Talk:Statistical model

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Could this be explained for the layman?

statical modelling

b As we discussed above the problem of main interest for us is to obtain a measure of both the complexityandthe(useful)informationinadataset.Asinthealgorithmictheorythecomplexity istheprimarynotion,whichthenallowsustode¯nethemoreintricatenotionofinformation.Our planistode¯nethecomplexityintermsoftheshortestcodelengthwhenthedataisencodedwith aclassofmodelsascodes.Intheprevioussectionwesawthatthisleadsintothenoncomputability problemifwelettheclassofmodelsincludethesetofallcomputerprograms,a`model'identi¯ed withacomputerprogram(code)thatgeneratesthegivendata.However,ifweselectasmallerclass thenoncomputabilityproblemcanbeavoidedbutwehavetoovercomeanotherdi±culty:Howare wetode¯netheshortestcodelength?ItseemsthatinordernottofallbacktotheKolmogorov complexitywemustspelloutexactlyhowthedistributionsasmodelsaretobeusedtorestrictthe codingoperations.Inuniversalcodingwedidjustthatbydoingthecodinginapredictiveway,in Lempel-Zivcodebytheindexoftheleafinthetreeofthesegmentsdeterminedbythepastdata,and inContextCodingbyapplyinganarithmeticcodetoeach`next'symbol,conditionedonacontext de¯nedbythealgorithmasafunctionofthepastdata.Hereweadoptadi®erentstrategy:we de¯netheideaofshortestcodelengthinaprobabilisticsense,whichturnsouttosatisfypractical requirements.Todothatwemustbemoreformalaboutmodels.

statical modelling

b Aswediscussedabovetheproblemofmaininterestforusistoobtainameasureofboththe complexityandthe(useful)informationinadataset.Asinthealgorithmictheorythecomplexity istheprimarynotion,whichthenallowsustode¯nethemoreintricatenotionofinformation.Our planistode¯nethecomplexityintermsoftheshortestcodelengthwhenthedataisencodedwith aclassofmodelsascodes.Intheprevioussectionwesawthatthisleadsintothenoncomputability problemifwelettheclassofmodelsincludethesetofallcomputerprograms,a`model'identi¯ed withacomputerprogram(code)thatgeneratesthegivendata.However,ifweselectasmallerclass thenoncomputabilityproblemcanbeavoidedbutwehavetoovercomeanotherdi±culty:Howare wetode¯netheshortestcodelength?ItseemsthatinordernottofallbacktotheKolmogorov complexitywemustspelloutexactlyhowthedistributionsasmodelsaretobeusedtorestrictthe codingoperations.Inuniversalcodingwedidjustthatbydoingthecodinginapredictiveway,in Lempel-Zivcodebytheindexoftheleafinthetreeofthesegmentsdeterminedbythepastdata,and inContextCodingbyapplyinganarithmeticcodetoeach`next'symbol,conditionedonacontext de¯nedbythealgorithmasafunctionofthepastdata.Hereweadoptadi®erentstrategy:we de¯netheideaofshortestcodelengthinaprobabilisticsense,whichturnsouttosatisfypractical requirements.Todothatwemustbemoreformalaboutmodels. —Preceding unsigned comment added by 220.227.55.53 (talk) 05:20, 6 March 2010 (UTC)[reply]