{"id":342935,"date":"2023-06-01T16:23:10","date_gmt":"2023-06-01T22:23:10","guid":{"rendered":"http:\/\/xianblog.wordpress.com\/?p=53139"},"modified":"2023-06-01T16:23:10","modified_gmt":"2023-06-01T22:23:10","slug":"galton-and-watson-voluntarily-skipping-some-generations","status":"publish","type":"post","link":"https:\/\/www.r-bloggers.com\/2023\/06\/galton-and-watson-voluntarily-skipping-some-generations\/","title":{"rendered":"Galton and Watson voluntarily skipping some generations"},"content":{"rendered":"\r\n\r\n
\r\n[This article was first published on R \u2013 Xi'an's Og<\/a><\/strong>, and kindly contributed to R-bloggers<\/a>]. (You can report issue about the content on this page here<\/a>)\r\n
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\"\"A<\/strong> riddle<\/a> on a form of a Galton-Watson process, starting from a single unit, where no one dies but rather, at each of 100 generations, Dog either opts for a Uniform number \u03c5 of additional units or increments a counter \u03b3 by this number \u03c5, its goal being to optimise \u03b3. The solution proposed by the Riddler<\/a> does not establish his solution\u2019s is the optimal strategy and considers anyway average<\/em> gains. Solution that consists in always producing more units until the antepenultimate hour (ie incrementing only at the 99th and 100th generations),\u00a0 I tried instead various logical (?) rules and compared outputs by bRute foRce<\/a>, resulting in higher maxima (over numerous repeated calls) for the alternative principle<\/p>\n

s<-function(p=.66){ \r\n   G=0;K=1 for(t in 1:9){ \r\n      i=sample(1:K,1) \r\n      K=K+i*(i>=K*p)\r\n      G=G+i*(i<K*p)}\r\n  return(c(G+sample(1:K,1),K))}<\/pre>\n\n\n
\r\n
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A riddle on a form of a Galton-Watson process, starting from a single unit, where no one dies but rather, at each of 100 generations, Dog either opts for a Uniform number \u03c5 of additional units or increments a counter \u03b3 by this number \u03c5, its goal being to optimise \u03b3. The solution proposed by [\u2026]<\/p>\n","protected":false},"author":56,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[4],"tags":[],"aioseo_notices":[],"jetpack-related-posts":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/posts\/342935"}],"collection":[{"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/comments?post=342935"}],"version-history":[{"count":22,"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/posts\/342935\/revisions"}],"predecessor-version":[{"id":381421,"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/posts\/342935\/revisions\/381421"}],"wp:attachment":[{"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/media?parent=342935"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/categories?post=342935"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/tags?post=342935"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}