Sky coordinate
Definition: A position on the celestial sphere expressed in a declared reference frame and epoch.
Why it matters here: In Identifiers and Cross-Matches, Sky coordinate is needed to reason about coordinates, angular separation, likelihood ratios, and background density rather than merely label the phenomenon.
Relationship: It is interpreted alongside Angular separation and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: This is not a posterior match probability until background density and competing candidates are included.
\(w=exp(-r^2/(2 sigma_r^2))/rho\)
Angular separation
Definition: The great-circle angle between two sky positions.
Why it matters here: In Identifiers and Cross-Matches, Angular separation is needed to reason about coordinates, angular separation, likelihood ratios, and background density rather than merely label the phenomenon.
Relationship: It is interpreted alongside Positional uncertainty and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: This is not a posterior match probability until background density and competing candidates are included.
Positional uncertainty
Definition: The probability distribution describing error in a reported source location.
Why it matters here: In Identifiers and Cross-Matches, Positional uncertainty is needed to reason about coordinates, angular separation, likelihood ratios, and background density rather than merely label the phenomenon.
Relationship: It is interpreted alongside Likelihood ratio and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: This is not a posterior match probability until background density and competing candidates are included.
Likelihood ratio
Definition: A comparison of how probable a candidate association is under match and background hypotheses.
Why it matters here: In Identifiers and Cross-Matches, Likelihood ratio is needed to reason about coordinates, angular separation, likelihood ratios, and background density rather than merely label the phenomenon.
Relationship: It is interpreted alongside False-match rate and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: This is not a posterior match probability until background density and competing candidates are included.
False-match rate
Definition: The expected fraction of accepted associations produced by unrelated background objects.
Why it matters here: In Identifiers and Cross-Matches, False-match rate is needed to reason about coordinates, angular separation, likelihood ratios, and background density rather than merely label the phenomenon.
Relationship: It is interpreted alongside Sky coordinate and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: This is not a posterior match probability until background density and competing candidates are included.