Error floors in this Bayesian analysis

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SUMMARY

This discussion centers on the estimation of error floors in Bayesian analysis, specifically using Markov Chain Monte Carlo (MCMC) methods. The authors of the referenced paper introduce a new algorithm utilizing Hamiltonian Monte Carlo (HMC) sampling implemented in PyMC3, which enhances sampling efficiency and allows for fitting error floor parameters directly within the model. This approach addresses systematic uncertainties that have previously affected the precision of measurements in astrophysical contexts. Section 4 of the paper provides a detailed outline and references for further exploration of these concepts.

PREREQUISITES
  • Understanding of Bayesian analysis principles
  • Familiarity with Markov Chain Monte Carlo (MCMC) methods
  • Knowledge of Hamiltonian Monte Carlo (HMC) techniques
  • Experience with PyMC3 for probabilistic programming
NEXT STEPS
  • Study the implementation of Hamiltonian Monte Carlo in PyMC3
  • Research the concept of "error floors" in statistical modeling
  • Explore advanced MCMC techniques for high-dimensional data
  • Review the references provided in section 4 of the discussed paper for deeper insights
USEFUL FOR

Researchers in astrophysics, statisticians working with Bayesian methods, and data scientists interested in advanced MCMC techniques will benefit from this discussion.

Artemisa
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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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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.
 

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