Internet dating cosmology
Discoblog: NCBI ROFL: Mirror, mirror on my Facebook wall: effects of exposure to Facebook on self-esteem. NCBI ROFL is the brainchild of two Molecular and Cell Biology graduate students at UC Berkeley and features real research articles from the Pub Med database (which is housed by the National Center for Biotechnology information, aka NCBI) that they find amusing (ROFL is a commonly-used internet acronym for "rolling on the floor, laughing").
Discoblog: NCBI ROFL: Why you want the men you can’t have.
Taking account of the empirical procedure by which corrections are made to their absolute magnitudes to allow for the varying shape of the light curve and extinction by dust, we find, rather surprisingly, that the data are still quite consistent with a constant rate of expansion..
Since then supernova cosmology has developed rapidly as an important probe of ‘dark energy’.
The physical mechanism(s) which give rise to the correlations that underlie these corrections remain uncertain To find the maximum likelihood estimator (MLE) from the data, we must define the appropriate likelihood:i.e. For a given SN Ia, the true data are drawn from some global distribution.
These values are contaminated by various sources of noise, yielding the observed values .
Introducing another set of vectors , the observed , and the estimated experimental covariance matrix Σ (including both statistical and systematic errors), the probability density of the data given some set of true parameters is: To combine the exponentials we introduce the vector and the block diagonal matrix With these, we have and so .
What remains is to specify the model of uncertainties on the data.
Empirical corrections are made to reduce the scatter in the observed magnitudes by exploiting the observed (anti) correlation between the peak luminosity and the light curve width and the colour wherein the SN Ia are standardised by fitting their light curve to an empirical template, and the parameters of this fit are used in the cosmological analysis.
(A more comprehensive statistical model of light curves spanning optical through near-infrared data has subsequently been constructed in a hierarchical Bayesian framework and c.
To eliminate the so-called ‘nuisance parameters’, we set similar bounds on the profile likelihood.
Writing the interesting parameters as θ and nuisance parameters as ϕ, the profile likelihood is defined as We substitute by in equation (10) in order to construct confidence regions in this lower dimensional space; ν is now the dimension of the remaining parameter space. However the actual distributions of and are close to gaussian, as seen in Fig. Moreover although this likelihood apparently integrates to unity, it accounts for only the data.