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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写随机分析stochastic analysisl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。我们的专家在代写随机分析stochastic analysisl代写方面经验极为丰富，各种代写随机分析stochastic analysisl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|随机分析作业代写stochastic analysis代写|Hidden Markov Model

The hidden Markov model (HMM) is a powerful tool for analyzing time series or even spatially distributed data. It has been widely used in numerous applications such as image processing, speech recognition, data compression, bioinformatics, and pattern recognition, etc. [EAM95, Rab89]. The fundamental issue in the HMM is to infer the underlying hidden Markov transition rules based on the sequences of observations. In this sense, it can be understood as an inverse problem to the direct problem of generating state sequences from a known Markov chain.

We will limit ourselves to the discrete time setting. The data that is available to us is a time series $\boldsymbol{Y}=\left(Y_{1: N}\right)=\left(Y_{1}, \ldots, Y_{N}\right)$, resulting from the partial observation of a trajectory $\boldsymbol{X}=\left(X_{1: N}\right)=\left(X_{1}, \ldots, X_{N}\right)$ of the underlying Markov chain with initial distribution $\boldsymbol{\mu}=\left(\mu_{i}\right){i \in S}$ and transition probability matrix $\boldsymbol{P}=\left(p{i j}\right){i, j \in S}$. The schematic figure of a hidden Markov model is shown in Figure 3.3. We assume that the observations are in state space $O$ and the probability of the observations is given by the so-called emission matrix $\boldsymbol{R}=\left(r{i j}\right){i \in S, j \in O}$, where $r{i j}$ is the probability of observing $j$ when the hidden state is $i$; i.e..
$$r_{i j}=\mathbb{P}(Y=j \mid X=i), \quad i \in S \text { and } j \in O .$$

## 统计代写|随机分析作业代写stochastic analysis代写|Networks and Markov Chains

As another example of the application of Markov chains, we take a brief look at networks, which provide a general setting for analyzing interactions between agents in social, biological, and other settings.

A network is a directed or undirected weighted graph $G$. Its structure is specified by a set of nodes, here denoted by $S$, and the set of weights $W$, $G=(S, W)$. We assume that the network has $I$ nodes with $S={1,2, \ldots, I}$ The weight matrix $W=\left{e_{i j}\right}_{i, j \in S}$, where $e_{i j}$ is the weight for the edge from node $i$ to node $j$. The simplest example of the weight matrix is given by the adjacency matrix: $e_{i j}=0$ or 1 , depending on whether $i$ and $j$ are connected. Below we will focus on the situation when the network is undirected; i.e., $W$ is symmetric.

Given a network, one can define naturally a discrete time Markov chain, with the transition probability matrix $\boldsymbol{P}=\left(p_{i j}\right){i, j \in S}$ given by $$p{i j}=\frac{e_{i j}}{d_{i}}, \quad d_{i}=\sum_{k \in S} e_{i k} .$$
Here $d_{i}$ is the degree of the node $i$ [Chu97, Lov96]. Let
$$\pi_{i}=\frac{d_{i}}{\sum_{k \in S} d_{k}} .$$
Then it is easy to see that
$$\sum_{i \in S} \pi_{i} p_{i j}=\pi_{j}$$
i.e., $\pi$ is an invariant distribution of this Markov chain. Furthermore, one has the detailed balance relation:
$$\pi_{i} p_{i j}=\pi_{j} p_{j i} .$$
For $\boldsymbol{u}=\left(u_{i}\right){i \in S}, \boldsymbol{v}=\left(v{i}\right){i \in S}$ defined on $S$, introduce the inner product $$(\boldsymbol{u}, \boldsymbol{v}){\pi}=\sum_{i \in S} u_{i} v_{i} \pi_{i} .$$

## 统计代写|随机分析作业代写stochastic analysis代写|Hidden Markov Model

$$r_{i j}=\mathbb{P}(Y=j \mid X=i), \quad i \in S \text { and } j \in O$$

## 统计代写|随机分析作业代写stochastic analysis代写|Networks and Markov Chains

$S=1,2, \ldots, I$ 权重矩阵 \left 的分隔符缺失或无法识别，，在哪里 $e_{i j}$ 是来自节点的边的权重 $i$ 到节点 $j$. 权重矩阵的最简 单示例由邻接矩阵给出： $e_{i j}=0$ 或 1 ，取决于是否 $i$ 和 $j$ 连接。下面我们将重点介绍网络无向时的情况；IE， $W$ 是对称的。

$$p i j=\frac{e_{i j}}{d_{i}}, \quad d_{i}=\sum_{k \in S} e_{i k} .$$

$$\pi_{i}=\frac{d_{i}}{\sum_{k \in S} d_{k}}$$

$$\sum_{i \in S} \pi_{i} p_{i j}=\pi_{j}$$
$\mathrm{IE}$ 。 $\pi$ 是这个马尔可夫链的不变分布。此外，还有一个详细的平衡关系:
$$\pi_{i} p_{i j}=\pi_{j} p_{j i} .$$

$$(\boldsymbol{u}, \boldsymbol{v}) \pi=\sum_{i \in S} u_{i} v_{i} \pi_{i}$$

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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
assignmentutor™您的专属作业导师