ASTR 430 Lecture 04: Identifiers and Cross-Matches

Terms Developed in Context

These terms form the lecture's reasoning chain from observable through model to a bounded physical conclusion.

Sky coordinate

A position on the celestial sphere expressed in a declared reference frame and epoch. In this lecture it supports the evidence-to-model chain for coordinates, angular separation, likelihood ratios, and background density.

Use and relationship: Read it together with False-match rate and Angular separation. The governing relation \(w=exp(-r^2/(2 sigma_r^2))/rho\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: This is not a posterior match probability until background density and competing candidates are included. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Angular separation

The great-circle angle between two sky positions. In this lecture it supports the evidence-to-model chain for coordinates, angular separation, likelihood ratios, and background density.

Use and relationship: Read it together with Sky coordinate and Positional uncertainty. The governing relation \(w=exp(-r^2/(2 sigma_r^2))/rho\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: This is not a posterior match probability until background density and competing candidates are included. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Positional uncertainty

The probability distribution describing error in a reported source location. In this lecture it supports the evidence-to-model chain for coordinates, angular separation, likelihood ratios, and background density.

Use and relationship: Read it together with Angular separation and Likelihood ratio. The governing relation \(w=exp(-r^2/(2 sigma_r^2))/rho\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: This is not a posterior match probability until background density and competing candidates are included. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Likelihood ratio

A comparison of how probable a candidate association is under match and background hypotheses. In this lecture it supports the evidence-to-model chain for coordinates, angular separation, likelihood ratios, and background density.

Use and relationship: Read it together with Positional uncertainty and False-match rate. The governing relation \(w=exp(-r^2/(2 sigma_r^2))/rho\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: This is not a posterior match probability until background density and competing candidates are included. This caveat prevents the term from being treated as a unique explanation or a context-free number.

False-match rate

The expected fraction of accepted associations produced by unrelated background objects. In this lecture it supports the evidence-to-model chain for coordinates, angular separation, likelihood ratios, and background density.

Use and relationship: Read it together with Likelihood ratio and Sky coordinate. The governing relation \(w=exp(-r^2/(2 sigma_r^2))/rho\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: This is not a posterior match probability until background density and competing candidates are included. This caveat prevents the term from being treated as a unique explanation or a context-free number.