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As a quick introduction to Bayesian analysis, we use an example, described in Hoff (2009, 3),
of estimating the prevalence of a rare infectious disease in a small city. A small random sample of
20 subjects from the city will be checked for infection. The parameter of interest 2 [0; 1] is the
fraction of infected individuals in the city. Outcome y records the number of infected individuals in
the sample. A reasonable sampling model for y is a binomial model: yj Binomial(20; ). Based
on the studies from other comparable cities, the infection rate ranged between 0.05 and 0.20, with
an average prevalence of 0.10. To use this information, we must conduct Bayesian analysis. This
information can be incorporated into a Bayesian model with a prior distribution for , which assigns
a large probability between 0.05 and 0.20, with the expected value of close to 0.10. One potential
prior that satisfies this condition is a Beta(2; 20) prior with the expected value of 2=(2+20) = 0.09.
So, let’s assume this prior for the infection rate , that is, Beta(2; 20). We sample individuals
and observe none who have an infection, that is, y = 0. This value is not that uncommon for a small
sample and a rare disease. For example, for a true rate = 0.05, the probability of observing 0
infections in a sample of 20 individuals is about 36% according to the binomial distribution. So, our
Bayesian model can be defined as follows:

讲座主题:因果推断: 内生性问题与工具变量法
讲座时间:5月19日15:00-16:00
讲座概述:因果推断模型与方法是现代社会科学研究者利用计量模型发表高水平实证论文的核心利器。其中,工具变量法则举足轻重,是计量研究中无法避开的挑战之一。此专题就内生性问题与解决路径、工具变量选择的方法及分类、工具变量的检验及工具变量回归模型(2SLS+GMM)等进行专题讨论,探讨工具变量法的基本思想、原理、模型、方法及适用范围,并以真实数据为演示案例,分享因果推断的思辨、工具变量回归模型的构建、应用及结果解读的路径,为发表高水平的实证研究论文奠定基础。

What is Bayesian analysis?
Bayesian analysis is a statistical analysis that answers research questions about unknown parameters
of statistical models by using probability statements. Bayesian analysis rests on the assumption that
all model parameters are random quantities and thus are subjects to prior knowledge. This assumption
is in sharp contrast with the more traditional, also called frequentist, statistical inference where all
parameters are considered unknown but fixed quantities. Bayesian analysis follows a simple rule
of probability, the Bayes rule, which provides a formalism for combining prior information with
evidence from the data at hand. The Bayes rule is used to form the so called posterior distribution of
model parameters. The posterior distribution results from updating the prior knowledge about model
parameters with evidence from the observed data. Bayesian analysis uses the posterior distribution to
form various summaries for the model parameters including point estimates such as posterior means,
medians, percentiles, and interval estimates such as credible intervals. Moreover, all statistical tests
about model parameters can be expressed as probability statements based on the estimated posterior
distribution.

2019年6月Stata 15正式发布。这是Stata有史以来大的一次版本更新。我们贴出了Statalist并且列出了16项重要的新功能。这篇文章会重点谈谈这些新功能:
扩展回归模型
潜在类别分析(LCA)
贝叶斯前缀指令
线性动态随机一般均衡(DSGE)模型
web 的动态Markdown文档
非线性混合效应模型
空间自回归模型(SAR)
区间删失参数生存时间模型
有限混合模型(FMMs)
混合Logit模型
非参数回归
聚类随机设计和回归模型的功率分析
Word和PDF文档
图形颜色透明度/不透明度
ICD-10-CM/PCS支持
联邦储备经济数据(FRED)支持
其他
上面列出的十六功能当然是重要的, 但还有其他值得一提的。比较*想到的是:
. 贝叶斯多级模型
. 门限回归
. 具有随机系数的面板数据tobit
. 区间测量结果的多层回归
. 删失结果的多级Tobit回归
. 面板数据的协整测试
. 时间序列中多断点的测试
. 多组广义 SEM
. 异方差的线性回归
. Heckman风格的样本选择Poisson模型
. 具有随机系数的面板数据非线性模型
. 贝叶斯面板数据模型
. 随机系数的面板数据区间回归
. SVG的导出
. 贝叶斯生存模型
. 零膨胀有序概率
. 添加您自己的电源和样本大小的方法
. 贝叶斯样本选择模型
. 支持瑞典语
. 对DO文件编辑器的改进
. 流随机数生成器
. 对于java插件的改进
. Stata / MP更多的并行化
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