May 28th, 2008| 01:00 pm | Posted by vlk

The most widely used tool for detecting sources in X-ray images, especially Chandra data, is the wavelet-based `wavdetect`, which uses the Mexican Hat (MH) wavelet. Now, the MH is not a very popular choice among wavelet aficianados because it does not form an orthonormal basis set (i.e., scale information is not well separated), and does not have compact support (i.e., the function extends to inifinity). So why is it used here?

Continue reading ‘Mexican Hat [EotW]’ »

Tags:

Chandra,

ciao,

convolution,

correlation,

EotW,

Equation,

Equation of the Week,

Fourier Transform,

gaussian,

MexHat,

Mexican Hat,

MH,

multiscale,

wavdetect,

wavelet Category:

Algorithms,

Astro,

Imaging,

Jargon |

1 Comment
May 21st, 2008| 01:00 pm | Posted by vlk

There is a lesson that statisticians, especially of the Bayesian persuasion, have been hammering into our skulls for ages: __do not subtract__ background. Nevertheless, old habits die hard, and old codes die harder. Such is the case with X-ray aperture photometry. Continue reading ‘Background Subtraction [EotW]’ »

Tags:

aperture photometry,

background,

background marginalization,

background subtraction,

celldetect,

Chandra,

ciao,

EotW,

Equation,

error propagation,

ldetect,

local detect,

wavdetect,

X-ray Category:

Algorithms,

Astro,

Jargon |

6 Comments
May 14th, 2008| 01:00 pm | Posted by vlk

Spectral lines are a ubiquitous feature of astronomical data. This week, we explore the special case of optically thin emission from low-density and high-temperature plasma, and consider the component factors that determine the line intensity. Continue reading ‘Line Emission [EotW]’ »

Tags:

abundance,

emission,

emission measure,

emissivity,

EotW,

Equation,

Equation of the Week,

flux,

ion balance,

line Category:

Astro,

Jargon,

Misc,

Physics,

Stars |

2 Comments
May 6th, 2008| 06:12 pm | Posted by vlk

The *gamma* function [not the Gamma -- note upper-case G -- which is related to the factorial] is one of those insanely useful functions that after one finds out about it, one wonders “why haven’t we been using this all the time?” It is defined only on the ~~positive~~ non-negative real line, is a highly flexible function that can emulate almost any kind of skewness in a distribution, and is a perfect complement to the Poisson likelihood. In fact, it is the conjugate prior to the Poisson likelihood, and is therefore a natural choice for a prior in all cases that start off with counts. Continue reading ‘*gamma* function (Equation of the Week)’ »

May 2nd, 2008| 06:06 pm | Posted by vlk

Starting a new feature — highlighting some equation that is widely used in astrophysics or astrostatistics. Today’s featured equation: what instruments do to incident photons. Continue reading ‘Equation of the Week: Confronting data with model’ »

Tags:

ARF,

effective area,

EotW,

Equation,

Equation of the Week,

LRF,

point spread function,

PSF,

response matrix,

RMF,

source Category:

Astro,

Jargon |

Comment