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统计代写|广义线性模型代写Generalized linear model代考|No specified distribution

There are occasions when the distribution of the response variable is unknown, but the experimenter believes that the link function $g(\cdot)$ and variance function $V(\mu)$ can be specified. Without knowledge of the distribution, the $\log$ likelihood function $\ell(\boldsymbol{\beta})$ cannot be constructed. However, a quasi-likelihood may be formulated. The mathematical details are provided in McCullagh \& Nelder (1989, Chapter 9 ). To perform an analysis in $\mathrm{R}$, one needs to make some modifications to the arguments of the $g l m$ function in R. An example is given in Faraway (2006, Section 7.4).
Faraway (2006, Section 3.1) contains the analysis of data from a dataset called gala (for Galapagos Islands) under the assumption that the response variable has a Poisson distribution. Running the commands
data(gala)
gala <- gala $[,-2]$
modp <- glm(Species $.$, family $=$ poisson, data $=$ gala $)$
summary (modp)
gives the output
Deviance Residuals:

$$\begin{array}{rrrrr} \text { Min } & 1 Q & \text { Median } & 3 Q & \text { Max } \ -8.2752 & -4.4966 & -0.9443 & 1.9168 & 10.1849 \end{array}$$
Coefficients:

统计代写|广义线性模型代写Generalized linear model代考|Bayesian Experimental Design

Bayesian analysis is a large and rapidly growing field of statistics. An oversimplified description is to say that, when estimating some parameter(s), one begins with an expression of prior knowledge or belief about the value of the parameters. This is combined with empirical knowledge about the value of the parameters that is gained by conducting an experiment. The result is a posterior description of the statistical behaviour of the parameters. Many books, including Carlin \& Louis (2009), provide a coverage of Bayesian analysis.

Estimation of parameter values does not occur in the determination of an optimal design. However, the expression Bayesian experimental design is often used for the procedure about to be described because we use prior belief about the value of the vector of parameters, $\boldsymbol{\beta}$, to assist us in the determination of the design.

Of course, we have been expressing prior belief about the value of $\boldsymbol{\beta}$ in previous chapters, when using the nominated value of $\boldsymbol{\beta}$ as though we are certain that it is correct. In what follows, we recognise some uncertainty about our knowledge of $\boldsymbol{\beta}$. Many people who feel uncomfortable specifying the value of the parameter vector $\boldsymbol{\beta}$ in the methods considered in previous chapters may feel happier using Bayesian design methods.
An approach that is fully Bayesian, often referred to as a decisiontheoretic approach, was reviewed by Chaloner \& Verdinelli (1995), and is addressed by Overstall \& Woods (2017). Consult either of these references for more information. The aim of this approach is to maximise the experimenter’s gain from using one of a collection of designs if given one of a collection of vectors of response variables when the parameter vertor is one from a collection of such vectors. It requires the maximisation of an expected utility function (Overstall \& Woods, 2017, eq. 1)
$$U(\boldsymbol{\delta})=\iint_{\Psi, \mathcal{Y}} u(\boldsymbol{\delta}, \boldsymbol{\psi}, \boldsymbol{y}) \pi(\boldsymbol{y}, \boldsymbol{\psi} \mid \boldsymbol{\delta}) d \boldsymbol{y} d \boldsymbol{\psi}$$
where the symbols are defined in Overstall \& Woods $(2017$, p. 458).

统计代写|义线性模型代写Generalized linear model代考|No specified distribution

Faraway (2006 年，第 $3.1$ 节) 在假设响应变量具有泊松分布的情况下，对来自名为 gala (加拉帕戈斯群岛) 的数据集的数据 进行了分析。运行命令 data(gala)
gala<- gala[, $-2]$
modp <-glm(物种.， 家庭=泊松，数据=节日)
summary (modp)

$\begin{array}{lllllllll}\text { Min } 1 Q & \text { Median } & 3 Q \quad \operatorname{Max}-8.2752 & -4.4966 & -0.9443 & 1.9168 & 10.1849\end{array}$

统计代写|广义线性模型代写Generalized linear model代考|Bayesian Experimental Design

Louis (2009)，都隄供了贝叶斯分析的内容。

Chaloner $\backslash \&$ \& Verdinelli (1995) 回顾了完全贝叶斯的方法，通常称为决策理论方法，并由 Overstall $\ \&$ Woods (2017) 解决。

2017, eq. 1)
$$U(\boldsymbol{\delta})=\iint_{\Psi, \mathcal{Y}} u(\boldsymbol{\delta}, \boldsymbol{\psi}, \boldsymbol{y}) \pi(\boldsymbol{y}, \boldsymbol{\psi} \mid \boldsymbol{\delta}) d \boldsymbol{y} d \boldsymbol{\psi}$$

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。

Posted on Categories:Linear Model, 数据科学代写, 线性模型代写, 统计代写, 统计代考

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统计代写|线性模型代写Linear Model代考|Multivariate density functions

In considering $n$ random variables $X_{1}, X_{2}, \ldots, X_{n}$, for which $x_{1}, x_{2}, \ldots$, $x_{n}$ represents a set of realized values we write the cumulative density function as
$$\operatorname{Pr}\left(X_{1} \leq x_{1}, X_{2} \leq x_{2}, \ldots, X_{n} \leq x_{n}\right)=F\left(x_{1}, x_{2}, \ldots, x_{n}\right)$$
Then the density function is
$$f\left(x_{1}, x_{2}, \ldots, x_{n}\right)=\frac{\partial^{n}}{\partial x_{1} \partial x_{2} \ldots \partial x_{n}} F\left(x_{1}, x_{2}, \ldots, x_{n}\right) \text {. }$$
Conditions which $f\left(x_{1}, x_{2}, \ldots, x_{n}\right)$ must satisfy are and
$$\begin{gathered} f\left(x_{1}, x_{2}, \ldots, x_{n}\right) \geq 0 \text { for }-\infty<x_{i}<\infty \text { for all } i \ \int_{-\infty}^{\infty} \cdots \int_{-\infty}^{\infty} f\left(x_{1}, x_{2}, \ldots, x_{n}\right) d x_{1} d x_{2} \ldots d x_{n}=1 \end{gathered}$$

