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<!DOCTYPE html>
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<a href="https://www.nustar.caltech.edu/image/nustar151217c" target="_blank"><img src="figures/nustar_torus.jpg" alt="" class="img-fluid rounded-circle"></img></a>
<p></p>
<h1 class="specific"><a href="#welcome">X-ray torus models</a></h1>
<div class="social-links mt-3 text-center">
<a href="#contact"><i class="bx bx-envelope"></i></a>
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<li><a href="#welcome"><i class="bx bx-star"></i> <span>Welcome</span></a></li>
<li><a href="#links"><i class="bx bx-bookmarks"></i> <span>Useful links</span></a></li>
<li><a href="#phenom"><i class="icofont-gear"></i> <span>Phenomenological models</span></a></li>
<li><a href="#pexrav"><i class="bx bx-chevron-right"></i>pexrav</a></li>
<li><a href="#pexmon"><i class="bx bx-chevron-right"></i>pexmon</a></li>
<li><a href="#physical"><i class="icofont-gear"></i> <span>Physical models</span></a></li>
<li><a href="#spheres"><i class="bx bx-chevron-right"></i>Spheres</a></li>
<li><a href="#etorus"><i class="bx bx-chevron-right"></i>etorus</a></li>
<li><a href="#borus02"><i class="bx bx-chevron-right"></i>borus02</a></li>
<li><a href="#mytorus"><i class="bx bx-chevron-right"></i>MYtorus</a></li>
<li><a href="#rxtorus"><i class="bx bx-chevron-right"></i>RXtorus</a></li>
<li><a href="#ctorus"><i class="bx bx-chevron-right"></i>Ctorus</a></li>
<li><a href="#xclumpy"><i class="bx bx-chevron-right"></i>XClumpy</a></li>
<li><a href="#uxclumpy"><i class="bx bx-chevron-right"></i>UXCLUMPY</a></li>
<li><a href="#warpeddisk"><i class="bx bx-chevron-right"></i>warpeddisk</a></li>
<li><a href="#others"><i class="bx bx-chevron-right"></i>other</a></li>
<li><a href="#contact"><i class="icofont-letter"></i>Contact</a></li>
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<h1><i class="bx bx-star"></i> <span class="typed" data-typed-items="Hello!, Dobrý den!, Kon'nichiwa!, Hallo!, Ciao!, Hola!, Mholweni!, Sawubona!, Marhaba!, Nǐ hǎo!, God dag!, Bonjour!, Shalom!, Namaste!, Zdravstvuyte!, Zdravo!, Ahoj!, Hallå!, Annyeonghaseyo!, Tena jistilign!, Moni!, Salama alaikum!, Ndêwó, Muraho!, Mbote!, Ki kati!, Malagasy!, Miarahaba!, Salibonani!, Dumêlang!, Ashamaa!, Dumela!, Mhoro!, Jambo!, Sawubona!, Selam!, Avuxeni!, Dumela!, Salaam aleekum, Molo!, Bawo!, Barev dzez!, Salam!, Assalamualaikum!, Nômoshkar!, Mingalarba!, Chum reap suor!, Néih hóu!, Kuzu-zangpo!, Gamarjoba!, Halo!, Salamatsyzby!, Sabaidee!, Namaskaram!, Sain baina uu!, Salaam!, Sat sri akal ji!, Āyubōvan!, Lí-hó!, Vaṇakkam!, Isänmesez!, Namaskārām!, Sà-wàt-dee!, Tashi delek!, Āssālam ‘alaykum!, Ässalamu läykum!, Assalomu aleykum!, Xin chào!, Tungjatjeta!, Kaixo!, Vitaju!, Demat!, Dobar dan!, Bok!, Tere!, Hyvää päivää!, Goeie!, Dia duit!, Halò!, Guten tag!, Yasass!, Szervusz!, Góðan dag!, Buon giorno!, Sveika!, Labas!, Moïen!, Dzień dobry!, Salut!, Živjo!, Dobriy den!, Helo!, A gutn tog!, As-salām ‘alaykum!, Merheba!, Merhaba!, Ni sa bula!, Aloha!, Tēnā koe!, Yokwe!, Alii!, Tālofa!, Ia ora na!, Gude!, Mālō e lelei!"></span></h1>
<h3>Welcome to the <a target="_blank" href="https://github.com/JohannesBuchner/BXA">Bayesian X-ray Analysis (BXA)</a> tutorial page.</h3>
</br>
<p>BXA connects <a target="_blank" href="https://heasarc.gsfc.nasa.gov/xanadu/xspec/python/html/index.html">PyXspec</a>/<a target="_blank" href="https://cxc.cfa.harvard.edu/sherpa/">Sherpa</a> to <a target="_blank" href="https://johannesbuchner.github.io/UltraNest/method.html">nested sampling algorithms</a> for Bayesian parameter estimation and model comparison with the Bayesian evidence.</p>
</br>
If you have any questions/comments/suggestions concerning the tutorial, please <a href="#contact">get in touch</a>!
