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Frequentist inference is based on the sampling distributions of estimators of parameters and provides
parameter point estimates and their standard errors as well as confidence intervals. The exact sampling
distributions are rarely known and are often approximated by a large-sample normal distribution.
Bayesian inference is based on the posterior distribution of the parameters and provides summaries of
this distribution including posterior means and their MCMC standard errors (MCSE) as well as credible
intervals. Although exact posterior distributions are known only in a number of cases, general posterior
distributions can be estimated via, for example, Markov chain Monte Carlo (MCMC) sampling without
any large-sample approximation.
Frequentist confidence intervals do not have straightforward probabilistic interpretations as do
Bayesian credible intervals. For example, the interpretation of a 95% confidence interval is that if
we repeat the same experiment many times and compute confidence intervals for each experiment,
then 95% of those intervals will contain the true value of the parameter. For any given confidence
interval, the probability that the true value is in that interval is either zero or one, and we do not
know which. We may only infer that any given confidence interval provides a plausible range for the
true value of the parameter. A 95% Bayesian credible interval, on the other hand, provides a range
for a parameter such that the probability that the parameter lies in that range is 95%.

扩展功能
使用Mata进行矩阵编程
跨平台兼容
真正的文档
当Stata执行您的分析或理解使用的方法时,Stata不会让您孤立无援或订购
很多书籍来了解每个细节。
我们每一个数据管理功能都有完整的解释,并记录在案,并在实践中显示
实际的例子。每一个估计都有完全记录,包含几个真实数据的例子,真正讨论
如何解释结果。这些例子都给了数据,您可以直接在Stata中使用,甚至扩展
您的分析。我们给您快速启动每一个功能,展示一些常用用途。想要了解更
多细节,我们的方法和公式部分提供了计算的细节,我们参考部分会给出更多
信息。
Stata
Stata的编程功能让开发者和用户
每天都可以添加各种新功能以便满足
现代研究者日益增加的功能需求。
Mata是一个成熟的编程语言,可
编译您所输入的任何字节,并进行优
化和准确执行。
尽管您不需要使用Stata进行编程,
但是它作为一个快速完成矩阵的编程
语言,是Stata功能中不可或缺的一部
分。Mata既是一个操作矩阵的互动环
境,也是一个完整开发环境,可以生
产编译和优化代码。它还包含了一些
功能来处理面板数据、执行真实
或复制的矩阵运算,提供完整的支持
面向对象的编程,并完全兼容Stata。

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.
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