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<h1 class="specific"><a href="#session0">BXA Tutorial</a></h1>
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<li><a href="#welcome"><i class="bx bx-star"></i> <span>Welcome</span></a></li>
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<li><a href="./tutorial/setup.html"><i class="icofont-tools-alt-2"></i> <span>Setup</span></a></li>
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<li><a href="./tutorial/session0.html#ex01"><i class="bx bx-chevron-right"></i>0.1 - binning data</a></li>
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<li><a href="./tutorial/session1.html#ex11"><i class="bx bx-chevron-right"></i>1.1 - prior predictive checks</a></li>
<li><a href="./tutorial/session1.html#ex12"><i class="bx bx-chevron-right"></i>1.2 - fitting a model</a></li>
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<li><a href="./tutorial/session1.html#ex14"><i class="bx bx-chevron-right"></i>1.4 - error propagation</a></li>
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<li><a href="./tutorial/session3.html#ex32"><i class="bx bx-chevron-right"></i>3.2 - type I errors</a></li>
<li><a href="./tutorial/session3.html#ex33"><i class="bx bx-chevron-right"></i>3.3 - type II errors</a></li>
<li><a href="./tutorial/session3.html#ex34"><i class="bx bx-chevron-right"></i>3.4 - extension</a></li>
<li><a href="./tutorial/session4.html"><i class="bx bx-bar-chart-alt-2"></i>Session 4 - parent distributions</a></li>
<li><a href="./tutorial/session4.html#ex41"><i class="bx bx-chevron-right"></i>4.1 - generating data</a></li>
<li><a href="./tutorial/session4.html#ex42"><i class="bx bx-chevron-right"></i>4.2 - Gaussian model</a></li>
<li><a href="./tutorial/session4.html#ex43"><i class="bx bx-chevron-right"></i>4.3 - histogram model</a></li>
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<li><a href="./tutorial/session5.html#ex51"><i class="bx bx-chevron-right"></i>5.1 - information gain</a></li>
<li><a href="./tutorial/session5.html#ex52"><i class="bx bx-chevron-right"></i>5.2 - custom priors</a></li>
<li><a href="./tutorial/session5.html#ex53"><i class="bx bx-chevron-right"></i>5.3 - speeding up BXA</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.
</br>
See the <a href="./tutorial/whybxa.html" target="_blank">Why use BXA?</a> page for a few of the many reasons BXA can be useful for X-ray spectral fitting!</p>
<div class="col-lg-16">
<a target="_blank" href="https://en.wikipedia.org/wiki/Bayes%27_theorem"><img src="bxa//bayestheorem.png" class="img-fluid" alt=""></a>
</div>
</br>
For any questions/comments/suggestions concerning the tutorial, please <a href="#contact">get in touch</a>!
</br></br>If you found this tutorial useful, please consider citing Buchner and Boorman (2023): <a target="_blank" href="https://ui.adsabs.harvard.edu/abs/2023arXiv230905705B/abstract">https://ui.adsabs.harvard.edu/abs/2023arXiv230905705B/abstract</a>
(BibTeX: <button class="cpbt" onclick="cx('@ARTICLE{2023arXiv230905705B,\n author = {{Buchner}, Johannes and {Boorman}, Peter},\n title = "{Statistical Aspects of X-ray Spectral Analysis}",\n journal = {arXiv e-prints},\n keywords = {Astrophysics - High Energy Astrophysical Phenomena, Astrophysics - Instrumentation and Methods for Astrophysics},\n year = 2023,\n month = sep,\n eid = {arXiv:2309.05705},\n pages = {arXiv:2309.05705},\n doi = {10.48550/arXiv.2309.05705},\narchivePrefix = {arXiv},\n eprint = {2309.05705},\n primaryClass = {astro-ph.HE},\n adsurl = {https://ui.adsabs.harvard.edu/abs/2023arXiv230905705B},\n adsnote = {Provided by the SAO/NASA Astrophysics Data System}\n}')"><i class="icofont-copy"></i></button>)
</br></br>
Note: this tutorial was updated on 30th January 2023. For the previous version, see <a href="tutorial_bxa_original.html" target="_blank">here</a>.
