Model selection and model averaging
上传者:丁国强|上传时间:2015-05-05|密次下载
Model selection and model averaging
Cambridge University Press
978-0-521-85225-8 - Model Selection and Model Averaging
Gerda Claeskens and Nils Lid Hjort
ExcerptMore information
1
Modelselection:dataexamplesandintroduction
Thisbookisaboutmakingchoices.Ifthereareseveralpossibilitiesformod-
ellingdata,whichshouldwetake?Ifmultipleexplanatoryvariablesaremea-
sured,shouldtheyallbeusedwhenformingpredictions,makingclassi?cations,
orattemptingtosummariseanalysisofwhatin?uencesresponsevariables,or
willincludingonlyafewofthemworkequallywell,orbetter?Ifso,which
onescanwebestinclude?Modelselectionproblemsarriveinmanyformsand
onwidelyvaryingoccasions.Inthischapterwepresentsomedataexamples
http://wendang.chazidian.comterinthebookwecomeback
tothesedataandsuggestsomeanswers.Ashortpreviewofwhatistocomein
laterchaptersisalsoprovided.
1.1Introduction
Withthecurrenteaseofdatacollectionwhichinmany?eldsofappliedsciencehasbecomecheaperandcheaper,thereisagrowingneedformethodswhichpointtointer-esting,importantfeaturesofthedata,andwhichhelptobuildamodel.Themodelwewishtoconstructshouldberichenoughtoexplainrelationsinthedata,butontheotherhandsimpleenoughtounderstand,explaintoothers,anduse.Itiswhenwenegotiatethisbalancethatmodelselectionmethodscomeintoplay.Theyprovideformalsupporttoguidedatausersintheirsearchforgoodmodels,orfordeterminingwhichvariablestoincludewhenmakingpredictionsandclassi?cations.
Statisticalmodelselectionisanintegralpartofalmostanydataanalysis.Modelselectioncannotbeeasilyseparatedfromtherestoftheanalysis,andthequestion‘whichmodelisbest’isnotfullywell-poseduntilsupplementinginformationisgivenaboutwhatoneplanstodoorhopestoachievegiventhechoiceofamodel.Thesurveyofdataexamplesthatfollowsindicatesthebroadvarietyofapplicationsandrelevanttypesofquestionsthatarise.
Beforegoingontothissurveyweshallbrie?ydiscusssomeofthekeygeneralissuesinvolvedinmodelselectionandmodelaveraging.1© Cambridge University http://wendang.chazidian.com
内容需要下载文档才能查看
Cambridge University Press
978-0-521-85225-8 - Model Selection and Model Averaging
Gerda Claeskens and Nils Lid Hjort
ExcerptMore information
2Modelselection:dataexamplesandintroduction
(i)Modelsareapproximations:Whendealingwiththeissuesofbuildingorselectingamodel,itneedstoberealisedthatinmostsituationswewillnotbeabletoguessthe‘correct’or‘true’model.Thistruemodel,whichinthebackgroundgeneratedthedatawecollected,mightbeverycomplex(andalmostalwaysunknown).Forworkingwiththedataitmightbeofmorepracticalvaluetoworkinsteadwithasimpler,butalmost-as-goodmodel:‘Allmodelsarewrong,butsomeareuseful’,asamaximformulatedbyG.E.P.Boxexpressesthisview.Severalmodelselectionmethodsstartfromthisperspective.
(ii)Thebias–variancetrade-off:Thebalanceandinterplaybetweenvarianceandbiasisfundamentalinseveralbranchesofstatistics.Intheframeworkofmodel?ttingandselectionittakestheformofbalancingsimplicity(fewerparameterstoestimate,leadingtolowervariability,butassociatedwithmodellingbias)againstcomplexity(enteringmoreparametersinamodel,e.g.regressionparametersformorecovariates,meansahigherdegreeofvariabilitybutsmallermodellingbias).Statisticalmodelselectionmethodsmustseekaproperbalancebetweenover?tting(amodelwithtoomanyparameters,morethanactuallyneeded)andunder?tting(amodelwithtoofewparameters,notcapturingtherightsignal).
(iii)Parsimony:‘Theprincipleofparsimony’takesmanyformsandhasmanyfor-mulations,inareasrangingfromphilosophy,physics,arts,communication,andindeedstatistics.TheoriginalOckham’srazoris‘entitiesshouldnotbemultipliedbeyondne-cessity’.Forstatisticalmodellingareasonabletranslationisthatonlyparametersthatreallymatteroughttobeincludedinaselectedmodel.Onemight,forexample,bewillingtoextendalinearregressionmodeltoincludeanextraquadratictermifthismanifestlyimprovespredictionquality,butnototherwise.
