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mean and posterior standard deviation, involve integration. If the integration cannot be performed
analytically to obtain a closed-form solution, sampling techniques such as Monte Carlo integration
and MCMC and numerical integration are commonly used.
Bayesian hypothesis testing can take two forms, which we refer to as interval-hypothesis testing
and model-hypothesis testing. In an interval-hypothesis testing, the probability that a parameter or
a set of parameters belongs to a particular interval or intervals is computed. In model hypothesis
testing, the probability of a Bayesian model of interest given the observed data is computed.
Model comparison is another common step of Bayesian analysis. The Bayesian framework provides
a systematic and consistent approach to model comparison using the notion of posterior odds and
related to them Bayes factors. See [BAYES] bayesstats ic for details.
Finally, prediction of some future unobserved data may also be of interest in Bayesian analysis.
The prediction of a new data point is performed conditional on the observed data using the so-called
posterior predictive distribution, which involves integrating out all parameters from the model with
respect to their posterior distribution. Again, Monte Carlo integration is often the only feasible option
for obtaining predictions. Prediction can also be helpful in estimating the goodness of fit of a model.
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较新。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?
Stata 16 Feature highlights:
1. Lasso
2. Reporting
3. Meta-analysis
4. Choice models
5. Python integration
6. New in Bayesian analysis—Multiple chains, predictions, and more
7. Panel-data ERMs
8. Import data from SAS and SPSS
9. Nonparametric series regression
10. Multiple datasets in memory
11. Sample-size analysis for confidence intervals
12. Nonlinear DSGE models
13. Multiple-group IRT models
14. xtheckman
15. Multiple-dose pharmacokinetic modeling
16. Heteroskedastic ordered probit models
17. Graph sizes in printer points, centimeters, and inches
18. Numerical integration
19. Linear programming
20. Stata in Korean
21. Mac interface now supports Dark Mode and native tabbed windows
22. Do-file Editor—Autocompletion and more syntax highlighting
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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