Bayesian statistics uses an approach whereby beliefs are updated based on data that has been collected. This can be an iterative process, whereby a prior belief is replaced by a posterior belief based on additional data, after which the posterior belief becomes a new prior belief to be refined based on even more data. The initial prior belief in this series may be based on intuition, previous studies, experience, etc.
In inferential statistics, we commonly test hypotheses, estimate parameters, and make predictions. In the traditional approach to statistics, commonly called the frequentist approach, parameters are constants whose values we aim to discern. Bayesian statistics uses a different approach: we treat these parameters as variables that have a probability distribution.
Topics
References
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., Rubin, D. B. (2014) Bayesian data analysis, 3rd Ed. CRC Press
https://statisticalsupportandresearch.files.wordpress.com/2017/11/bayesian_data_analysis.pdf
Marin, J-M and Robert, C. R. (2014) Bayesian essentials with R. 2nd Ed. Springer
https://www.springer.com/gp/book/9781461486862
Jordan, M. (2010) Bayesian modeling and inference. Course notes
https://people.eecs.berkeley.edu/~jordan/courses/260-spring10/lectures/index.html
Lee, P. M. (2012) Bayesian statistics an introduction. 4th Ed. Wiley
https://www.wiley.com/en-us/Bayesian+Statistics%3A+An+Introduction%2C+4th+Edition-p-9781118332573
As for medical diagnostic tests, there are online calculators available for computing sensitivity, specificity, positive predictive value, negative predictive value etc. Bayesian statistics is applied when prevalence is taken into consideration to interpret test results.
https://www.medcalc.org/calc/diagnostic_test.php
Excel model can be created also.
Bayesian statistics is applied in interpreting Covid-19 diagnostic test results and vaccine efficacy expressed as credible interval such as Pfizer-Moderna vaccine.
It would be beneficial to have such Excel applications available in the menu. Thanks.
I am in the process of adding new information to the Bayesian statistics part of the website, so the timing of your suggestion is good.
Even now, you can use some of the Bayesian capabilities on the Real Statistics website to perform covid-19 analyses.
Can you tell me which topics you would like to see added?
Charles
Covid-19 Diagnostic tests – sensitivity, specificity, PPV and NPV including confidence intervals. Thanks.
This is a huge topic.
This can be done for each of the vaccines (Pfizer, Moderna, J&J, Astra-Zenica). It can be done for various cohorts (16-30, 30,40, 40-50, 50-60, 60-70, 70+ age). It could be done for severe illness. It could be done for the initial field trials. It could be done for the population that received a vaccine Etc.
Is there a way to limit the focus?
Charles
Specifically, please refer to “A LOOK AT BIONTECH/PFIZER’S BAYESIAN ANALYSIS OF THEIR COVID-19 VACCINE TRIAL”
http://skranz.github.io//r/2020/11/11/CovidVaccineBayesian.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+skranz_R+%28Economics+and+R+%28R+Posts%29%29
Thanks for sending this link to me. It looks similar to an analysis I did a couple of weeks ago regarding Moderna. I will look into adding an example like this, probably to the following webpage:
https://www.real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/beta-conjugate-prior/
Charles