|How to: -estimation|
|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).
|estimate a scale (width) in presence of a background, heteroscedastic errors and when
||(velocity) dispersion, scatter, width of a distribution, Beers scale, etc.
| 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.
dwarf on giant ratio
|Andreon, Punzi & Grado (2005).
|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
|as above, but with noisy errors
||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.
||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
|How to: -model selection
|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.
|What is the question?
|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
|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,
|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?
|Mantra: model what you guess and compare complex and simple models.