Calibrating the multiplicative bias
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+
+
+ $\hat \gamma = c +
+ (1+\color{orange}{m})\gamma_\text{true}, \quad
+ |m|<10^{-3}$
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+
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+ +
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+ +
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+ +
+ Metacalibration: Taylor expansion, assuming $\gamma \ll 1$
+
+ $e = e|_{\gamma=0} + \underset{R = 1 + + m}{\underbrace{\dfrac{\partial e}{\partial + \gamma}\Big|_{\gamma = 0}}} \gamma + \mathcal{O}(\gamma^2)$ + +
+ + Response matrix by finite differentiation: +
+ $R_{ij} = \dfrac{e^+_i - e^+_i}{\Delta \gamma_{j}}$ + +
+ Requires to add anticorrelated noise to the data, + due to artificial shear. +
+ + $e = e|_{\gamma=0} + \underset{R = 1 + + m}{\underbrace{\dfrac{\partial e}{\partial + \gamma}\Big|_{\gamma = 0}}} \gamma + \mathcal{O}(\gamma^2)$ + +
+ + Response matrix by finite differentiation: +
+ $R_{ij} = \dfrac{e^+_i - e^+_i}{\Delta \gamma_{j}}$ + +
+ Requires to add anticorrelated noise to the data, + due to artificial shear. +
+ $\gamma \ll 1$ no longer true close to a cluster
+ ![]()
+ Requires to compute $\dfrac{\partial^2 e}{\partial
+ \gamma^2}\Big|_{\gamma = 0}$, $\dfrac{\partial^3 e}{\partial
+ \gamma^3}\Big|_{\gamma = 0}$, ...
+
+ 
+ Requires to compute $\dfrac{\partial^2 e}{\partial
+ \gamma^2}\Big|_{\gamma = 0}$, $\dfrac{\partial^3 e}{\partial
+ \gamma^3}\Big|_{\gamma = 0}$, ...
+
+ Let's do forward modeling instead
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+