Error floors in this Bayesian analysis

In summary, the authors of this article use a Bayesian analysis with markov chain monte carlo chains to estimate error floors in the positions of astrophysical bodies. They introduce a new algorithm utilizing the Hamiltonian Monte Carlo sampler to efficiently explore the typical set of complex and high-dimensional spaces. This method also allows for the inclusion of error floor parameters in the model, removing a source of systematic uncertainty and improving the precision of previous measurements. Section 4 of the paper provides a detailed outline and references for further understanding of the method.
  • #1
Artemisa
1
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TL;DR Summary
It is not clear to me how the estimation of the floor errors is made in this article (https://arxiv.org/pdf/2001.04581.pdf).
In this article((https://arxiv.org/pdf/2001.04581.pdf)), the authors use a Bayesian analysis based on the positions of astrophysical bodies and their errors in the medians. This statistical analysis uses the markov chain monte carlo chains.

The uncertainties in the positions are large, so what they do is an analysis to estimate the floor errors.

My Doubt is
How do they get these error floors?
Could someone give me some reference or provide an example of how to do it?

Thank you very much for your attention
 
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  • #2
Artemisa said:
How do they get these error floors?
Could someone give me some reference or provide an example of how to do it?
I have only skimmed the paper but section 4 at the top of page 9 seems to provide an outline with suitable references to follow up:
in this work we introduce instead a new algorithm utilizing the Hamiltonian Monte Carlo (HMC; Neal 2012) sampler implemented in PyMC36 (Salvatier et al. 2016). HMC methods take advantage of the posterior geometry to efficiently explore the "typical set" (i.e., the region containing the bulk of the probability mass) even in complex and high-dimensional spaces; see Betancourt (2017) for a concise overview of HMC. In addition to increased sampling effciency, the primary improvement provided by the new disk-fitting code is the ability to fit for the "error floor" parameters as part of the model, thereby removing a source of systematic uncertainty that has limited the precision of previous MCP measurements.
 

FAQ: Error floors in this Bayesian analysis

What are error floors in Bayesian analysis?

Error floors in Bayesian analysis refer to the minimum error rate that a Bayesian analysis can achieve, even with an infinite amount of data. It is a limitation that arises due to the assumptions made in the Bayesian model.

How do error floors impact the results of a Bayesian analysis?

Error floors can lead to biased estimates or inaccurate conclusions in a Bayesian analysis. They can limit the reliability and accuracy of the results obtained from the analysis.

What factors contribute to the presence of error floors in Bayesian analysis?

Factors such as the choice of prior distributions, the complexity of the model, and the amount of available data can contribute to the presence of error floors in Bayesian analysis. These factors can influence the uncertainty and variability in the results.

Can error floors be mitigated in Bayesian analysis?

Error floors can be mitigated to some extent by carefully selecting prior distributions, using informative data, and validating the model assumptions. However, completely eliminating error floors may not always be possible.

Are error floors a common issue in Bayesian analysis?

Error floors are a known issue in Bayesian analysis, especially in complex models or when dealing with limited data. Researchers are encouraged to be aware of the presence of error floors and consider their implications when interpreting the results of a Bayesian analysis.

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