# 统计代写|贝叶斯分析代写Bayesian Analysis代考|MAST90125

#### Doug I. Jones

Lorem ipsum dolor sit amet, cons the all tetur adiscing elit

couryes™为您提供可以保分的包课服务

couryes-lab™ 为您的留学生涯保驾护航 在代写贝叶斯分析Bayesian Analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写贝叶斯分析Bayesian Analysis代写方面经验极为丰富，各种代写贝叶斯分析Bayesian Analysis相关的作业也就用不着说。

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Multinomial model for categorical data

The binomial distribution that was emphasized in Chapter 2 can be generalized to allow more than two possible outcomes. The multinomial sampling distribution is used to describe data for which each observation is one of $k$ possible outcomes. If $y$ is the vector of counts of the number of observations of each outcome, then
$$p(y \mid \theta) \propto \prod_{j=1}^k \theta_j^{y_j},$$
where the sum of the probabilities, $\sum_{j=1}^k \theta_j$, is 1 . The distribution is typically thought of as implicitly conditioning on the number of observations, $\sum_{j=1}^k y_j=n$. The conjugate prior distribution is a multivariate generalization of the beta distribution known as the Dirichlet,
$$p(\theta \mid \alpha) \propto \prod_{j=1}^k \theta_j^{\alpha_j-1},$$
where the distribution is restricted to nonnegative $\theta_j$ ‘s with $\sum_{j=1}^k \theta_j=1$; see Appendix A for details. The resulting posterior distribution for the $\theta_j$ ‘s is Dirichlet with parameters $\alpha_j+y_j$.

The prior distribution is mathematically equivalent to a likelihood resulting from $\sum_{j=1}^k \alpha_j$ observations with $\alpha_j$ observations of the $j$ th outcome category. As in the binomial there are several plausible noninformative Dirichlet prior distributions. A uniform density is obtained by setting $\alpha_j=1$ for all $j$; this distribution assigns equal density to any vector $\theta$ satisfying $\sum_{j=1}^k \theta_j=1$. Setting $\alpha_j=0$ for all $j$ results in an improper prior distribution that is uniform in the $\log \left(\theta_j\right)$ ‘s. The resulting posterior distribution is proper if there is at least one observation in each of the $k$ categories, so that each component of $y$ is positive. The bibliographic note at the end of this chapter points to other suggested noninformative prior distributions for the multinomial model.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Multivariate normal model with known variance

The basic model to be discussed concerns an observable vector $y$ of $d$ components, with the multivariate normal distribution,
$$y \mid \mu, \Sigma \sim \mathrm{N}(\mu, \Sigma)$$
where $\mu$ is a (column) vector of length $d$ and $\Sigma$ is a $d \times d$ variance matrix, which is symmetric and positive definite. The likelihood function for a single observation is
$$p(y \mid \mu, \Sigma) \propto|\Sigma|^{-1 / 2} \exp \left(-\frac{1}{2}(y-\mu)^T \Sigma^{-1}(y-\mu)\right),$$
and for a sample of $n$ independent and identically distributed observations, $y_1, \ldots, y_n$, is
\begin{aligned} p\left(y_1, \ldots, y_n \mid \mu, \Sigma\right) & \propto|\Sigma|^{-n / 2} \exp \left(-\frac{1}{2} \sum_{i=1}^n\left(y_i-\mu\right)^T \Sigma^{-1}\left(y_i-\mu\right)\right) \ & =|\Sigma|^{-n / 2} \exp \left(-\frac{1}{2} \operatorname{tr}\left(\Sigma^{-1} S_0\right)\right), \end{aligned}
where $S_0$ is the matrix of ‘sums of squares’ relative to $\mu$,
$$S_0=\sum_{i=1}^n\left(y_i-\mu\right)\left(y_i-\mu\right)^T$$

# 贝叶斯分析代考

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Multinomial model for categorical data

$$p(y \mid \theta) \propto \prod_{j=1}^k \theta_j^{y_j},$$

$$p(\theta \mid \alpha) \propto \prod_{j=1}^k \theta_j^{\alpha_j-1},$$

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Multivariate normal model with known variance

$$y \mid \mu, \Sigma \sim \mathrm{N}(\mu, \Sigma)$$

$$p(y \mid \mu, \Sigma) \propto|\Sigma|^{-1 / 2} \exp \left(-\frac{1}{2}(y-\mu)^T \Sigma^{-1}(y-\mu)\right),$$

\begin{aligned} p\left(y_1, \ldots, y_n \mid \mu, \Sigma\right) & \propto|\Sigma|^{-n / 2} \exp \left(-\frac{1}{2} \sum_{i=1}^n\left(y_i-\mu\right)^T \Sigma^{-1}\left(y_i-\mu\right)\right) \ & =|\Sigma|^{-n / 2} \exp \left(-\frac{1}{2} \operatorname{tr}\left(\Sigma^{-1} S_0\right)\right), \end{aligned}

$$S_0=\sum_{i=1}^n\left(y_i-\mu\right)\left(y_i-\mu\right)^T$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

Days
Hours
Minutes
Seconds

# 15% OFF

## On All Tickets

Don’t hesitate and buy tickets today – All tickets are at a special price until 15.08.2021. Hope to see you there :)