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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.
Style myregci was derived from style myreg. To create myregci from myreg, we only had to type three lines: . collect style autolevels result _r_b _r_ci , clear . collect layout (colname) (cmdset#result) . collect style column, dups(center)
In Bayesian analysis, we seek a balance between prior information in a form of expert knowledge or belief and evidence from data at hand. Achieving the right balance is one of the difficulties in Bayesian modeling and inference. In general, we should not allow the prior information to overwhelm the evidence from the data, especially when we have a large data sample. A famous theoretical result, the Bernstein–von Mises theorem, states that in large data samples, the posterior distribution is independent of the prior distribution and, therefore, Bayesian and likelihood-based inferences should yield essentially the same results. On the other hand, we need a strong enough prior to support weak evidence that usually comes from insufficient data. It is always good practice to perform sensitivity analysis to check the dependence of the results on the choice of a prior.
Advantages and disadvantages of Bayesian analysis Bayesian analysis is a powerful analytical tool for statistical modeling, interpretation of results, and prediction of data. It can be used when there are no standard frequentist methods available or the existing frequentist methods fail. However, one should be aware of both the advantages and disadvantages of Bayesian analysis before applying it to a specific problem. The universality of the Bayesian approach is probably its main methodological advantage to the traditional frequentist approach. Bayesian inference is based on a single rule of probability, the Bayes rule, which is applied to all parametric models. This makes the Bayesian approach universal and greatly facilitates its application and interpretation. The frequentist approach, however, relies on a variety of estimation methods designed for specific statistical problems and models. Often, inferential methods designed for one class of problems cannot be applied to another class of models.
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北京天演融智软件有限公司(亦称:融智软件)前身是北京世纪天演科技有限公司,成立于2001年,专注为国内高校、科研院所和以研发为主的企事业单位提供科研软件和服务的。 融智软件始终秉承“依托教育,服务教育”的经营理念,为我国各类高等院校、科研机构提供丰富的教学资源服务和*的科学软件服务,公司拥有多名国外留学归来的博士和硕士,在美国设有合资公司(TurnTech LLC.)。 截止目前,融智软件已获得数百家**软件公司正式授权,销售科研软件达1000余种。产品涵盖教育、、交通、通信、电力等行业。尤其是大数据相关软件方面,为诸如北京大学、清华大学、中国大学、中科院、农科院、社科院、、交通部、南方电网、电网等国内大型企事业单位、部委和科研机构长期提供相关产品。同时,还提供专业培训、视频课程(包含40款软件,80门课程)、实验室解决方案和项目咨询等服务。 2020年开始,融智软件申请高等教育司产学合作协同育人项目,“大数据”和“机器学习”师资培训项目,以及基于OBE的教考分离改革与教学评测项目已获得批准。融智软件将会跟更多的高校合作,产学融合协同育人。