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I'm a statistician, and am interested in applying the theory of algebraic Markov models to genomics. Here's one paper I'm interested in: Large-scale genome-wide association analysis of bipolar disorder identifies a new susceptibility locus near ODZ4. I'm also interested in other diseases (i.e. not just bipolar).

Are there any genomics databases that I can access publicly?

There are some links in Human Connectome Project, but I'm not sure if these are genomics databases (or which papers have used their research).

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    $\begingroup$ You're going to struggle to find public databases with genotype data for individuals because of concerns about de-identification. You can request access to the server where the data from that paper is stored here. If it's possible to run your analyses on summary statistics, these can usually be downloaded without restrictions. $\endgroup$ Jun 15 '18 at 14:41
  • $\begingroup$ Could you clarify what kind of data you need? "genomics databases" is a very broad term and most of what I would call genomics data is publicly available. It would be helpful if you could edit your question and explain exactly what sort of dataset you would want to work on. $\endgroup$
    – terdon
    Jun 16 '18 at 12:32
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Most genomics data that is published should be available in GEO (or SRA). Usually in the paper they mention the accession number. However, not every study ends up in there, and sometime studies that are in GEO are not reproducible (poor description of the samples, or design). But if you look at the original papers, most of the times you'll find an accession number.

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Another places you could look for SNP data would be 1000 genomes, the ExACT database and the genomAD database. Cancer specific data is available at the GDC and ICGC data portal.

Unfortunately a lot of what you'd like to work with is probably covered by restricted access due to privacy concerns. Lots of this data is stored in the dbGap database and the EGA. If you are an academic or employed by a company with a legitimate interest in the data you can usually apply for access to the restricted data, and I've never known anyone to be turned down if you have a legitimate reaons to access the data and can demonstrate your computer systems meet the required security standards.

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Yet another place I find useful is provided by Repositive. You can think of it as a meta-search engine which includes most of the databases already stated and links hits to relevant papers.

With respect to your question about bipolar, this search could get you started.

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