How to: -estimation | ||
What quantity? |
Example |
Reference |
estimate the intensity of a Poisson process in presence of a background |
n of photons i.e. flux or luminosity, n. of galaxies, i.e. richness, x-ray count-rate, etc. |
Almost every Bayesian book. Appendix B of Andreon et al. (2006) Discussion in sec 4.4.1 in Andreon et al. (2006) |
estimate the intensity of a structured (i.e spatially dependent) Poisson process in presence of a background |
-the x-ray flux of an extended source, including upper limit determinations. -the richness of a clusters using spatial information -the X-ray flux within r500, including uncertainties on T (used to estimate r500) and parameters of the radial profile - the total optical luminosity of galaxies in clusters (integral of the luminosity function) |
Appendix A of Andreon et al. (2008) Andreon et al. (2010). Andreon (2010) |
estimate a scale (width) in presence of a background, heteroscedastic errors and when |
(velocity) dispersion, scatter, width of a distribution, Beers scale, etc. |
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only a summary of the data is available |
cluster velocity dispersion |
Appendix A of Andreon et al. (2006) |
individual data are at hand |
cluster velocity dispersion | Appendix B of Andreon et al. (2008) |
estimate a fraction in absence of a background |
blue fraction, hardness ratio
(=1-2 f_b), AGN fraction, E+A fraction, completeness, fraction of
galaxies having large equivalent width, etc. |
Laplace (1812), almost every Bayesian textbook. |
estimate a fraction in presence of a background |
blue fraction, hardness ratio (=1-2 f_b), AGN fraction | Appendix C of Andreon et al. (2006) |
estimate the luminosity or mass function in presence of a background, or any other similar measurements of them. |
luminosity function dwarf on giant ratio |
Andreon, Punzi & Grado (2005). Andreon (2007) |
estimate a linear trend (correlation, regression) between quantities with heteroscedastic errors, in presence of an intrinsic scatter, and in absence of a background |
Fundamental Plane, Tully-Fisher, Colour-Magnitude stellar baryon fraction vs mass gas baryon fraction vs mass ratio of faint to bright galaxies vs z |
D'Agostini (2005) Andreon (2010) Andreon (2008) |
as above, but with noisy errors |
richness-mass regression |
Andreon & Hurn (2010) |
estimate a linear trend (correlation, regression) between quantities with heteroscedastic errors, in presence of an
intrinsic scatter, and in presence of a background, eventually showing itself a trend. |
colour-magnitude relation |
Appendix A of Andreon (2006) |
predict something, using a calibrating sample |
predict mass, given richness |
Andreon & Hurn (2010) |
estimate the colour distribution, for a sample contaminated by a uninteresting population |
the colour distribution of cluster galaxies |
Andreon et al. (2008) |
A lot of the above at once. |
Estimate the mass grow in galaxies | Andreon (2006) |
All the above in a organized paper |
Andreon (2008), by Camdrige University Press |
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How to: -model selection |
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Read first Liddle (2004),
then note that evidence, BIC, and likelihood ratio are three estimates,
with decreasing accuracy, of the number you are looking for: the
relative probability of two hypothesis. Trotta (2007),
especially the first astro-ph version, also clarifies the subject and
introduce the Savage-Dickey density ratio, computationally quite useful
for nested models. |
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What is the question? |
Example |
Reference |
Is there a trend? Model it and compare with no trend at all. |
Does the blue fraction depend on the cluster velocity dispersion? Does the fraction of obscured AGN depends on x-ray luminosity? Is my source variable? |
Andreon et al. (2006), sec 6.2 Tajer et al. (2007), sec 8.1 |
Is the trend a linear one ? Compare the simple linear trend with a more complicate one. |
Does the colour-magnitude relation bend? | Andreon et al. (2006), sec 4.1 |
Are two trends equal? Model them as equal first, and then as different. Then, compare them. |
Does the fraction of absorbed and obscured AGNs shows the same trend? Does the slope of a trend, as measured with a dataset the same of the one measured on another one? |
Tajer et al. (2007), sec 8.1 Andreon (2009) |
Is the feature hinted in my plot significant? Add the feature to the model and compare with the simpler model. You are asking a reply to: Do I need to consider a more complex model? |
Is there a dip in the LF? Is the colour-magnitude relation curved? Is there an emission line in the spectrum? Is there a cluster (detection) here? Is it a cluster or a blend of two groups? |
Andreon et al. (2006), sec 4.3 Andreon et al. (2006), sec 4.1 Protassov et al. (2002) Andreon et al. 2009, sec 3.2 Andreon et al. 2009, sec 3.6 |
Should I refine my model adding one more parameter/feature? Do it and compare with the simpler model. |
Must the mass function of galaxy in clusters expected from simple model be refined with a further evolutionary term? |
Andreon (2006) |
Mantra: model what you guess and compare complex and simple models. |
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