How are Bayesian analysis methods using Monte Carlo sampling applied to estimate the parameters of dark energy models based on observational data?

I have come across references to Markov Chain Monte Carlo (MCMC) in the context of CMB and supernova analyses, but it is unclear how to interpret the resulting posterior distributions.

I would appreciate any clarifications or references to tutorials or review articles.

As I understand it, MCMC helps to find the parameters of dark energy that best fit the observational data, and the posterior distributions show which parameter values are most likely. Isn’t that so?🤔

1 hour ago, Aiaru Smat said:

How are Bayesian analysis methods using Monte Carlo sampling applied to estimate the parameters of dark energy models based on observational data?

I have come across references to Markov Chain Monte Carlo (MCMC) in the context of CMB and supernova analyses, but it is unclear how to interpret the resulting posterior distributions.

I would appreciate any clarifications or references to tutorials or review articles.

As I understand it, MCMC helps to find the parameters of dark energy that best fit the observational data, and the posterior distributions show which parameter values are most likely. Isn’t that so?🤔

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1 hour ago, Aiaru Smat said:

How are Bayesian analysis methods using Monte Carlo sampling applied to estimate the parameters of dark energy models based on observational data?

I have come across references to Markov Chain Monte Carlo (MCMC) in the context of CMB and supernova analyses, but it is unclear how to interpret the resulting posterior distributions.

I would appreciate any clarifications or references to tutorials or review articles.

I would consult Dmitri Jerkinov's seminal paper on the use of Markov Chains in analyzing both posterior and anterior distributions of Type Ia supernovae (white dwarves).

Hi! That’s a really interesting question 🔭
It’s a bit outside my research area, since I mainly work on modeling Nova-like variable stars using PHOEBE, but Bayesian methods and MCMC always sounded fascinating to me.
I like how these approaches can deal with uncertainties and complex data — something we also face in stellar modeling.
I’ll definitely check out some of the references you mentioned, thanks for sharing!

Great question! In cosmology, MCMC is used to explore how likely different parameter values are, given the observational data. The spread of samples shows which regions of parameter space fit the data best. I’d suggest checking out Trotta (2008) for a clear overview and Lewis & Bridle (2002) for practical examples. You can also experiment with emcee and (link removed) to visualize the posteriors.

MCMC helps find which parameter values best match the data.The posterior shows how likely each value is — peaks mean higher probability.

14 hours ago, Sayora said:

16 hours ago, Aiaru Smat said:

How are Bayesian analysis methods using Monte Carlo sampling applied to estimate the parameters of dark energy models based on observational data?

I have come across references to Markov Chain Monte Carlo (MCMC) in the context of CMB and supernova analyses, but it is unclear how to interpret the resulting posterior distributions.

I would appreciate any clarifications or references to tutorials or review articles.

👋 Hi everyone!
I’m not working in this field myself 🧑‍🔬, but I know some scientists from the INP 🔬.
I can share the article 📄 they’re using for their research 💡 if anyone’s interested! 😊

1808.08490

16 hours ago, Aiaru Smat said:

How are Bayesian analysis methods using Monte Carlo sampling applied to estimate the parameters of dark energy models based on observational data?

I have come across references to Markov Chain Monte Carlo (MCMC) in the context of CMB and supernova analyses, but it is unclear how to interpret the resulting posterior distributions.

I would appreciate any clarifications or references to tutorials or review articles.

Hi! 👋
That’s a really good question — Bayesian inference with Monte Carlo sampling is one of the main tools in modern cosmology. Markov Chain Monte Carlo (MCMC) methods are used to explore the parameter space of dark energy models by generating samples from the posterior probability distribution based on observational data (like CMB, BAO, or supernovae).

In practice, you interpret the posterior as showing which regions of parameter space are most probable, given your data and priors. The shape and spread of the distribution tell you about uncertainties and parameter correlations.

A very clear introduction is in Lewis & Bridle (2002, Phys. Rev. D), where they describe CosmoMC, and a good modern review is Trotta (2017, Reports on Progress in Physics) on Bayesian methods in cosmology. You might also check tutorials on the emcee (Foreman-Mackey et al., 2013) Python package — it’s widely used and beginner-friendly.

Hope this helps — good luck exploring those posteriors!

As a nuclear medicine researcher, I see MCMC as a very useful method for understanding uncertainty in complex data.

In dark energy studies, it helps scientists see how different model parameters fit real observations from space. Instead of giving one exact answer, it shows how likely each possibility is — almost like analyzing radiation signals where you look for the most probable pattern, not just one measurement.

It’s a clear, visual way to understand how confident we can be in our models and what range of values truly makes sense.

Another common method for estimating dark energy parameters is Nested Sampling (e.g., the MultiNest algorithm):

• How it works: instead of a traditional chain, Nested Sampling builds a sequence of nested regions with increasing likelihood, gradually narrowing the parameter space while estimating the integral over the posterior.

• Advantages: works well for multimodal and high-dimensional distributions; directly provides the marginal likelihood (evidence), which is useful for model comparison.

• Application in cosmology: used with CMB, supernovae, and BAO data to simultaneously estimate dark energy parameters and compare different models

7 hours ago, Mamatova Sagira said:

A very clear introduction is in Lewis & Bridle (2002, Phys. Rev. D), where they describe CosmoMC, and a good modern review is Trotta (2017, Reports on Progress in Physics) on Bayesian methods in cosmology. You might also check tutorials on the emcee (Foreman-Mackey et al., 2013) Python package — it’s widely used and beginner-friendly.

Citations need to be complete (issue and page numbers, article title) and links to the should be included

8 hours ago, Alisher said:

I’d suggest checking out Trotta (2008) for a clear overview and Lewis & Bridle (2002)

Same thing - proper citation and links needed