统计代写|线性模型代写Linear Model代考|Moments

The $k$ th moment about zero of the $i$ th variable is $E\left(x_{i}^{k}\right)$, the expected value of the $k$ th power of $x_{i}$ :
$$\mu_{x_{i}}^{(k)}=E\left(x_{i}^{k}\right)=\int_{-\infty}^{\infty} x_{i}^{k} g\left(x_{i}\right) d x_{i}$$
and on substituting from (7) for $g\left(x_{i}\right)$ this gives
$$\mu_{x_{i}}^{(k)}=\int_{-\infty}^{\infty} \cdots \int_{-\infty}^{\infty} x_{i}^{k} f\left(x_{1}, x_{2}, \ldots, x_{n}\right) d x_{1} d x_{2} \ldots d x_{n} .$$
In particular, when $k=1$, the superscript $(k)$ is usually omitted and $\mu_{i}$ is written for $\mu_{i}^{(1)}$.
The covariance between the $i$ th and $j$ th variables for $i \neq j$ is
\begin{aligned} \sigma_{i j} &=E\left(x_{i}-\mu_{i}\right)\left(x_{j}-\mu_{j}\right) \ &=\int_{-\infty}^{\infty} \int_{-\infty}^{\infty}\left(x_{i}-\mu_{i}\right)\left(x_{j}-\mu_{j}\right) g\left(x_{i}, x_{j}\right) d x_{i} d x_{j} \ &=\int_{-\infty}^{\infty} \cdots \int_{-\infty}^{\infty}\left(x_{i}-\mu_{i}\right)\left(x_{j}-\mu_{j}\right) f\left(x_{1}, x_{2}, \ldots, x_{n}\right) d x_{1} \ldots d x_{n}, \end{aligned}
and similarly the variance of the $i$ th variable is
\begin{aligned} \sigma_{i i} \equiv \sigma_{i}^{2} &=E\left(x_{i}-\mu_{i}\right)^{2} \ &=\int_{-\infty}^{\infty}\left(x_{i}-\mu_{i}\right)^{2} g\left(x_{i}\right) d x_{i} \ &=\int_{-\infty}^{\infty} \cdots \int_{-\infty}^{\infty}\left(x_{i}-\mu_{i}\right)^{2} f\left(x_{1}, x_{2}, \ldots, x_{n}\right) d x_{1} \ldots d x_{n} \end{aligned}

统计代写|线性模型代写Linear Model代考|Multivariate density functions

$$\operatorname{Pr}\left(X_{1} \leq x_{1}, X_{2} \leq x_{2}, \ldots, X_{n} \leq x_{n}\right)=F\left(x_{1}, x_{2}, \ldots, x_{n}\right)$$

$$f\left(x_{1}, x_{2}, \ldots, x_{n}\right)=\frac{\partial^{n}}{\partial x_{1} \partial x_{2} \ldots \partial x_{n}} F\left(x_{1}, x_{2}, \ldots, x_{n}\right)$$

$$f\left(x_{1}, x_{2}, \ldots, x_{n}\right) \geq 0 \text { for }-\infty<x_{i}<\infty \text { for all } i \int_{-\infty}^{\infty} \cdots \int_{-\infty}^{\infty} f\left(x_{1}, x_{2}, \ldots, x_{n}\right) d x_{1} d x_{2} \ldots d x_{n}=1$$

统计代写|线性模型代写Linear Model代考|Moments

$$\mu_{x_{i}}^{(k)}=E\left(x_{i}^{k}\right)=\int_{-\infty}^{\infty} x_{i}^{k} g\left(x_{i}\right) d x_{i}$$

$$\mu_{x_{i}}^{(k)}=\int_{-\infty}^{\infty} \cdots \int_{-\infty}^{\infty} x_{i}^{k} f\left(x_{1}, x_{2}, \ldots, x_{n}\right) d x_{1} d x_{2} \ldots d x_{n}$$

$$\sigma_{i j}=E\left(x_{i}-\mu_{i}\right)\left(x_{j}-\mu_{j}\right) \quad=\int_{-\infty}^{\infty} \int_{-\infty}^{\infty}\left(x_{i}-\mu_{i}\right)\left(x_{j}-\mu_{j}\right) g\left(x_{i}, x_{j}\right) d x_{i} d x_{j}=\int_{-\infty}^{\infty} \ldots \int_{-\infty}^{\infty}\left(x_{i}-\mu_{i}\right)\left(x_{j}-\mu_{j}\right) f\left(x_{1}, x_{2}, \ldots, x_{n}\right) d x_{1} \ldots d x_{n}$$

$$\sigma_{i i} \equiv \sigma_{i}^{2}=E\left(x_{i}-\mu_{i}\right)^{2} \quad=\int_{-\infty}^{\infty}\left(x_{i}-\mu_{i}\right)^{2} g\left(x_{i}\right) d x_{i}=\int_{-\infty}^{\infty} \ldots \int_{-\infty}^{\infty}\left(x_{i}-\mu_{i}\right)^{2} f\left(x_{1}, x_{2}, \ldots, x_{n}\right) d x_{1} \ldots d x_{n}$$

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。