{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T22:49:45Z","timestamp":1773442185077,"version":"3.50.1"},"reference-count":17,"publisher":"MIT Press - Journals","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2002,2,1]]},"abstract":"<jats:p> Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model's validity prior to using it to make inferences about a particular neural system. Assessing goodness-of-fit is a challenging problem for point process neural spike train models, especially for histogram-based models such as perstimulus time histograms (PSTH) and rate functions estimated by spike train smoothing. The time-rescaling theorem is a well-known result in probability theory, which states that any point process with an integrable conditional intensity function may be transformed into a Poisson process with unit rate. We describe how the theorem may be used to develop goodness-of-fit tests for both parametric and histogram-based point process models of neural spike trains. We apply these tests in two examples: a comparison of PSTH, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the supplementary eye field of a macque monkey and a comparison of temporal and spatial smoothers, inhomogeneous Poisson, inhomogeneous gamma, and inhomogeneous inverse gaussian models of rat hippocampal place cell spiking activity. To help make the logic behind the time-rescaling theorem more accessible to researchers in neuroscience, we present a proof using only elementary probability theory arguments.We also show how the theorem may be used to simulate a general point process model of a spike train. Our paradigm makes it possible to compare parametric and histogram-based neural spike train models directly. These results suggest that the time-rescaling theorem can be a valuable tool for neural spike train data analysis. <\/jats:p>","DOI":"10.1162\/08997660252741149","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:56:30Z","timestamp":1027770990000},"page":"325-346","source":"Crossref","is-referenced-by-count":437,"title":["The Time-Rescaling Theorem and Its Application to Neural Spike Train Data Analysis"],"prefix":"10.1162","volume":"14","author":[{"given":"Emery N.","family":"Brown","sequence":"first","affiliation":[{"name":"Neuroscience Statistics Research Laboratory, Department of Anesthesia and Critical Care, Massachusetts General Hospital, Boston, MA 02114, U.S.A., and Division of Health Sciences and Technology, Harvard Medical School = Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Riccardo","family":"Barbieri","sequence":"additional","affiliation":[{"name":"Neuroscience Statistics Research Laboratory, Department of Anesthesia and Critical Care, Massachusetts General Hospital, Boston, MA 02114, U.S.A.,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Val\u00e9rie","family":"Ventura","sequence":"additional","affiliation":[{"name":"Department of Statistics, Carnegie Mellon University, Center for the Neural Basis of Cognition, Pittsburg, PA 15213, U.S.A."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert E.","family":"Kass","sequence":"additional","affiliation":[{"name":"Department of Statistics, Carnegie Mellon University, Center for the Neural Basis of Cognition, Pittsburg, PA 15213, U.S.A."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Loren M.","family":"Frank","sequence":"additional","affiliation":[{"name":"Neuroscience Statistics Research Laboratory, Department of Anesthesia and Critical Care, Massachusetts General Hospital, Boston, MA 02114, U.S.A."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-2312(01)00450-7"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0270(00)00344-7"},{"key":"p_3","first-page":"412","volume":"50","author":"Berman M.","year":"1983","journal-title":"Bulletin Internatl. 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