(iv)Thecontext:Allmodellingisrootedinanappropriatescienti?ccontextandisforacertainpurpose.AsDarwinoncewrote,‘Howodditisthatanyoneshouldnotseethatallobservationmustbefororagainstsomeviewifitistobeofanyservice’.Onemustrealisethat‘thecontext’isnotalwaysapreciselyde?nedconcept,anddifferentresearchersmightdiscoverorlearndifferentthingsfromthesamedatasets.Also,differentschoolsofsciencemighthavedifferentpreferencesforwhattheaimsandpurposesarewhenmodellingandanalysingdata.Breiman(2001)discusses‘thetwocultures’ofstatistics,broadlysortingscienti?cquestionsintorespectivelythoseofpredictionandclassi?cationononehand(whereevena‘blackbox’modelis?neaslongasitworkswell)andthoseof‘deeperlearningaboutmodels’ontheotherhand(wherethediscoveryofanon-nullparameterisimportantevenwhenitmightnothelpimproveinferenceprecision).ThusS.Karlin’sstatementthat‘Thepurposeofmodelsisnotto?tthedata,buttosharpenthequestions’(inhisR.A.Fishermemoriallecture,1983)isimportantinsomecontextsbutlessrelevantinothers.Indeedtherearedifferentlyspiritedmodelselectionmethods,gearedtowardsansweringquestionsraisedbydifferentcultures.© Cambridge University http://wendang.chazidian.com
内容需要下载文档才能查看
Cambridge University Press
978-0-521-85225-8 - Model Selection and Model Averaging
Gerda Claeskens and Nils Lid Hjort
ExcerptMore information
1.2Egyptianskulldevelopment3
(v)Thefocus:Inappliedstatisticsworkitisoftenthecasethatsomequantitiesorfunctionsofparametersaremoreimportantthanothers.Itisthenfruitfultogearmodelbuildingandmodelselectioneffortstowardscriteriathatfavourgoodperformancepreciselyforthosequantitiesthataremoreimportant.Thatdifferentaimsmightleadtodifferentlyselectedmodels,forthesamedataandthesamelistofcandidatemodels,shouldnotbeconsideredaparadox,asitre?ectsdifferentpreferencesanddifferentlossfunctions.Inlaterchaptersweshallinparticularworkwithfocussedinformationcriteriathatstartfromestimatingthemeansquarederror(varianceplussquaredbias)ofcandidateestimators,foragivenfocusparameter.
(vi)Con?ictingrecommendations:Asisclearfromtheprecedingpoints,questionsabout‘whichmodelisbest’areinherentlymoredif?cultthanthoseofthetype‘foragivenmodel,howshouldwecarryoutinference’.Sometimesdifferentmodelselectionstrategiesendupofferingdifferentadvice,forthesamedataandthesamelistofcandidatemodels.Thisisnotacontradictionassuch,butstressestheimportanceoflearninghowthemostfrequentlyusedselectionschemesareconstructedandwhattheiraimsandpropertiesare.
(vii)Modelaveraging:Mostselectionstrategiesworkbyassigningacertainscoretoeachcandidatemodel.Insomecasestheremightbeaclearwinner,butsometimesthesescoresmightrevealthatthereareseveralcandidatesthatdoalmostaswellasthewinner.Insuchcasestheremaybeconsiderableadvantagesincombininginferenceoutputacrossthesebestmodels.