</div>
</div>
</section>
<!-- End Welcome Section -->
<section id="links" class="services">
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<h2><i class="bx bx-bookmarks"></i> Useful links <a class="headerlink" href="#links" title="Permalink to this headline" style="font-size: 20px;"><i class="icofont-link-alt"></i></a></h2>
</a>
<div class="collapse show" id="collapse-links">
<h4>Documentation</h4>
<ul>
<li>Xspec & PyXspec documentation:<br/><a target="_blank" href="https://heasarc.gsfc.nasa.gov/xanadu/xspec/">https://heasarc.gsfc.nasa.gov/xanadu/xspec/</a>
</li>
<li>Sherpa reference for commands:<br/><a target="_blank" href="https://cxc.cfa.harvard.edu/sherpa/ahelp/sherpa4.html">https://cxc.cfa.harvard.edu/sherpa/ahelp/sherpa4.html</a>
</li>
<li>UltraNest documentation:<br><a target="_blank" href="https://johannesbuchner.github.io/UltraNest/readme.html">https://johannesbuchner.github.io/UltraNest/readme.html</a>
</li>
<li>BXA documentation:</br>
<a href="https://johannesbuchner.github.io/BXA/index.html" target="_blank">https://johannesbuchner.github.io/BXA/index.html</a>
</li>
</ul>
<h4>Places to ask questions</h4>
<ul>
<li>Xspec Facebook group:<br/><a target="_blank" href="https://www.facebook.com/groups/320119452570/?ref=share">https://www.facebook.com/groups/320119452570/?ref=share</a>
</li>
<li>Astrostatistics Facebook group:<br/><a target="_blank" href="https://www.facebook.com/groups/astro.r/?ref=share">https://www.facebook.com/groups/astro.r/?ref=share</a>
</li>
<li><a href="#contact">Email</a>!</li>
</ul>
<h4>Useful papers & documents</h4>
<ul>
<li>X-ray Data Primer by CXC:<br/><a target="_blank" href="https://cxc.cfa.harvard.edu/cdo/xray_primer.pdf">https://cxc.cfa.harvard.edu/cdo/xray_primer.pdf</a>
</li>
<li>Information on C-statistics (& modified C-statistics, aka W-stat) used in Xspec & Sherpa by Giacomo Vianello:<br/><a target="_blank" href="https://giacomov.github.io/Bias-in-profile-poisson-likelihood/">https://giacomov.github.io/Bias-in-profile-poisson-likelihood/</a>
</li>
<li>Nested sampling review - Buchner (2021)<br><a target="_blank" href="https://arxiv.org/abs/2101.09675">https://arxiv.org/abs/2101.09675</a>
</li>
<li>PCA background - Simmonds et al., (2018, A&A)<br><a target="_blank" href="https://ui.adsabs.harvard.edu/abs/2018A%26A...618A..66S/abstract">https://ui.adsabs.harvard.edu/abs/2018A%26A...618A..66S/abstract</a>
</li>
<li>Simulation-based calibration of false-positive & false-negative rates - Baronchelli et al., (2018, MNRAS)<br><a target="_blank" href="https://ui.adsabs.harvard.edu/abs/2018MNRAS.480.2377B/abstract">https://ui.adsabs.harvard.edu/abs/2018MNRAS.480.2377B/abstract</a>
</li>
<li>Bayesian Hierarchical Modelling with BXA:
<ul>
<li>Baronchelli et al., (2020, MNRAS), Section A1<br><a target="_blank" href="https://ui.adsabs.harvard.edu/abs/2020MNRAS.498.5284B/abstract">https://ui.adsabs.harvard.edu/abs/2020MNRAS.498.5284B/abstract</a></li>
<li>Kuraszkiewicz et al., (2021, ApJ), Section A1<br><a target="_blank" href="https://ui.adsabs.harvard.edu/abs/2021ApJ...913..134K/abstract">https://ui.adsabs.harvard.edu/abs/2021ApJ...913..134K/abstract</a></li>
<li>Liu et al., (2021, arXiv), Section 3.7<br><a target="_blank" href="https://ui.adsabs.harvard.edu/abs/2021arXiv210614522L/abstract">https://ui.adsabs.harvard.edu/abs/2021arXiv210614522L/abstract</a></li>
</ul>
</li>
</ul>
<h4>Lectures & videos</h4>
<ul>
<li>BiD4BEST Bayesian X-ray Spectral Analysis lectures by Johannes Buchner:<br/>
<ol>
<li><a target="_blank" href="https://youtu.be/_r4ecpje7nE">https://youtu.be/_r4ecpje7nE</a></li>
<li><a href="https://youtu.be/EIzhDG-0Ji8">https://youtu.be/EIzhDG-0Ji8</a></li>
</ol>
</li>
