{"id":22807,"date":"2023-03-06T09:31:05","date_gmt":"2023-03-06T14:31:05","guid":{"rendered":"https:\/\/carleton.ca\/math\/?p=22807"},"modified":"2023-03-06T09:32:32","modified_gmt":"2023-03-06T14:32:32","slug":"probability-statistics-seminar-virtual","status":"publish","type":"post","link":"https:\/\/carleton.ca\/math\/2023\/probability-statistics-seminar-virtual\/","title":{"rendered":"Probability & Statistics Seminar (Virtual)"},"content":{"rendered":"

Title: Investigating the Relationship Between the Bayes Factor and the Separation of Credible Intervals.
\nSpeaker: Farouk Nathoo, University of Victoria (https:\/\/www.math.uvic.ca\/~nathoo\/<\/a>
\nLocation: via zoom (https:\/\/carleton-ca.zoom.us\/j\/97371740556<\/a>)
\nDate: Friday, March 17, 2023
\nTime: 1:00 \u2013 2:00 pm<\/p>\n

Abstract:\u00a0 <\/strong>The relationship between confidence intervals and null hypothesis significance testing is well known and is a topic taught in introductory\u00a0statistics. In contrast, within the Bayesian paradigm, the relationship between the Bayes factor and credible intervals is not well known.\u00a0We examined the relationship between the Bayes factor and the separation of credible intervals in between- and within-subject designs\u00a0under a range of effect and sample sizes. For the within-subject case, we considered five intervals: (1) the within-subject confidence\u00a0interval of Loftus and Masson (1994), (2) the within-subject Bayesian interval developed by Nathoo, Kilshaw, and Masson (2018), whose\u00a0derivation conditions on estimated random effects, (3) and (4) two modifications of (2) based on a proposal by Heck (2019) to allow for\u00a0shrinkage and account for uncertainty in the estimation of random effects, and (5) the standard Bayesian highest-density interval. We\u00a0derived and observed through simulations a clear and consistent relationship between the Bayes factor and the separation of credible\u00a0intervals. Remarkably, this relationship, for a given sample size, is well described by a simple quadratic exponential curve and is most\u00a0precise in case (4). This observation is formalized through a limiting theorem for the case of between-subject designs with two conditions.<\/p>\n","protected":false},"excerpt":{"rendered":"

Title: Investigating the Relationship Between the Bayes Factor and the Separation of Credible Intervals. Speaker: Farouk Nathoo, University of Victoria (https:\/\/www.math.uvic.ca\/~nathoo\/ Location: via zoom (https:\/\/carleton-ca.zoom.us\/j\/97371740556) Date: Friday, March 17, 2023 Time: 1:00 \u2013 2:00 pm Abstract:\u00a0 The relationship between confidence intervals and null hypothesis significance testing is well known and is a topic taught in […]<\/p>\n","protected":false},"author":44,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":"","_mi_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":"","_links_to":"","_links_to_target":""},"categories":[1,3],"tags":[],"yoast_head":"\nProbability & Statistics Seminar (Virtual) - School of Mathematics and Statistics<\/title>\n<meta name=\"description\" content=\"Title: Investigating the Relationship Between the Bayes Factor and the Separation of Credible Intervals. 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