{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/explicit-moments-of-decision-times-for-single","title":"Explicit moments of decision times for single- and double-threshold drift-diffusion processes","arxiv_id":"1601.06420","date":"2016-01-24","proceeding":null,"authors":[],"abstract":"We derive expressions for the first three moments of the decision time (DT)\ndistribution produced via first threshold crossings by sample paths of a\ndrift-diffusion equation. The \"pure\" and \"extended\" diffusion processes are\nwidely used to model two-alternative forced choice decisions, and, while simple\nformulae for accuracy, mean DT and coefficient of variation are readily\navailable, third and higher moments and conditioned moments are not generally\navailable. We provide explicit formulae for these, describe their behaviors as\ndrift rates and starting points approach interesting limits, and, with the\nsupport of numerical simulations, discuss how trial-to-trial variability of\ndrift rates, starting points, and non-decision times affect these behaviors in\nthe extended diffusion model. Both unconditioned moments and those conditioned\non correct and erroneous responses are treated. We argue that the results will\nassist in exploring mechanisms of evidence accumulation and in fitting\nparameters to experimental data.","url_abs":"http://arxiv.org/abs/1601.06420v1","url_pdf":"http://arxiv.org/pdf/1601.06420v1.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":"explicit-moments-of-decision-times-for-single","repo_url":"https://github.com/PrincetonUniversity/higher_moments_ddm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}