{"id":426,"date":"2020-01-28T17:49:27","date_gmt":"2020-01-28T17:49:27","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=426"},"modified":"2020-01-28T17:49:27","modified_gmt":"2020-01-28T17:49:27","slug":"the-elvis-problem-revisited","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2020\/01\/28\/the-elvis-problem-revisited\/","title":{"rendered":"The Elvis problem revisited"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Here&#8217;s a problem from <a href=\"https:\/\/amzn.to\/3aPoNjQ\">Bayesian Data Analysis<\/a>:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>Elvis Presley had a twin brother (who died at birth). What is the probability that Elvis was an identical twin?<\/p><\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">I will answer this question in three steps:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>First, we need some background information about the relative frequencies of identical and fraternal twins.<\/li><li>Then we will use Bayes&#8217;s Theorem to take into account one piece of data, which is that Elvis&#8217;s twin was male.<\/li><li>Finally, living up to the name of this blog, I will overthink the problem by taking into account a second piece of data, which is that Elvis&#8217;s twin died at birth.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">For background information, I&#8217;ll use data from 1935, the year Elvis was born, from the U.S. Census Bureau, <a href=\"https:\/\/www.cdc.gov\/nchs\/data\/vsushistorical\/birthstat_1935.pdf\">Birth, Stillbirth, and Infant Mortality Statistics for the Continental United States, the Territory of Hawaii, the Virgin Islands 1935<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">It includes this table:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"593\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/01\/birth_data_1935.png\" alt=\"\" class=\"wp-image-427\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/01\/birth_data_1935.png 600w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/01\/birth_data_1935-300x297.png 300w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/01\/birth_data_1935-273x270.png 273w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">With a few reasonable assumptions, we can use this data to compute the probability that Elvis was an identical twin, given that his twin brother died at birth.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/colab.research.google.com\/github\/AllenDowney\/BiteSizeBayes\/blob\/master\/elvis.ipynb\">You can see my solution in this Jupyter notebook.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here&#8217;s a problem from Bayesian Data Analysis: Elvis Presley had a twin brother (who died at birth). What is the probability that Elvis was an identical twin? I will answer this question in three steps: First, we need some background information about the relative frequencies of identical and fraternal twins. Then we will use Bayes&#8217;s Theorem to take into account one piece of data, which is that Elvis&#8217;s twin was male. Finally, living up to the name of this blog,&#8230;<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/www.allendowney.com\/blog\/2020\/01\/28\/the-elvis-problem-revisited\/\"> Read More<span class=\"screen-reader-text\">  Read More<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_hide_featured_image":false,"_jetpack_featured_image_duplicate_dismissed":0,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[1],"tags":[64],"class_list":["post-426","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-elvis"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The Elvis problem revisited - Probably Overthinking It<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.allendowney.com\/blog\/2020\/01\/28\/the-elvis-problem-revisited\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Elvis problem revisited - Probably Overthinking It\" \/>\n<meta property=\"og:description\" content=\"Here&#8217;s a problem from Bayesian Data Analysis: Elvis Presley had a twin brother (who died at birth). What is the probability that Elvis was an identical twin? I will answer this question in three steps: First, we need some background information about the relative frequencies of identical and fraternal twins. Then we will use Bayes&#8217;s Theorem to take into account one piece of data, which is that Elvis&#8217;s twin was male. Finally, living up to the name of this blog,... Read More Read More\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.allendowney.com\/blog\/2020\/01\/28\/the-elvis-problem-revisited\/\" \/>\n<meta property=\"og:site_name\" content=\"Probably Overthinking It\" \/>\n<meta property=\"article:published_time\" content=\"2020-01-28T17:49:27+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/01\/birth_data_1935.png\" \/>\n<meta name=\"author\" content=\"Allen B. Downey\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@AllenDowney\" \/>\n<meta name=\"twitter:site\" content=\"@AllenDowney\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Allen B. Downey\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2020\\\/01\\\/28\\\/the-elvis-problem-revisited\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2020\\\/01\\\/28\\\/the-elvis-problem-revisited\\\/\"},\"author\":{\"name\":\"Allen B. 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