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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.
Stata 是一套提供其使用者数据分析、数据管理以及绘制图表的完整及整合性统计软件。它提供许许多多功能,包含线性混合模型、均衡重复反复及多项式普罗比模式。用Stata绘制的统计图形相当精美。
Many (maybe hundreds or thousands of) potential covariates
With a style in hand, all we do is ask the system to use that style. collect will then lay out, format, and style the table according to the specified style. We can then preview the table.
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