Selection function
Definition: The probability that a source with specified properties enters the analyzed sample.
Why it matters here: It is needed to answer Two sky tiles each recover 84 of 100 injections, but one tile has twice the thermal noise. Why is the same aggregate completeness not evidence of equal selection functions? and to interpret A flux-limited survey samples more volume for brighter objects, while beaming and pulse broadening affect detectability.
Relationships: Use it with Injection-recovery test and Completeness; the lecture model is \(\hat p=\frac{k}{N},\qquad\sigma_{\hat p}\simeq\sqrt{\frac{\hat p(1-\hat p)}{N}}\).
Boundary or common confusion: Binomial errors assume independent trials with one common recovery probability; a heterogeneous sky requires a stratified completeness model.
Completeness
Definition: The fraction of a target population recovered by the survey and analysis pipeline.
Why it matters here: It is needed to answer Two sky tiles each recover 84 of 100 injections, but one tile has twice the thermal noise. Why is the same aggregate completeness not evidence of equal selection functions? and to interpret A flux-limited survey samples more volume for brighter objects, while beaming and pulse broadening affect detectability.
Relationships: Use it with Selection function and Fluence; the lecture model is \(\hat p=\frac{k}{N},\qquad\sigma_{\hat p}\simeq\sqrt{\frac{\hat p(1-\hat p)}{N}}\).
Boundary or common confusion: Binomial errors assume independent trials with one common recovery probability; a heterogeneous sky requires a stratified completeness model.
Fluence
Definition: Time-integrated flux density, often used to characterize short radio bursts.
Why it matters here: It is needed to answer Two sky tiles each recover 84 of 100 injections, but one tile has twice the thermal noise. Why is the same aggregate completeness not evidence of equal selection functions? and to interpret A flux-limited survey samples more volume for brighter objects, while beaming and pulse broadening affect detectability.
Relationships: Use it with Completeness and Detection threshold; the lecture model is \(\hat p=\frac{k}{N},\qquad\sigma_{\hat p}\simeq\sqrt{\frac{\hat p(1-\hat p)}{N}}\).
Boundary or common confusion: Binomial errors assume independent trials with one common recovery probability; a heterogeneous sky requires a stratified completeness model.
Detection threshold
Definition: The decision boundary in a search statistic above which candidates are retained.
Why it matters here: It is needed to answer Two sky tiles each recover 84 of 100 injections, but one tile has twice the thermal noise. Why is the same aggregate completeness not evidence of equal selection functions? and to interpret A flux-limited survey samples more volume for brighter objects, while beaming and pulse broadening affect detectability.
Relationships: Use it with Fluence and Injection-recovery test; the lecture model is \(\hat p=\frac{k}{N},\qquad\sigma_{\hat p}\simeq\sqrt{\frac{\hat p(1-\hat p)}{N}}\).
Boundary or common confusion: Binomial errors assume independent trials with one common recovery probability; a heterogeneous sky requires a stratified completeness model.
Injection-recovery test
Definition: A completeness experiment that adds controlled synthetic signals and measures their recovery rate.
Why it matters here: It is needed to answer Two sky tiles each recover 84 of 100 injections, but one tile has twice the thermal noise. Why is the same aggregate completeness not evidence of equal selection functions? and to interpret A flux-limited survey samples more volume for brighter objects, while beaming and pulse broadening affect detectability.
Relationships: Use it with Detection threshold and Selection function; the lecture model is \(\hat p=\frac{k}{N},\qquad\sigma_{\hat p}\simeq\sqrt{\frac{\hat p(1-\hat p)}{N}}\).
Boundary or common confusion: Binomial errors assume independent trials with one common recovery probability; a heterogeneous sky requires a stratified completeness model.