# 统计代写|贝叶斯分析代写Bayesian Analysis代考|Computation and software

#### Doug I. Jones

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## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Computation and software

At the time of writing, the authors rely primarily on the software package $\mathrm{R}$ for graphs and basic simulations, fitting of classical simple models (including regression, generalized linear models, and nonparametric methods such as locally weighted regression), optimization, and some simple programming. We use the Bayesian inference package Stan (see Appendix C) for fitting most models, but for teaching purposes in this book we describe how to perform most of the computations from first principles. Even when using Stan, we typically work within $\mathrm{R}$ to plot and transform the data before model fitting, and to display inferences and model checks afterwards.
Specific computational tasks that arise in Bayesian data analysis include:

• Vector and matrix manipulations (see Table 1.1)
• Computing probability density functions (see Appendix A)
• Drawing simulations from probability distributions (see Appendix A for standard distributions and Exercise 1.9 for an example of a simple stochastic process)
• Structured programming (including looping and customized functions)
• Calculating the linear regression estimate and variance matrix (see Chapter 14)
• Graphics, including scatterplots with overlain lines and multiple graphs per page (see Chapter 6 for examples).
Our general approach to computation is to fit many models, gradually increasing the complexity. We do not recommend the strategy of writing a model and then letting the computer run overnight to estimate it perfectly. Rather, we prefer to fit each model relatively quickly, using inferences from the previously fitted simpler models as starting values, and displaying inferences and comparing to data before continuing.

We discuss computation in detail in Part III of this book after first introducing the fundamental concepts of Bayesian modeling, inference, and model checking. Appendix $\mathrm{C}$ illustrates how to perform computations in $\mathrm{R}$ and Stan in several different ways for a single example.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Summarizing inferences by simulation

Simulation forms a central part of much applied Bayesian analysis, because of the relative ease with which samples can often be generated from a probability distribution, even when the density function cannot be explicitly integrated. In performing simulations, it is helpful to consider the duality between a probability density function and a histogram of a set of random draws from the distribution: given a large enough sample, the histogram can provide practically complete information about the density, and in particular, various sample moments, percentiles, and other summary statistics provide estimates of any aspect of the distribution, to a level of precision that can be estimated. For example, to estimate the 95th percentile of the distribution of $\theta$, draw a random sample of size $S$ from $p(\theta)$ and use the $0.95 S$ th order statistic. For most purposes, $S=1000$ is adequate for estimating the 95 th percentile in this way.

Another advantage of simulation is that extremely large or small simulated values often flag a problem with model specification or parameterization (for example, see Figure 4.2) that might not be noticed if estimates and probability statements were obtained in analytic form.

Generating values from a probability distribution is often straightforward with modern computing techniques based on (pseudo)random number sequences. A well-designed pseudorandom number generator yields a deterministic sequence that appears to have the same properties as a sequence of independent random draws from the uniform distribution on $[0,1]$. Appendix A describes methods for drawing random samples from some commonly used distributions.

# 贝叶斯分析代考

## 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。

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