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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写统计推断Statistical inference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。我们的专家在代写统计推断Statistical inference代写方面经验极为丰富，各种代写统计推断Statistical inference相关的作业也就用不着说。

• 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|统计推断代写Statistical inference代考|Simple observation schemes—Examples

In Gaussian o.s.

• the observation space $(\Omega, \Pi)$ is the space $\mathbf{R}^{d}$ with Lebesgue measure;
• the family $\left{p_{\mu}(\cdot): \mu \in \mathcal{M}\right}$ is the family of Gaussian densities $\mathcal{N}(\mu, \Theta)$, with fixed positive definite covariance matrix $\Theta$; distributions from the family are parameterized by their expectations $\mu$. Thus,
$$\mathcal{M}=\mathbf{R}^{d}, p_{\mu}(\omega)=\frac{1}{(2 \pi)^{d / 2} \sqrt{\operatorname{Det}(\Theta)}} \exp \left{-\frac{1}{2}(\omega-\mu)^{T} \Theta^{-1}(\omega-\mu)\right}$$
• the family $\mathcal{F}$ is the family of all affine functions on $\mathbf{R}^{d}$.
It is immediately seen that Gaussian o.s. meets all requirements imposed on a simple o.s. For example,
$$\ln \left(p_{\mu}(\omega) / p_{\nu}(\omega)\right)=(\nu-\mu)^{T} \Theta^{-1} \omega+\frac{1}{2}\left[\nu^{T} \Theta^{-1} \nu-\mu^{T} \Theta^{-1} \mu\right]$$
is an affine function of $\omega$ and thus belongs to $\mathcal{F}$. Besides this, a function $\phi(\cdot) \in \mathcal{F}$ is affine: $\phi(\omega)=a^{T} \omega+b$, implying that
\begin{aligned} f(\mu) &:=\ln \left(\int_{\mathbf{R}^{d}} e^{\phi(\omega)} p_{\mu}(\omega) d \omega\right)=\ln \left(\mathbf{E}{\xi \sim \mathcal{N}\left(0, I{d}\right)}\left{\exp \left{a^{T}\left(\Theta^{1 / 2} \xi+\mu\right)+b\right}\right}\right) \ &=a^{T} \mu+b+\text { const, } \ \text { const } &=\ln \left(\mathbf{E}{\xi \sim \mathcal{N}\left(0, I{d}\right)}\left{\exp \left{a^{T} \Theta^{1 / 2} \xi\right}\right}\right)=\frac{1}{2} a^{T} \Theta a \end{aligned}
is an affine (and thus a concave) function of $\mu_{\text {. }}$.
As we remember from Chapter 1, Gaussian o.s. is responsible for the standard signal processing model where one is given a noisy observation
$$\omega=A x+\xi \quad[\xi \sim \mathcal{N}(0, \Theta)]$$
of the image $A x$ of unknown signal $x \in \mathbf{R}^{n}$ under linear transformation with known $d \times n$ sensing matrix, and the goal is to infer from this observation some knowledge about $x$. In this situation, a hypothesis that $x$ belongs to some set $X$ translates into the hypothesis that the observation $\omega$ is drawn from Gaussian distribution with known covariance matrix $\Theta$ and expectation known to belong to the set $M={\mu=$ $A x: x \in X}$. Therefore, deciding upon various hypotheses on where $x$ is located reduces to deciding on hypotheses on the distribution of observations in Gaussian o.s.

## 统计代写|统计推断代写Statistical inference代考|Executive summary of convex-concave saddle point problems

The results to follow are absolutely standard, and their proofs can be found in all textbooks on the subject, see, e.g., [221] or [15, Section D.4].

Let $U$ and $V$ be nonempty sets, and let $\Phi: U \times V \rightarrow \mathbf{R}$ be a function. These data define an antagonistic game of two players, I and II, where player I selects a point $u \in U$, and player II selects a point $v \in V$; as an outcome of these selections, player I pays to player II the sum $\Phi(u, v)$. Clearly, player I is interested in minimizing this payment, and player $\mathrm{II}$ in maximizing it. The data $U, V, \Phi$ are known to the players in advance, and the question is, what should be their selections?