<li>Graduate-level course: <i>Monte Carlo inference methods</i> by Johannes Buchner:</br>
<ol>
<li><i>Bayesian inference workflow in astronomy and physics</i>:</br>
<a href="https://youtu.be/D2P6xBR_2bQ" target="_blank">https://youtu.be/D2P6xBR_2bQ</a></li>
<li><i>Bayesian model comparison, curse of dimensionality, Importance Sampling</i>:</br>
<a href="https://youtu.be/TfaGfFnsmW8" target="_blank">https://youtu.be/TfaGfFnsmW8</a></li>
<li><i>Markov Chain Monte Carlo (MCMC) and diagnostics</i>:</br>
<a href="https://youtu.be/YA6Ezh8CsrY" target="_blank">https://youtu.be/YA6Ezh8CsrY</a></li>
<li><i>Hamiltonian Monte Carlo (HMC) by Dr. Francesca Capel</i>:</br>
<a href="https://youtu.be/nmHGyXsiaeI" target="_blank">https://youtu.be/nmHGyXsiaeI</a></li>
<li><i>Nested Sampling from scratch - Practical Inference for Researchers in the Physical Sciences</i>:</br>
<a href="https://youtu.be/baLFl_4ZwXw" target="_blank">https://youtu.be/baLFl_4ZwXw</a></li>
<li><i>State-of-the art in nested sampling and MCMC: literature review</i>:</br>
<a href="https://youtu.be/HFaqcB_H6MA" target="_blank">https://youtu.be/HFaqcB_H6MA</a></li>
</ol>
</li>
<li> BXA Tutorial at <a href="https://cxc.harvard.edu/cdo/cds2021/schedule.html" target="_blank">Chandra Data Science 2021</a> by Peter Boorman & Johannes Buchner:</br>
<ul>
<li><a href="https://youtu.be/c1pMDhKFAWA" target="_blank">https://youtu.be/c1pMDhKFAWA</a></li>
</ul>
</li>
<li>Interactive visualisation of the nested sampling algorithm in UltraNest:<br>
<a href="https://johannesbuchner.github.io/UltraNest/method.html?highlight=demo#visualisation" target="_blank">https://johannesbuchner.github.io/UltraNest/method.html?highlight=demo#visualisation</a>
</li>
</ul>
<h4>Scripts</h4>
<ul>
<li>Sherpa script for fitting obscured AGN with BXA:<br/><a target="_blank" href="https://github.com/JohannesBuchner/BXA/blob/master/examples/sherpa/xagnfitter.py">https://github.com/JohannesBuchner/BXA/blob/master/examples/sherpa/xagnfitter.py</a>
</li>
<li>PosteriorStacker (for deriving sample distributions from individual source posterior distributions)<br><a target="_blank" href="https://github.com/JohannesBuchner/PosteriorStacker">https://github.com/JohannesBuchner/PosteriorStacker</a>
</li>
<li>example_advanced_priors.py (shows how to include custom priors in BXA)<br><a target="_blank" href="https://github.com/JohannesBuchner/BXA/blob/master/examples/xspec/example_advanced_priors.py">https://github.com/JohannesBuchner/BXA/blob/master/examples/xspec/example_advanced_priors.py</a>
</li>
</ul>
<h4>Citations</h4>
<ul>
<li>Xspec (& PyXspec) citation - Arnaud et al., (1996; ASPC):<br><a target="_blank" href="https://ui.adsabs.harvard.edu/abs/1996ASPC..101...17A/abstract">https://ui.adsabs.harvard.edu/abs/1996ASPC..101...17A/abstract</a>
</li>
<li>Sherpa citation - Freeman et al., (2001; SPIE):<br><a target="_blank" href="https://ui.adsabs.harvard.edu/abs/2001SPIE.4477...76F/abstract">https://ui.adsabs.harvard.edu/abs/2001SPIE.4477...76F/abstract</a></br>
In CIAO 4.13, you can use this command to get information on the latest release:</br>
<code>sherpa> sherpa.citation('latest')</code> <button class="cpbt" onclick="cx('sherpa.citation(\'latest\')')"><i class="icofont-copy"></i></button>
</li>
<li>BXA citation - Buchner et al., (2014; A&A)<br><a target="_blank" href="https://ui.adsabs.harvard.edu/abs/2014A%26A...564A.125B/abstract">https://ui.adsabs.harvard.edu/abs/2014A%26A...564A.125B/abstract</a>
</li>
<li>UltraNest citation - Buchner (2021, JOSS)<br><a target="_blank" href="https://arxiv.org/abs/2101.09604">https://arxiv.org/abs/2101.09604</a>
</li>
</ul>
<li><b>Do you know of any others?</b> Please <a href="#contact">get in touch</a>!
