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Homework 4Question 1Suppose that has a multinomial distribution with PMF.Suppose that the prior distribution for � is�0. Derive a Gibbs sampling algorithm to sample from the posteriordistribution of �. Implement your algorithm in Matlab for the case where / = 5, (8,7,6,5,4), = ,6 = 1 to obtain an estimate of the posterior mean of �. Use =1000Gibbs iterations and 7 = 100 burn-in samples.Question 2Let�is a random sample from. Choose the prior forProvide a Gibbs sampling algorithm for sampling from the posterior distribution of.Question 3Write a Matlab code to implement model selection based on the LASSO method (use the Matlabquadprog function). Please select the parameter X by finding the minimum of BIC[on a grid of Xvalues.Apply your code to the data shown in the table below. Consider the full model 8�, and evaluateBIC[ on the grid C0,0.001,0.002, … ,1F of X values .Compare your results to the Bayesian variable selection method described in the slides. Set c =10, c7 = 0, G = 0.05, , = 0.5, and (d) = ∏ 0.5f$0.5f$>.In addition, compare with model selection results obtained with the PRESS and BIC criteria. Question 4:Write a Matlab code to fit a stationary (implies mean and variance are constants) Gaussianrandom field model with Gaussian correlation function and compute its posterior mean and 95%interval predictions (for simplicity, you may write a code that works just for the case of a singlereal input ). Apply your code to the data below, and plot the data, posterior mean, 95%prediction intervals, and the true function q = sin (7) in the same figure. Please report themaximum likelihood estimates of the prior mean :, prior variance , and parameter Q in theGaussian correlation function.q0 sin(7 × 0)0.2 sin(7 × 0.2)0.4 sin(7 × 0.4)0.6 sin(7 × 0.6)0.8 sin(7 × 0.8)1 sin(7 × 1)本团队核心人员组成主要包括硅谷工程师、BAT一线工程师，精通德英语！我们主要业务范围是代做编程大作业、课程设计等等。我们的方向领域：window编程 数值算法 AI人工智能 金融统计 计量分析 大数据 网络编程 WEB编程 通讯编程 游戏编程多媒体linux 外挂编程 程序API图像处理 嵌入式/单片机 数据库编程 控制台 进程与线程 网络安全 汇编语言 硬件编程 软件设计 工程标准规等。其中代写编程、代写程序、代写留学生程序作业语言或工具包括但不限于以下范围:C/C++/C#代写Java代写IT代写Python代写辅导编程作业Matlab代写Haskell代写Processing代写Linux环境搭建Rust代写Data Structure Assginment 数据结构代写MIPS代写Machine Learning 作业 代写Oracle/SQL/PostgreSQL/Pig 数据库代写/代做/辅导Web开发、网站开发、网站作业ASP.NET网站开发Finance Insurace Statistics统计、回归、迭代Prolog代写Computer Computational method代做因为专业，所以值得信赖。如有需要，请加QQ：99515681 或邮箱：[email protected] 微信：codehelp