Detecting Periodicity in Sparse Discrete Event Data

##### Description
<span></span><p dir="ltr"><span><b>The Problem</b></span></p><p dir="ltr"><span>We are interested in analyzing arrival time data. Most signal analysis is based on evenly-spaced discrete signals or continuous signals with discrete, evenly spaced samples. In some cases, arrivals are frequent enough relative to the time period under consideration that we can just bin them are use techniques from the previous scenarios. However, binning is somewhat arbitrary in many cases and can discard important information. This is especially true when arrivals are sparse within the considered time period. However, there are techniques for dealing with this and they can be found in astronomy literature. See </span><a href="http://www.astrobetter.com/wiki/tiki-index.php?page=Periodicity+Analysis"><span>http://www.astrobetter.com/wiki/tiki-index.php?page=Periodicity+Analysis</span></a><span>, particularly the section entitled &#8220;very sparsely sampled data in the form of discrete events.&#8221;</span></p><p dir="ltr"><span><b>The Interface</b></span></p><p dir="ltr"><span>Since we are dealing with sparse discrete arrival times, it probably makes most sense to take a long[] as input, where each entry is an arrival time (possibly denoting milliseconds from epoch). Your algorithm should output any detected periodicity information, preferably with associated uncertainties if you can get them.</span></p><p dir="ltr"><span><b>The Algorithm</b></span></p><span>We don&#8217;t know of any publicly available implementations, so you&#8217;ll probably have to go off of the papers linked to in the blog post above. For more general context, read </span><a href="http://www.phas.ubc.ca/~gregory/papers/bayesrevol.pdf"><span>http://www.phas.ubc.ca/~gregory/papers/bayesrevol.pdf</span></a><span> and the relevant references.</span>
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• Gregory-Loredo Algorithm

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Computes the Gregory-Loredo algorithm on a list of arrival times This function computes the likelihood of a set of arrival times originating from a periodic process rather than con...

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