</li>
</div>
</div>
</section>
<section id="phenom" class="services">
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<a class="collapselink" data-toggle="collapse" href="#collapse-phenom" aria-expanded="true" aria-controls="collapse-phenom" style="color: #173b6c;">
<h2><i class="icofont-gear"></i> Phenomenological models <a class="headerlink" href="#phenom" title="Permalink to this headline" style="font-size: 20px;"><i class="icofont-link-alt"></i></a></h2>
</a>
</div>
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<h3><i class="bx bx-chevron-right"></i> <code>pexrav</code> <a class="headerlink" href="#pexrav" title="Permalink to this headline" style="font-size: 20px;"><i class="icofont-link-alt"></i></a></h3>
</a>
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<div class="collapse show" id="collapse-pexrav">
<code><pre>
model constant*TBabs(zTBabs*cabs*cutoffpl + pexrav + constant*cutoffpl + zgauss)
Input parameter value, delta, min, bot, top, and max values for ...
1 0.01( 0.01) 0 0 1e+10 1e+10
1:constant:factor>
1 0.001( 0.01) 0 0 100000 1e+06
2:TBabs:nH>
1 0.001( 0.01) 0 0 100000 1e+06
3:zTBabs:nH>
0 -0.01( 0.01) -0.999 -0.999 10 10
4:zTBabs:Redshift>
1 0.001( 0.01) 0 0 100000 1e+06
5:cabs:nH>
1 0.01( 0.01) -3 -2 9 10
6:cutoffpl:PhoIndex>
15 0.01( 0.15) 0.01 1 500 500
7:cutoffpl:HighECut>
1 0.01( 0.01) 0 0 1e+20 1e+24
8:cutoffpl:norm>
2 0.01( 0.02) -10 -9 9 10
9:pexrav:PhoIndex>
100 10( 1) 1 1 1e+06 1e+06
10:pexrav:foldE>
0 0.01( 0.01) 0 0 1e+06 1e+06
11:pexrav:rel_refl>
0 -0.01( 0.01) -0.999 -0.999 10 10
12:pexrav:Redshift>
1 -0.01( 0.01) 0 0 1e+06 1e+06
13:pexrav:abund>
1 -0.01( 0.01) 0 0 1e+06 1e+06
14:pexrav:Fe_abund>
0.45 -0.01( 0.0045) 0.05 0.05 0.95 0.95
15:pexrav:cosIncl>
1 0.01( 0.01) 0 0 1e+20 1e+24
16:pexrav:norm>
1 0.01( 0.01) 0 0 1e+10 1e+10
17:constant:factor>
1 0.01( 0.01) -3 -2 9 10
18:cutoffpl:PhoIndex>
15 0.01( 0.15) 0.01 1 500 500
19:cutoffpl:HighECut>
1 0.01( 0.01) 0 0 1e+20 1e+24
20:cutoffpl:norm>
6.5 0.05( 0.065) 0 0 1e+06 1e+06
21:zgauss:LineE>
0.1 0.05( 0.001) 0 0 10 20
22:zgauss:Sigma>
0 -0.01( 0.01) -0.999 -0.999 10 10
23:zgauss:Redshift>
1 0.01( 0.01) 0 0 1e+20 1e+24
24:zgauss:norm>
</pre></code>
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