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Posterior / Likelihood Prior
If the posterior distribution can be derived in a closed form, we may proceed directly to the
inference stage of Bayesian analysis. Unfortunately, except for some special models, the posterior
distribution is rarely available explicitly and needs to be estimated via simulations. MCMC sampling
can be used to simulate potentially very complex posterior models with an arbitrary level of precision.
MCMC methods for simulating Bayesian models are often demanding in terms of specifying an efficient
sampling algorithm and verifying the convergence of the algorithm to the desired posterior distribution.
Inference is the next step of Bayesian analysis. If MCMC sampling is used for approximating the
posterior distribution, the convergence of MCMC must be established before proceeding to inference.
Point and interval estimators are either derived from the theoretical posterior distribution or estimated
from a sample simulated from the posterior distribution. Many Bayesian estimators, such as posterior

Stata是一款完整的、集成的统计软件包,提供您需要的一切数据分析、数据管理和图形。
快速,简单并易于使用
点击式的界面和强大,直观的命令语言让Stata使用起来快速,并易于使用。
所有的分析结果都可以被复制和存档,并用来出版和审查。不管您什么时候写的内容,版本控制系统确保统计程序可继续生成同样的结果。
Stata的作图模块,主要提供如下八种基本图形的制作 : 直方图(histogram),条形图(bar),百分条图 (oneway),百分圆图(pie),散点图(two way),散点图矩阵(matrix),星形图(star),分位数图。这些图形的巧妙应用,可以满足绝大多数用户的统计作图要求。在有些非绘图命令中,也提供了绘制某种图形的功能,如在生存分析中,提供了绘制生存曲线图,回归分析中提供了残差图等。
Stata的矩阵运算功能
矩阵代数是多元统计分析的重要工具, Stata提供了多元统计分析中所需的矩阵基本运算,如矩阵的加、积、逆、 Cholesky分解、 Kronecker内积等;还提供了一些运算,如特征根、特征向量、奇异值分解等;在执行完某些统计分析命令后,还提供了一些系统矩阵,如估计系数向量、估计系数的协方差矩阵等。
统计功能
Stata使得大量的统计工具用于指尖
标准方法,如
基本表格和总结
案例对照分析
ARIMA
ANOVA 和MANOVA
线性回归
时间序列平滑
广义线性模型(GLM)
聚类分析
对比和比较
功率分析
样本选择
……
方法,如
多层模型
生存分析
动态面板数据回归
结构方程建模
二进制,计数和审查结果
ARCH
多重替代法
调查数据
Treatment effects
统计
贝叶斯分析
……

In Stata 16, we introduce a new, unified suite of commands for modeling choice data. We have added new commands for summarizing choice data. We renamed and improved existing commands for fitting choice models. We even added a new command for fitting mixed logit models for panel data. And we document them together in the new Choice Models Reference Manual.
And here’s the best part: margins now works after fitting choice models. This means you can now easily interpret the results of your choice models. While the coefficients estimated in choice models are often almost uninterpretable, margins allows you to ask and answer very specific questions based on your results. Say that you are modeling choice of transportation. You can answer questions such as
• What proportion of travelers are expected to choose air travel?
• How does the probability of traveling by car change for each additional $10,000 in income?
• If wait times at the airport increase by 30 minutes, how does this affect the choice of each mode of transportation?
What else is new? You now cmset your data before fitting a choice model. For instance,
. cmset personid transportmethod
Then, you use cmsummarize, cmchoiceset, cmtab, and cmsample to explore, summarize, and look for potential problems in your data.
And you use cm estimation commands to fit one of the following choice models:
• cmclogit conditional logit (McFadden’s choice) model
• cmmixlogit mixed logit model
• cmxtmixlogit panel-data mixed logit model
• cmmprobit multinomial probit model
• cmroprobit rank-ordered probit model
• cmrologit rank-ordered logit model
Unlike the others, cmxtmixlogit is not renamed and improved. It is completely new in Stata 16, and

The posterior density (shown in red) is more peaked and shifted to the left compared with the prior
distribution (shown in blue). The posterior distribution combined the prior information about with
intro — Introduction to Bayesian analysis 3
the information from the data, from which y = 0 provided evidence for a low value of and shifted
the prior density to the left to form the posterior density. Based on this posterior distribution, the
posterior mean estimate of is 2=(2 + 40) = 0.048 and the posterior probability that, for example,
< 0.10 is about 93%.
If we compute a standard frequentist estimate of a population proportion as a fraction of the
infected subjects in the sample, y = y=n, we will obtain 0 with the corresponding 95% confidence
interval (y �� 1.96
p
y (1 �� y)=n; y + 1.96
p
y (1 �� y)=n) reducing to 0 as well. It may be difficult
to convince a health policy maker that the prevalence of the disease in that city is indeed 0, given
the small sample size and the prior information available from comparable cities about a nonzero
prevalence of this disease.
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