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For\nexample, nucleotides in a DNA sequence, children's names in a given state and\nyear, and text documents are all commonly modeled with multinomial\ndistributions. In all of these cases, we expect some form of dependency between\nthe draws: the nucleotide at one position in the DNA strand may depend on the\npreceding nucleotides, children's names are highly correlated from year to\nyear, and topics in text may be correlated and dynamic. These dependencies are\nnot naturally captured by the typical Dirichlet-multinomial formulation. Here,\nwe leverage a logistic stick-breaking representation and recent innovations in\nP\\'olya-gamma augmentation to reformulate the multinomial distribution in terms\nof latent variables with jointly Gaussian likelihoods, enabling us to take\nadvantage of a host of Bayesian inference techniques for Gaussian models with\nminimal overhead.","url_abs":"http://arxiv.org/abs/1506.05843v1","url_pdf":"http://arxiv.org/pdf/1506.05843v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"dependent-multinomial-models-made-easy-stick","repo_url":"https://github.com/HIPS/pgmult","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":null,"task_name":"Position"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1506.05843","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1506.05843"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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