperparameter values in these models (Habier et al. 2010, 2011), it is important to point out that the values used by default in BGLR work reasonably well and that it is not easy to find other combinations that work better in all applications, and when you want to use other combinations of hyperparameters you need to be very careful because you can dramatically affect the predictive performance of the model that uses the default hyperparameters.

## 广义线性模型代考

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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。