When player I makes his selection $u$ first, and player II makes his selection $v$ with $u$ already known, player I should be ready to pay for a selection $u \in U$ a toll as large as
$$\bar{\Phi}(u)=\sup {v \in V} \Phi(u, v) .$$ In this situation, a risk-averse player $\mathrm{T}$ would select $u$ hy minimizing the ahove worst-case payment, by solving the primal problem $$\operatorname{Opt}(P)=\inf {u \in U} \bar{\Phi}(u)=\inf {u \in U} \sup {v \in V} \Phi(u, v)$$
associated with the data $U, V, \Phi$.
Similarly, if player II makes his selection $v$ first, and player I selects $u$ after $v$ becomes known, player II should be ready to get, as a result of selecting $v \in V$, the amount as small as
$$\underline{\Phi}(v)=\inf {u \in U} \Phi(u, v) .$$ In this situation, a risk-averse player II would select $v$ by maximizing the above worst-case payment, by solving the dual problem $$\operatorname{Opt}(D)=\sup {v \in V} \Phi(v)=\sup {v \in V} \inf {u \in U} \Phi(u, v) .$$

# 统计推断代考

## 统计代写|统计推断代写Statistical inference代考|Simple observation schemes—Examples

• 观察空间 $(\Omega, \Pi)$ 是空间 $\mathbf{R}^{d}$ 用勒贝格测度；
• 家庭\1eft 的分隔符缺失或无法识别
是高斯密度族 $\mathcal{N}(\mu, \Theta)$ ，具有固定的正定协方差矩阵 $\Theta$; 来自家庭的分布由他们的期望参数化 $\mu$. 因此，
\left 的分隔符缺失或无法识别
• 家庭 $\mathcal{F}$ 是所有仿射函数的族 $\mathbf{R}^{d}$.
立即可以看出，Gaussian os 满足了对简单 os 的所有要求，例如，
$$\ln \left(p_{\mu}(\omega) / p_{\nu}(\omega)\right)=(\nu-\mu)^{T} \Theta^{-1} \omega+\frac{1}{2}\left[\nu^{T} \Theta^{-1} \nu-\mu^{T} \Theta^{-1} \mu\right]$$
是一个仿射函数 $\omega$ 因此属于 $\mathcal{F}$. 除此之外，还有一个功能 $\phi(\cdot) \in \mathcal{F}$ 是仿射的: $\phi(\omega)=a^{T} \omega+b$, 意味着
$\backslash 1$ left 的分隔符缺失或无法识别
是仿射 (因此是凹) 函数 $\mu .$
正如我们在第 1 章中记得的那样，Gaussian os 负责标准信号处理模型，其中给定一个噪声观察值
$$\omega=A x+\xi \quad[\xi \sim \mathcal{N}(0, \Theta)]$$
图像的 $A x$ 末知信号 $x \in \mathbf{R}^{n}$ 在已知的线性变换下 $d \times n$ 感知矩阵，目标是从这个观察中推断出一些关于 $x$. 在这种情况下，假设 $x$ 属于某个集合 $X$ 转化为假设 观察 $\omega$ 从具有已知协方差矩阵的高斯分布中得出 $\Theta$ 和已知属于集合的期望 $M=\mu=\$ \$A x: x \in X$. 因此，决定在哪里的各种假设 $x$ 位于降低到决定高斯 os 中观察分布的假设

## 统计代写|统计推断代写Statistical inference代考|Executive summary of convex-concave saddle point problems

$$\bar{\Phi}(u)=\sup v \in V \Phi(u, v) .$$

$$\operatorname{Opt}(P)=\inf u \in U \bar{\Phi}(u)=\inf u \in U \sup v \in V \Phi(u, v)$$

$$\Phi(v)=\inf u \in U \Phi(u, v) .$$

$$\operatorname{Opt}(D)=\sup v \in V \Phi(v)=\sup v \in V \inf u \in U \Phi(u, v) .$$

## 有限元方法代写

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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。

assignmentutor™您的专属作业导师
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