Astronomy & Astrophysics

All Figures

$\begin{figure} \par\includegraphics[width=7.5cm]{4927fig1a.eps}\vspace*{1mm} \par\includegraphics[width=7.5cm]{4927fig1b.eps}\end{figure}$ Figure 1: Top: normalized source models used in this study. An example model (black) and its neighbours (dark gray) are highlighted for better clarity. Inlet: the example model and its neighbours in parameter space $(kT,N_{\rm H})$ . Bottom: normalized background model.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm]{4927fig2.eps}\end{figure}$ Figure 2: Schematic construction of a continuous non-homogeneous Poisson process by the rejection method: out of $N_{\rm p}$ uniform random points in the rectangle $B \times [0,\max (f)]$ only those beneath the curve f(E) are accepted; their abscissae constitute the event list (ticks). The number $N_{\rm p}$ itself is Poisson distributed with expectation value $\vert B\vert \times \max (f)$ .
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In the text

$\begin{figure} \par\includegraphics[width=7cm,height=7cm]{4927fig3.eps} \end{figure}$ Figure 3: Receiver-operator characteristics for the binary classification problem with only two models (inlet).
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In the text

$\begin{figure} { \includegraphics[width=3.8cm]{4927fig4a.eps}\hspace*{3mm} \includegraphics[width=3.8cm]{4927fig4b.eps} }\end{figure}$ Figure 4: The probability of successful identifications versus the number of $d_{\chi ^2}$ -ordered candidate models ( left), and versus the maximal distance of the candidates from the true model ( right). See text. The simulation has $10 < {\cal N}_{\rm src} < 100$ , ${\cal N}_{\rm bg}$ = 0, and the binned methods use uqual-size bins based on Sturges' rule, resulting on average in $\langle n^* \rangle = 9.1$ counts per bin.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm]{4927fig5.eps} \end{figure}$ Figure 5: Average f-space ( top left) and parameter ( other panels) deviations between true and estimated models. The number m of candidate models delineates the tested volume in parameter space.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm]{4927fig6.eps} \end{figure}$ Figure 6: Average chi-square distance between true and estimated models as a function of the true model parameters (marginal distributions).
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In the text

$\begin{figure} {\includegraphics[width=8cm]{4927fig7.eps} }\end{figure}$ Figure 7: Similar to Fig. 5 but with m proportional to the density of candidate models in parameter space.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm]{4927fig8.eps} \end{figure}$ Figure 8: The effect of binning on the performances of ( $C,\chi ^2,\chi ^2_{\rm N}$ ). The corresponding unbinned L values are shown for comparison.
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In the text

$\begin{figure} \par\includegraphics[width=8cm]{4927fig9.eps} \end{figure}$ Figure 9: Dependence of the estimation errors on the true expected counts ${\cal N}$ .
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In the text

$\begin{figure} { \includegraphics[width=3.9cm]{4927fig10a.eps}\hspace*{3mm} \includegraphics[width=3.9cm]{4927fig10b.eps} }\end{figure}$ Figure 10: Similar to Fig. 4, but including background ( ${\cal N}_{\rm bg}$ = 50).
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In the text

$\begin{figure} {\includegraphics[width=7.5cm]{4927fig11.eps} }\end{figure}$ Figure 11: XMM-Newton/EPIC observation of Haro 6-13, comprising 128 counts. Solid line: maximum-L solution $f_{\rm src}(E)$ ; dashed: background spectrum $f_{\rm bkg}(E)$ ; ticks: observed counts. Inlets: best-fit parameters (crosses) and likelihood profiles (contours) at nominal confidence levels 68% (boldface), 90% and 99%. See Sect. 6.3.
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In the text

$\begin{figure} {\includegraphics[width=8cm]{4927fig12.eps} }\end{figure}$ Figure 12: Comparison of the unbinned estimates with results from binned one-temperature XSPEC fits. For kT and $N_{\rm H}$ , the error bars refer to unbinned 68% likelihood projections and XSPEC $\Delta \chi ^2_{\rm N}$ = 1 levels (3 DOF). For L_X, only the best-fit values are indicated.
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In the text

