A new Bayesian inference tool (BIE) has been published on astro-ph today (http://arxiv.org/abs/1203.3816). It has several advanced MCMC algorithms to sample the posterior and some stand alone programs to test a convergence and to compute a marginal likelihood for Bayesian model selection. It is designed for a general purpose Bayesian inference and is possible to add any user likelihood module to solve one’s own problem. It has potentially many interesting applications not limited to astronomy. Two case studies (Bayesian semi-analytic galaxy formation model and GALPHAT) have been introduced in this paper.

## What’s the best model of galaxy surface brightness distribution?

•March 12, 2012 • Leave a CommentFrom the experiments that we have done over the last few years, my advisors and I were convinced that Sersic-based galaxy surface brightness model is not good for model selection. Simply speaking, it is impossible to tell whether a galaxy data is supported by single Sersic profile or bulge-disc profile, which consists of Sersic bulge and exponential disc (i.e. specific case of Sersic profile with n=1) if the galaxy is truly generated from single Sersic profile. Although this has been perceived by the experts of galaxy image modeling, it was a bit surprising to note that reliable Bayes factor estimation from accurate marginal likelihood computation of each model also tells the same.

More detail studies on this subject including practical choice of Bayes factor and hierarchical prior elicitation to improve a reliability of Bayes factor model selection for galaxy bulge-disc decomposition will be ready for submitting to a journal very soon.

However, if possible, we believe that one should find a better model with minimal parameter degeneracy for the best analysis result. One candidate for better model is a set of orthogonal basis function for modeling galaxy light distribution as suggested by some people.

Bayesian goodness-of-fit test for a galaxy surface brightness distribution model is possible using the Verdinelli and Wasserman algorithm implemented in the BIE for finding the best model supported by galaxy data. This would be an interesting study.

## Marginal likelihood computation

•December 13, 2011 • Leave a CommentI’ve worked on new methods to compute the marginal likelihood. It is a difficult task owing to the curse of dimensionality. However my advisors and I found that adding more samples from tempered MCMC chains sampling the posterior tails and isolating independent parameter posterior by Laplace approximation, greatly reduces the required number of independent posterior samples for convergence to the true value. The effect is more significant for higher dimension. I’ve tested multivariate Gaussian posterior up to a 12 dimension. This new methods will be introduced in another paper and used for GALPHAT galaxy morphology analysis.

## Bayesian MCMC galaxy SED modeling -cont.

•April 3, 2011 • Leave a CommentIt is interesting to see that very recently the following three papers are posted on astro-ph. They are about SED fitting using Markov chain Monte Carlo.

1.http://arxiv.org/abs/1104.0054 2.http://arxiv.org/abs/1103.3269 3.http://arxiv.org/abs/1101.2215

They’re sharing the same motivation: the correct characterization of galaxy SED model parameter space including the degeneracy and parameter covariance which has been intrinsically difficult to reveal by conventional “chi^2” minimization-based best fit parameter approach. Although they are using different population synthesis models, all of them demonstrated the existence of the severe degeneracy between some model parameters.

These results again motivates the full Bayesian approach with advanced MCMC sampler, which can potentially achieve the following improvements.

1. Parameter constraint power can be improved by informative prior. For example, the mm/sub-mm SED modeling has a degeneracy between redshift and dust temperature, which might be broken by constraining the redshift using other part of SED (i.e. optical or emission lines). The Bayesian approach allows us to model a subset of data, then later to add more data to improve the inference. So one can first model the optical SED and use the posterior as a new prior when modeling the other part of SED (e.g. mm/sub-mm). This approach helps to constraint the model parameters with strong degeneracy.

2. The different hypothesis can be tested using the Bayes factor. For example, one can test whether the two stellar population is better description than the single stellar population or not. In addition, the different forms of IMF can be tested against the data over different redshift or environment.

Although I expect that SED modeling is highly non-linear compare to the GALPHAT galaxy morphology modeling, the full Bayesian approach using the BIE will certainly improve our inference which is still poor in some cases, using even MCMC approach recently developed by these several groups.

## Bayesian MCMC galaxy SED modeling

•April 3, 2011 • 2 CommentsIn these days, galaxy SED modeling becomes popular since the current and forthcoming large scale surveys will produce multi-bands photometric data points sufficient to sample the galaxy integrated spectral energy distribution, which allows us to infer many interesting aspects of galaxy properties including stellar mass, star formation history, dust contents etc.

Currently there are several versions of widely used software package to model the galaxy spectra (i.e. stellar population thesis code). However the model parameter space is large and not well constrained, and thus in most cases, people use the population synthesis code with very strong assumptions about IMF and star formation history, which significantly affect our inference of galaxy stellar mass.

To improve this situation, Bayesian MCMC approach to model the galaxy integrated SED is very powerful solution not only for estimating the parameter and its uncertainty but also for assessing the statistical power of different models based on different assumptions made by user (different IMF, star formation history and multiple population etc.), using the Bayes factor model selection.

The successful demonstration of this approach to the galaxy morphology analysis (GALPHAT) convinces me that it will be straight forward to apply BIE to galaxy SED modeling. This is certainly my next project in the near future.

Link to the publically avaliable stellar population synthesis codes

CIGALE : SED fitting code

www.sedfitting.org : useful site

## Why am I doing an astronomy PhD?

•March 15, 2011 • Leave a Comment“Do not undertake a scientific career in quest of fame or money. There are easier and better ways to reach them. Undertake it if nothing else will satisfy you; for nothing else is probably what you will receive.” — Cecilla Payne

When one starts to lose his/her own patience and becomes nervous about the future in this discouraged job market, it is always good idea to recollect the moment when one first got fascinated and decided to pursue a scientific career, and to adjust the compass to the right direction.

## Research update2

•February 23, 2011 • Leave a Comment1. At long last, I finished the potential well paper and the paper has been accepted to MNRAS.

2. I’m working on testing the Tempered Differential evolution MCMC algorithm for GALPHAT analysis to efficiently sample many independent MCMC samples, compared to the parallel chains, which will improve the convergence with shorter run time than the parallel chain algorithm does for the same number of converged sample.

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