- #1

Buzz Bloom

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- TL;DR Summary
- In several threads I have seen discussions of the difference between using Bayesian and frequentist statistics. In particular, the use of Bayesian statistics in cosmology and frequentist statistics in QM. I have come to understand that Bayesian statistics generally do not produce any error range and confidence level, in contrast with those results in frequentist statistics based on the calculation of a standard deviation. I have some questions about this.

About cosmology:

About QM:

I would much appreiate it if someone would post a simple example of how Bayesian statistics calculates an error range and confidence level. Before I retired I had some occasions to use frequentist statistics to create models for data mining, so I am familiar with how to calculate an error range and confidence level using frequentist statistics, but I have no experience or familiarity for using Bayesian statistics for this purpose.

Regards,

Buzz

Orodruin said:There are two main type of statistics used in physics: frequentist and Bayesian. The one most commonly used in cosmology is Bayesian statistics, which Planck also states that they are using at the beginning of page 4.

Planck paper:

As in PCP13 we adopt a Bayesian framework for testing theoretical models.

In the Planck paper, pages 38-40, equations 45 through 52, there are values given for parameters with error ranges and confidence levels. Here is an example.Ω

_{K}=0.000±0.005 (95%,PlanckTT+lowP+lensing+BAO). (50)About QM:

Post #17

These are not only philosophical points of view, but from these interpretations come different methods of inferences.

For example, the debate that took place during the discovery of the Higgs Bosons is about the difference between frequentist and Bayesian inferences: http://tonyohagan.co.uk/academic/pdf/HiggsBoson.pdf

I would much appreiate it if someone would post a simple example of how Bayesian statistics calculates an error range and confidence level. Before I retired I had some occasions to use frequentist statistics to create models for data mining, so I am familiar with how to calculate an error range and confidence level using frequentist statistics, but I have no experience or familiarity for using Bayesian statistics for this purpose.

Regards,

Buzz