</div>
</div>
</section>
<!-- End Welcome Section -->
<section id="setup" class="services">
<div class="container">
<div class="section-title">
<a class="titlelink" href="./tutorial/setup.html" style="color: #173b6c;">
<h2><i class="icofont-tools-alt-2"></i> Setup <a class="headerlink" href="#setup" title="Permalink to this headline" style="font-size: 20px;"><i class="icofont-link-alt"></i></a></h2>
</a>
The setup page contains:
<ul>
<li>Information/links for installing PyXspec and/or Sherpa</li>
<li>Step-by-step to install BXA</li>
<li>Download links for the data used in the exercises</li>
</ul>
</div>
</div>
</section>
<section id="session0" class="services">
<div class="container">
<div class="section-title">
<a class="titlelink" href="./tutorial/session0.html" style="color: #173b6c;">
<h2><i class="bx bx-terminal"></i> Session 0 - X-ray spectral fitting <a class="headerlink" href="#session0" title="Permalink to this headline" style="font-size: 20px;"><i class="icofont-link-alt"></i></a></h2>
</a>
This session aims to provide a sufficient background with
<a href="https://heasarc.gsfc.nasa.gov/xanadu/xspec/" target="_blank">Xspec</a>/<a href="https://heasarc.gsfc.nasa.gov/xanadu/xspec/python/html/" target="_blank">PyXspec</a>
and/or <a href="https://cxc.cfa.harvard.edu/sherpa/ahelp/sherpa4.html" target="_blank">Sherpa</a> to complete the remaining BXA tutorial exercises. For a complete and in-depth
understanding of the features available in these software packages, see the <a href="#links">useful links</a> for the excellent online material provided by each team.
</br></br>
Key objectives:
<ul>
<li>Load a spectrum and fit a model to it in Xspec, PyXspec and/or Sherpa</li>
<li>Manually explore a parameter space and avoid local minima</li>
<li>Get to grips with plotting in Xspec, PyXspec and Sherpa</li>
</ul>
</div>
</div>
</section>
<section id="session1" class="services">
<div class="container">
<div class="section-title">
<a class="titlelink" href="./tutorial/session1.html" style="color: #173b6c;">
<h2><i class="bx bx-line-chart"></i> Session 1 - using BXA <a class="headerlink" href="#session1" title="Permalink to this headline" style="font-size: 20px;"><i class="icofont-link-alt"></i></a></h2>
</a>
This session introduces how to construct a BXA fit to spectra in a variety of different setups.
</br></br>
<p>Key objectives:</p>
<ul>
<li>Fit a spectrum with BXA in Sherpa and/or PyXspec</li>
<li>Interact with posteriors</li>
<li>Fit more than one spectrum simultaneously with BXA</li>
</ul>
</div>
</section>
<section id="session2" class="services">
<div class="container">
<div class="section-title">
<a class="titlelink" href="./tutorial/session2.html" style="color: #173b6c;">
<h2><i class="bx bx-check-circle"></i> Session 2 - model checking <a class="headerlink" href="#session2" title="Permalink to this headline" style="font-size: 20px;"><i class="icofont-link-alt"></i></a></h2>
</a>
After fitting a model to the data, how can you check the quality of the fit? This session delves into a variety of ways to examine your fits and check that the model is able to explain the data to a satisfactory level.
</br></br>
Key objectives:
<ul>
<li>Learn how to plot the posterior model with the data</li>
<li>Visualise goodness-of-fit without requiring the data to be re-binned</li>
<li>Compare predicted model counts to observed counts to estimate goodness-of-fit</li>
</ul>
</div>
</section>
<section id="session3" class="services">
<div class="container">
<div class="section-title">
<a class="titlelink" href="./tutorial/session3.html" style="color: #173b6c;">
<h2><i class="bx bx-select-multiple"></i> Session 3 - model comparison <a class="headerlink" href="#session3" title="Permalink to this headline" style="font-size: 20px;"><i class="icofont-link-alt"></i></a></h2>
</a>
Rather than considering models in isolation, how do different models' fits to the same data compare? This sessions considers ways to quantify a model fit relative to others.
