Some memos, documents and tidbits on statistics and uncertainty analysis
(Written by F. Masci, purely for reference and fun)
Probabilistic Source (centroid) Matching
Dependency of relative photometric uncertainty on flat-fielding accuracy
Computing flux upper-limits for non-detections
The email that started it all
Validating model photometric uncertainties (priors) empirically
A method to find variable/transient sources in a stack of image data:
The Consecutive Signed-Slope (CSS) Method (vsn 4/27/2021)
The impact of correlations on the optimum location (mean) measure and its variance
Uncertainty and average absolute deviation for two measurements with Gaussian distributed errors
Cauchy versus Gaussian and 1/√N behavior
Correlated versus dependent normally-distributed variables (a paradox?)
Example of
Uncorrelated
but dependent normally-distributed variables
Generating Light Curves from Forced PSF-fit Photometry on ZTF Difference Images (white paper)
Generating Light Curves from Forced PSF-fit Photometry on PTFIDE Difference-images (white paper)
Optimal Detection of Rare "sub-significant" Events in the Time-Domain (white paper)
On the relationship between linear correlation and slope from a linear regression fit
A study of the bias from inverse Poisson-variance weighting
Optimal image combination with variable seeing and photometric zero-point calibrations
The danger of statistical inference in magnitude space
Noise-variance in magnitude space
Quick 'n dirty way to derive the point-source sensitivity from image data
Noise-variance (and sigma) in magnitude space
Aperture photometry and uncertainty estimation assuming priors and correlated noise
Simple aperture photometry and uncertainties without access to explicit priors
Optimum photometric aperture size for a Gaussian source profile
Computing the "Number of Noise-Pixels"
(HTML version)
Computing the "Number of Noise-Pixels"
(original PDF version)
Assessing the impact of noisy pixels on photometric signal-to-noise ratio
The MADTUT method for robustly estimating the background noise-sigma
A pixel-error model for WISE
(general for any detector using sample-up-the-ramp/non-destructive readout electronics)
Estimating relative pixel responsivities using the gradient method
Assessing the significance of radial proper motion measurements via the 2-D chi-square
An application of PCA to a chi-square minimization problem with correlated errors
Combining Random and Systematic Errors
Related: quoting/computing astrometric performance using robust metrics
Testing and Selecting Nested Models
Getting started with the "R" statistics programming language
Last modified: 2023 February 6