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# 统计代写|贝叶斯分析代考Bayesian Analysis代写|MULTIPLE PARAMETER DRAWS IN MODELS

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## 统计代写|贝叶斯分析代考Bayesian Analysis代写|MULTIPLE PARAMETER DRAWS IN MODELS

Consider the basic Bayesian model, in which parameters are drawn from a prior $p(\theta)$ and then the data is drawn from a distribution $p(X \mid \theta)$. Here, the data is abstractly represented using a random variable $X$, but it is often the case that the observed data is composed of multiple observations $x^{(1)}, \ldots, x^{(n)}$, all drawn from the distribution $p(X \mid \theta)$.
In this case, one way to write the joint distribution over the data and parameters is:
$$p\left(\theta, x^{(1)}, \ldots, x^{(n)}\right)=p(\theta) \prod_{i=1}^n p\left(x^{(i)} \mid \theta\right) .$$
A more careful look into this equation reveals that there is an additional degree of freedom in the placement of the prior. Instead of drawing the parameters once for all data points, one could draw a set of parameters for each data point. In such a case, the joint distribution is:
$$p\left(\theta^{(1)}, \ldots, \theta^{(n)}, x^{(1)}, \ldots, x^{(n)}\right)=\prod_{i=1}^n p\left(\theta^{(i)}\right) p\left(x^{(i)} \mid \theta^{(i)}\right)$$

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

A large body of work in Bayesian NLP focuses on cases in which the model structure is fixed. Model structure here is not rigorously defined, but it refers to the representation that makes the core underlying independence assumptions in the model. It can be, for example, a context-free grammar or a directed graphical model. For this structure to be functional in the context of data, it is associated with parameters for its various components. PCFGs, for example, associated each rule with a rule probability.

Since we usually assume the structure is fixed, the priors in Bayesian NLP are defined over the parameters of this structure. Setting a prior over the model structure is more complex. One implicit way to do it is to have the structure make very few independence assumptions, and incorporate many components that are potentially not used for a given fixed set of parameters (such as all possible right-hand sides for a context-free grammar). Then, choosing a sparse prior for this model (for example, a symmetric Dirichlet with a small concentration hyperparameter), will essentially lead to selecting a subset of these components from the model.

There are several more explicit examples of the use of structural priors in NLP. Eisner (2002), for example, defines a structural “transformational prior” over the right-hand sides of context-free rules. Eisner’s goal was to introduce rules into the grammar that were never seen in the training data. The introduction of rules is done by introducing local edit operations to existing rules. The full set of rules is represented as a graph, where the nodes correspond to the rules, and edges correspond to possible transitions from one rule to another using a local edit operation (removing a nonterminal in the right-hand side, adding one or replacing it). The edges in this graph are weighted, and determine the probability of the rule in the final grammar.
Other cases for setting structural priors in a Bayesian setting include that of Stolcke and Omohundro (1994). Stolcke was interested in learning the structure of a grammar using a “Bayesian merging model.” See Section 8.9 for more information.

# 贝叶斯分析代写

## 统计代写|贝叶斯分析代考Bayesian Analysis代写|MULTIPLE PARAMETER DRAWS IN MODELS

$$p\left(\theta, x^{(1)}, \ldots, x^{(n)}\right)=p(\theta) \prod_{i=1}^n p\left(x^{(i)} \mid \theta\right) .$$

$$p\left(\theta^{(1)}, \ldots, \theta^{(n)}, x^{(1)}, \ldots, x^{(n)}\right)=\prod_{i=1}^n p\left(\theta^{(i)}\right) p\left(x^{(i)} \mid \theta^{(i)}\right)$$

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

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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。