Thermal noise
Definition: Random receiver and sky fluctuations that average down approximately with the square root of independent samples.
Why it matters here: It is needed to answer Two sources share the same 5% flux-scale error but have independent 1% thermal errors. Which uncertainty cancels in their flux ratio, and which does not? and to interpret Independent small fractional errors combine in quadrature, whereas shared calibration errors correlate many image pixels.
Relationships: Use it with Jackknife test and Flux-scale uncertainty; the lecture model is \(\left(\frac{\sigma_S}{S}\right)^2=\sum_j f_j^2+2\sum_{i<j}\rho_{ij}f_i f_j\).
Boundary or common confusion: Quadrature is justified only for independent zero-mean errors; common-mode flux-scale uncertainty requires covariance-aware comparisons.
Flux-scale uncertainty
Definition: A multiplicative calibration uncertainty shared by targets using the same amplitude reference.
Why it matters here: It is needed to answer Two sources share the same 5% flux-scale error but have independent 1% thermal errors. Which uncertainty cancels in their flux ratio, and which does not? and to interpret Independent small fractional errors combine in quadrature, whereas shared calibration errors correlate many image pixels.
Relationships: Use it with Thermal noise and Primary-beam correction; the lecture model is \(\left(\frac{\sigma_S}{S}\right)^2=\sum_j f_j^2+2\sum_{i<j}\rho_{ij}f_i f_j\).
Boundary or common confusion: Quadrature is justified only for independent zero-mean errors; common-mode flux-scale uncertainty requires covariance-aware comparisons.
Primary-beam correction
Definition: Division by the antenna sensitivity pattern to estimate off-axis sky brightness.
Why it matters here: It is needed to answer Two sources share the same 5% flux-scale error but have independent 1% thermal errors. Which uncertainty cancels in their flux ratio, and which does not? and to interpret Independent small fractional errors combine in quadrature, whereas shared calibration errors correlate many image pixels.
Relationships: Use it with Flux-scale uncertainty and Covariance; the lecture model is \(\left(\frac{\sigma_S}{S}\right)^2=\sum_j f_j^2+2\sum_{i<j}\rho_{ij}f_i f_j\).
Boundary or common confusion: Quadrature is justified only for independent zero-mean errors; common-mode flux-scale uncertainty requires covariance-aware comparisons.
Covariance
Definition: A quantitative description of how errors in different measurements vary together.
Why it matters here: It is needed to answer Two sources share the same 5% flux-scale error but have independent 1% thermal errors. Which uncertainty cancels in their flux ratio, and which does not? and to interpret Independent small fractional errors combine in quadrature, whereas shared calibration errors correlate many image pixels.
Relationships: Use it with Primary-beam correction and Jackknife test; the lecture model is \(\left(\frac{\sigma_S}{S}\right)^2=\sum_j f_j^2+2\sum_{i<j}\rho_{ij}f_i f_j\).
Boundary or common confusion: Quadrature is justified only for independent zero-mean errors; common-mode flux-scale uncertainty requires covariance-aware comparisons.
Jackknife test
Definition: A repeat analysis on deliberately split data used to expose systematic differences.
Why it matters here: It is needed to answer Two sources share the same 5% flux-scale error but have independent 1% thermal errors. Which uncertainty cancels in their flux ratio, and which does not? and to interpret Independent small fractional errors combine in quadrature, whereas shared calibration errors correlate many image pixels.
Relationships: Use it with Covariance and Thermal noise; the lecture model is \(\left(\frac{\sigma_S}{S}\right)^2=\sum_j f_j^2+2\sum_{i<j}\rho_{ij}f_i f_j\).
Boundary or common confusion: Quadrature is justified only for independent zero-mean errors; common-mode flux-scale uncertainty requires covariance-aware comparisons.