1.2Egyptianskulldevelopment
MeasurementsonskullsofmaleEgyptianshavebeencollectedfromdifferentarchaeo-logicaleras,withaviewtowardsestablishingbiometricaldifferences(ifany)andmoregenerallystudyingevolutionaryaspects.Changesovertimeareinterpretedanddiscussedinacontextofinterbreedingandin?uxofimmigrantpopulations.Thedataconsistoffourmeasurementsforeachof30skullsfromeachof?vetimeeras,originallypresentedbyThomsonandRandall-Maciver(1905).The?vetimeperiodsaretheearlypredy-nastic(around4000b.c.),latepredynastic(around3300b.c.),12thand13thdynasties(around1850b.c.),theptolemaicperiod(around200b.c.),andtheRomanperiod(around150a.d.).Foreachofthe150skulls,thefollowingmeasurementsaretaken(allinmil-limetres):x1=maximalbreadthoftheskull(MB),x2=basibregmaticheight(BH),x3=basialveolarlength(BL),andx4=nasalheight(NH);seeFigure1.1,adaptedfromManly(1986,page6).Figure1.2givespairwisescatterplotsofthedataforthe?rstandlasttimeperiod,respectively.Similarplotsareeasilymadefortheothertimeperiods.Wenotice,forexample,thatthelevelofthex1measurementappearstohaveincreasedwhilethatofthex3measurementmayhavedecreasedsomewhatovertime.Statisticalmodellingandanalysisarerequiredtoaccuratelyvalidatesuchclaims.© Cambridge University http://wendang.chazidian.com
内容需要下载文档才能查看
Cambridge University Press
978-0-521-85225-8 - Model Selection and Model Averaging
Gerda Claeskens and Nils Lid Hjort
ExcerptMore information
4Modelselection:dataexamplesand
内容需要下载文档才能查看introduction
Fig.1.1.Thefourskullmeasurementsx1=MB,x2=BH,x3=BL,x4=NH;fromManly(1986,page6).
Thereisafour-dimensionalvectorofobservationsyt,iassociatedwithskulliandtimeperiodt,fori=1,...,30andt=1,...,5,wheret=1correspondsto4000b.c.,
¯t,?todenotethefour-dimensionalvectorandsoon,uptot=5for150a.d.Weusey
ofaveragesacrossthe30skullsfortimeperiodt.Thisyieldsthefollowingsummarymeasures:
¯1,?=(131.37,133.60,99.17,50.53),y
¯2,?=(132.37,132.70,99.07,50.23),y
¯3,?=(134.47,133.80,96.03,50.57),y
¯4,?=(135.50,132.30,94.53,51.97),y
¯5,?=(136.27,130.33,93.50,51.37).y
Standarddeviationsforthefourmeasurements,computedfromaveragingvarianceesti-matesoverthe?vetimeperiods(intheorderMB,BH,BL,NH),are4.59,4.85,4.92,
3.19.WeassumethatthevectorsYt,iareindependentandfour-dimensionalnormallydistributed,withmeanvectorξtandvariancematrix??tforerast=1,...,5.However,itisnotgiventoushowthesemeanvectorsandvariancematricescouldbestruc-tured,orhowtheymightevolveovertime.Hence,althoughwehavespeci?edthatdatastemfromfour-dimensionalnormaldistributions,themodelforthedataisnotyetfullyspeci?ed.
Wenowwishto?ndastatisticalmodelthatprovidestheclearestexplanationofthemainfeaturesofthesedata.Giventheinformationandevolutionarycontextalludedtoabove,searchingforgoodmodelswouldinvolvetheirabilitytoanswerthefollowingquestions.Dothemeanparameters(populationaveragesofthefourmeasurements)© Cambridge University http://wendang.chazidian.com
内容需要下载文档才能查看
Cambridge University Press
978-0-521-85225-8 - Model Selection and Model AveragingGerda Claeskens and Nils Lid HjortExcerpt
More information
1.2Egyptianskulldevelopment
120 125 130 135 140 145
115
60
5
10580 85 90 95
NH
120
130
140
BH
BL
120130140
45
120
5055
130140
MB
115
60
MB
60
MB
105
55
NH
80 85 90 95
50
NH
120 125 130 135 140 145
BL
45
120 125 130 135 140 145
45
80 85 90 95
5055
105115
BH
120 125 130 135 140 145
115
BH
60
BL
10580 85 90 95
NH
120
130
140
BH
BL
120130140
45
120
5055
130140
MB
115
60
MB
60
MB
105
55
NH
80 85 90 95
50
NH
120 125 130 135 140 145
BL
45
120 125 130 135 140 145
45
80 85 90 95
5055
105115
BHBHBL
Fig.1.2.PairwisescatterplotsfortheEgyptianskulldata.Firsttworows:earlypredy-nasticperiod(http://wendang.chazidian.comsttworows:Romanperiod(150a.d.).