$\begin{figure} \mbox{\includegraphics[width=6.5cm,height=5.4cm,clip]{4927fig13a.... ...\includegraphics[width=6.5cm,height=5.4cm,clip]{4927fig13f.eps} }\end{figure}$ Figure 13: Exploration of the effect of energy band and binning on the HO Tau parameter estimates. Left column: energies from 0.3 to 2 keV; right column: energies from 0.3 to 4 keV. Top row: unbinned likelihood. Middle row: Neyman's chi square with 5 bins. Bottom row: Neyman's chi square with 4 bins. The binned data are marked by dotted line.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm]{4927fig1a.eps}\vspace*{1mm} \par\includegraphics[width=7.5cm]{4927fig1b.eps}\end{figure}$	Figure 1: Top: normalized source models used in this study. An example model (black) and its neighbours (dark gray) are highlighted for better clarity. Inlet: the example model and its neighbours in parameter space $(kT,N_{\rm H})$ . Bottom: normalized background model.
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$\begin{figure} \par\includegraphics[width=7.5cm]{4927fig2.eps}\end{figure}$	Figure 2: Schematic construction of a continuous non-homogeneous Poisson process by the rejection method: out of $N_{\rm p}$ uniform random points in the rectangle $B \times [0,\max (f)]$ only those beneath the curve f(E) are accepted; their abscissae constitute the event list (ticks). The number $N_{\rm p}$ itself is Poisson distributed with expectation value $\vert B\vert \times \max (f)$ .
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$\begin{figure} \par\includegraphics[width=7cm,height=7cm]{4927fig3.eps} \end{figure}$	Figure 3: Receiver-operator characteristics for the binary classification problem with only two models (inlet).
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$\begin{figure} \par\includegraphics[width=8.5cm]{4927fig5.eps} \end{figure}$	Figure 5: Average f-space ( top left) and parameter ( other panels) deviations between true and estimated models. The number m of candidate models delineates the tested volume in parameter space.
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$\begin{figure} \par\includegraphics[width=8.5cm]{4927fig6.eps} \end{figure}$	Figure 6: Average chi-square distance between true and estimated models as a function of the true model parameters (marginal distributions).
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$\begin{figure} {\includegraphics[width=8cm]{4927fig7.eps} }\end{figure}$	Figure 7: Similar to Fig. 5 but with m proportional to the density of candidate models in parameter space.
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$\begin{figure} \par\includegraphics[width=8.2cm]{4927fig8.eps} \end{figure}$	Figure 8: The effect of binning on the performances of ( $C,\chi ^2,\chi ^2_{\rm N}$ ). The corresponding unbinned L values are shown for comparison.
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$\begin{figure} \par\includegraphics[width=8cm]{4927fig9.eps} \end{figure}$	Figure 9: Dependence of the estimation errors on the true expected counts ${\cal N}$ .
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$\begin{figure} { \includegraphics[width=3.9cm]{4927fig10a.eps}\hspace*{3mm} \includegraphics[width=3.9cm]{4927fig10b.eps} }\end{figure}$	Figure 10: Similar to Fig. 4, but including background ( ${\cal N}_{\rm bg}$ = 50).
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$\begin{figure} {\includegraphics[width=7.5cm]{4927fig11.eps} }\end{figure}$	Figure 11: XMM-Newton/EPIC observation of Haro 6-13, comprising 128 counts. Solid line: maximum-L solution $f_{\rm src}(E)$ ; dashed: background spectrum $f_{\rm bkg}(E)$ ; ticks: observed counts. Inlets: best-fit parameters (crosses) and likelihood profiles (contours) at nominal confidence levels 68% (boldface), 90% and 99%. See Sect. 6.3.
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$\begin{figure} {\includegraphics[width=8cm]{4927fig12.eps} }\end{figure}$	Figure 12: Comparison of the unbinned estimates with results from binned one-temperature XSPEC fits. For kT and $N_{\rm H}$ , the error bars refer to unbinned 68% likelihood projections and XSPEC $\Delta \chi ^2_{\rm N}$ = 1 levels (3 DOF). For L_X, only the best-fit values are indicated.
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$\begin{figure} \mbox{\includegraphics[width=6.5cm,height=5.4cm,clip]{4927fig13a.... ...\includegraphics[width=6.5cm,height=5.4cm,clip]{4927fig13f.eps} }\end{figure}$	Figure 13: Exploration of the effect of energy band and binning on the HO Tau parameter estimates. Left column: energies from 0.3 to 2 keV; right column: energies from 0.3 to 4 keV. Top row: unbinned likelihood. Middle row: Neyman's chi square with 5 bins. Bottom row: Neyman's chi square with 4 bins. The binned data are marked by dotted line.
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