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$\begin{figure} \par\resizebox{8.8cm}{!}{% \input fig1.tex} \end{figure}$ Figure 1: The effect of a non-constant density on the effective weight. The plot shows, in the 1D case, the quantity $\rho (x) w_{\rm eff}(x)$ for three different densities, $\rho _1(x) = 1$ , $\rho _2(x) = 1 + H(x)/4$ , and $\rho_3(x) = 1 - (\cos x) / 2$ . In all cases the original weight function has been chosen to be such that the combination $w(x) \rho (x)$ is a Gaussian (see solid line plot).
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{% \input fig2.tex} \end{figure}$ Figure 2: Effective weight function in presence of boundaries. Three Gaussian weight function (shown in solid lines) centered on different parts of the field $\Omega = [-5, 5]$ produce significantly different effective weights (dashed lines). The weight function have been normalized according to Eq. (20); $\rho (x) = 1.5$ is constant for this plot.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{% \input fig3.tex} \end{figure}$ Figure 3: The variance $T_\sigma$ evaluated at different positions $x_A \equiv x_B$ . For this plot, we used a Gaussian weight function with variance 1/2; the measurement error $\sigma$ was kept constant on the field. Note that, in agreement with Eq. (51), the quantity $T_\sigma /\sigma ^2$ is always larger than $1/\mathcal{N}_{\rm eff}$ ; curiously, the quantity $1/\mathcal{N}$ gives a good first-order approximation for $T_\sigma$ even in the complex situation shown here.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{% \input fig2.tex} \end{figure}$	Figure 2: Effective weight function in presence of boundaries. Three Gaussian weight function (shown in solid lines) centered on different parts of the field $\Omega = [-5, 5]$ produce significantly different effective weights (dashed lines). The weight function have been normalized according to Eq. (20); $\rho (x) = 1.5$ is constant for this plot.
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