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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.

2021年4月20日Stata 新版本17正式发布,17版本在数据处理速度、计量模型以及与其他软件融合方面均有大的更新。Stata 17新功能,大家还不是特别了解,因此,北京天演融智软件有限公司(科学软件网)特意为大家安排一场Stata 17新功能解锁 的在线讲座。为您讲解Stata 17的新功能都有哪些,使用上又有哪些便利呢?

New reporting features in Stata 16:
• The dyndoc and markdown commands now create Word documents in addition to the HTML documents they previously created. Now, you can easily incorporate full Stata output and graphs with Markdown-formatted text to create customized Word documents.
• The Do-file Editor now provides syntax highlighting for Markdown language elements.
• The putdocx command now lets you include headers, footers, and page numbers. It also makes it easier to write large blocks of text.
• The html2docx command converts HTML documents, including CSS, to Word documents.
• The docx2pdf command converts Word documents to PDFs.

We used a beta prior distribution in this example, but we could have chosen another prior distribution
that supports our prior knowledge. For the final analysis, it is important to consider a range of different
prior distributions and investigate the sensitivity of the results to the chosen priors.
For more details about this example, see Hoff (2009). Also see Beta-binomial model in
[BAYES] bayesmh for how to fit this model using bayesmh.
Bayesian versus frequentist analysis, or why Bayesian analysis?
Why use Bayesian analysis? Perhaps a better question is when to use Bayesian analysis and when
to use frequentist analysis. The answer to this question mainly lies in your research problem. You
should choose an analysis that answers your specific research questions. For example, if you are
interested in estimating the probability that the parameter of interest belongs to some prespecified
interval, you will need the Bayesian framework, because this probability cannot be estimated within
the frequentist framework. If you are interested in a repeated-sampling inference about your parameter,
the frequentist framework provides that.
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