</br></br>
Key objectives:
<ul>
<li>Use the Bayesian evidence to perform model comparison</li>
<li>Quantify how often the more complex model selected incorrectly</li>
<li>Quantify how often the simpler model selected incorrectly</li>
</ul>
</div>
</section>
<section id="session4" class="services">
<div class="container">
<div class="section-title">
<a class="titlelink" href="./tutorial/session4.html" style="color: #173b6c;">
<h2><i class="bx bx-bar-chart-alt-2"></i> Session 4 - parent distributions <a class="headerlink" href="#session4" title="Permalink to this headline" style="font-size: 20px;"><i class="icofont-link-alt"></i></a></h2>
</a>
When constraining a parameter for a sample of sources, it can be useful to determine what parent model could have generated the parameter posteriors you have constrained. This session uses Hierarchical Bayesian modelling to do this.
</br></br>
Key objectives:
<ul>
<li>Understand the concept of parent distributions</li>
<li>Combine individual posteriors to constrain a parent distribution</li>
<li>Constrain a variety of parent distribution models for a given set of posteriors</li>
</ul>
</div>
</section>
<section id="session5" class="services">
<div class="container">
<div class="section-title">
<a class="titlelink" href="./tutorial/session5.html" style="color: #173b6c;">
<h2><i class="bx bx-analyse"></i> Session 5 - more advanced concepts <a class="headerlink" href="#session5" title="Permalink to this headline" style="font-size: 20px;"><i class="icofont-link-alt"></i></a></h2>
</a>
What else can you do with BXA? Check out this session to see some other interesting applications.
</br></br>
Key objectives:
<ul>
<li>Quantify the gain in information acquired on a parameter after fitting</li>
<li>Include custom priors in BXA fits</li>
<li>Speed up BXA runtimes with step samplers</li>
</ul>
</div>
</section>
<section id="tipsandtricks" class="services">
<div class="container">
<div class="section-title">
<a class="titlelink" href="./tutorial/tipsandtricks.html" style="color: #173b6c;">
<h2><i class="bx bx-bulb"></i> Tips & tricks <a class="headerlink" href="#tipsandtricks" title="Permalink to this headline" style="font-size: 20px;"><i class="icofont-link-alt"></i></a></h2>
</a>
Interested in some handy features in BXA? Check out this page to see:
<ul>
<li>Fitting 2D models to images</li>
<li>Using a BXA <code>solver</code> object with other fitting packages</li>
<li>Plotting packages for producing corner plots & posterior distributions</li>
<li>Many more!</li>
</div>
</div>
</section>
<section id="links" class="services">
<div class="container">
<div class="section-title">
<a class="titlelink" href="./tutorial/links.html" style="color: #173b6c;">
<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>
Check out this page for a living list of useful resources for astrostatistics and X-ray spectral fitting, including:
<ul>
<li>Documentation</li>
<li>Places to ask questions</li>
<li>Useful papers & documents</li>
<li>Lectures & videos</li>
<li>Scripts</li>
<li>Useful citations</li>
</div>
</div>
</section>
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<a href="./tutorial/links.html"><h4>Previous: Useful links</h4></a>
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<a href="./tutorial/whybxa.html"><h4>Next: Why use BXA?</h4></a>
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<h2><i class="bx bx-envelope"></i> Contact</a> <a class="headerlink" href="#contact" title="Permalink to this headline" style="font-size: 20px;"><i class="icofont-link-alt"></i></a></h2>
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<h4>Raising issues</h4>
<br>
<ul>
<li>BXA: <a href="https://github.com/JohannesBuchner/BXA/issues" target="_blank">github.com/JohannesBuchner/BXA/issues</a></li>
<li>UltraNest: <a href="https://github.com/JohannesBuchner/UltraNest/issues" target="_blank">github.com/JohannesBuchner/UltraNest/issues</a></li>
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<h4>Email</h4>
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<li>Peter Boorman: <a href="mailto:boorman[at]caltech[dot]edu">boorman[at]caltech[dot]edu</a></li>
<li>Johannes Buchner: <a href="mailto:jbuchner[at]mpe[dot]mpg[dot]de">jbuchner[at]mpe[dot]mpg[dot]de</a></li>
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