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, xray countrate, 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 xray flux of an extended source, including upper limit determinations. the richness of a clusters using spatial information the Xray 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. 

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
(=12 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 (=12 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, TullyFisher, ColourMagnitude 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 
richnessmass 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. 
colourmagnitude 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 

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 astroph version, also clarifies the subject and
introduce the SavageDickey density ratio, computationally quite useful
for nested models. 

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 xray 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 colourmagnitude 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 colourmagnitude 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. 
