{"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/analyzing-dynamic-decision-making-models","title":"Analyzing dynamic decision-making models using Chapman-Kolmogorov equations","arxiv_id":"1903.10131","date":"2019-03-25","proceeding":null,"authors":[],"abstract":"Decision-making in dynamic environments typically requires adaptive evidence\naccumulation that weights new evidence more heavily than old observations.\nRecent experimental studies of dynamic decision tasks require subjects to make\ndecisions for which the correct choice switches stochastically throughout a\nsingle trial. In such cases, an ideal observer's belief is described by an\nevolution equation that is doubly stochastic, reflecting stochasticity in the\nboth observations and environmental changes. In these contexts, we show that\nthe probability density of the belief can be represented using differential\nChapman-Kolmogorov equations, allowing efficient computation of ensemble\nstatistics. This allows us to reliably compare normative models to\nnear-normative approximations using, as model performance metrics, decision\nresponse accuracy and Kullback-Leibler divergence of the belief distributions.\nSuch belief distributions could be obtained empirically from subjects by asking\nthem to report their decision confidence. We also study how response accuracy\nis affected by additional internal noise, showing optimality requires longer\nintegration timescales as more noise is added. Lastly, we demonstrate that our\nmethod can be applied to tasks in which evidence arrives in a discrete,\npulsatile fashion, rather than continuously.","url_abs":"http://arxiv.org/abs/1903.10131v1","url_pdf":"http://arxiv.org/pdf/1903.10131v1.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":"analyzing-dynamic-decision-making-models","repo_url":"https://github.com/nwbarendregt/DynamicDecisionCKEquations","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"decision-making","task_name":"Decision Making"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}