© Cambridge University http://wendang.chazidian.com
内容需要下载文档才能查看下载文档
热门试卷
- 2016年四川省内江市中考化学试卷
- 广西钦州市高新区2017届高三11月月考政治试卷
- 浙江省湖州市2016-2017学年高一上学期期中考试政治试卷
- 浙江省湖州市2016-2017学年高二上学期期中考试政治试卷
- 辽宁省铁岭市协作体2017届高三上学期第三次联考政治试卷
- 广西钦州市钦州港区2016-2017学年高二11月月考政治试卷
- 广西钦州市钦州港区2017届高三11月月考政治试卷
- 广西钦州市钦州港区2016-2017学年高一11月月考政治试卷
- 广西钦州市高新区2016-2017学年高二11月月考政治试卷
- 广西钦州市高新区2016-2017学年高一11月月考政治试卷
- 山东省滨州市三校2017届第一学期阶段测试初三英语试题
- 四川省成都七中2017届高三一诊模拟考试文科综合试卷
- 2017届普通高等学校招生全国统一考试模拟试题(附答案)
- 重庆市永川中学高2017级上期12月月考语文试题
- 江西宜春三中2017届高三第一学期第二次月考文科综合试题
- 内蒙古赤峰二中2017届高三上学期第三次月考英语试题
- 2017年六年级(上)数学期末考试卷
- 2017人教版小学英语三年级上期末笔试题
- 江苏省常州西藏民族中学2016-2017学年九年级思想品德第一学期第二次阶段测试试卷
- 重庆市九龙坡区七校2016-2017学年上期八年级素质测查(二)语文学科试题卷
- 江苏省无锡市钱桥中学2016年12月八年级语文阶段性测试卷
- 江苏省无锡市钱桥中学2016-2017学年七年级英语12月阶段检测试卷
- 山东省邹城市第八中学2016-2017学年八年级12月物理第4章试题(无答案)
- 【人教版】河北省2015-2016学年度九年级上期末语文试题卷(附答案)
- 四川省简阳市阳安中学2016年12月高二月考英语试卷
- 四川省成都龙泉中学高三上学期2016年12月月考试题文科综合能力测试
- 安徽省滁州中学2016—2017学年度第一学期12月月考高三英语试卷
- 山东省武城县第二中学2016.12高一年级上学期第二次月考历史试题(必修一第四、五单元)
- 福建省四地六校联考2016-2017学年上学期第三次月考高三化学试卷
- 甘肃省武威第二十三中学2016—2017学年度八年级第一学期12月月考生物试卷
网友关注
- 第五次作文:学写游记
- 如何撰写本科毕业论文-媒体Word
- 投机倒把罪0Word
- 《认识人民币》课件2Word
- 金笔作文九级第16课 头脑风暴Word
- 《店铺数据分析及应用》货品主管必备Word
- 刘润泽 第四章·制度变迁分析Word
- 1.3.1 第1课时 青春飞扬Word
- 扁平化风格参考配色Word模板
- 如何演讲Word
- 伦敦金k线图特点
- 伦敦金和天通金的异同
- 四一班经典诗歌朗诵
- 人与狗
- 作文训练2017Word
- 镇江地区新版出口退税软件培训课件(外贸)Word
- 4.1_几何图形_第2课时三视图和展开图人教版数学七年级上册Word
- 伦敦金交易特点
- 广州市南沙珠江船务大厦工程可行性研究报告-广州中撰咨询
- 伦敦金银的特点
- 20170326高二物理第二章第二讲:表征交变电流的物理量(学生)
- 基层社会治理问题研究——党课讲稿(23页)
- 2017最新常用规范目录
- 拯救蓝心Word
- 2017届计算机系毕业设计答辩计划
- 阿尔伯塔大学有什么特点
- 人生的一面镜子,生活的诺亚方舟
- 第二章 财产损失保险Word
- 教学设计稿
- 2017年立思辰留学网:加拿大湖首大学怎样
网友关注视频
- 沪教版牛津小学英语(深圳用) 五年级下册 Unit 10
- 【部编】人教版语文七年级下册《过松源晨炊漆公店(其五)》优质课教学视频+PPT课件+教案,江苏省
- 冀教版小学英语五年级下册lesson2教学视频(2)
- 8 随形想象_第一课时(二等奖)(沪教版二年级上册)_T3786594
- 沪教版牛津小学英语(深圳用) 四年级下册 Unit 4
- 第19课 我喜欢的鸟_第一课时(二等奖)(人美杨永善版二年级下册)_T644386
- 化学九年级下册全册同步 人教版 第22集 酸和碱的中和反应(一)
- 【部编】人教版语文七年级下册《泊秦淮》优质课教学视频+PPT课件+教案,广东省
- 3.2 数学二年级下册第二单元 表内除法(一)整理和复习 李菲菲
- 外研版英语七年级下册module3 unit2第一课时
- 沪教版牛津小学英语(深圳用)五年级下册 Unit 1
- 《空中课堂》二年级下册 数学第一单元第1课时
- 第五单元 民族艺术的瑰宝_15. 多姿多彩的民族服饰_第二课时(市一等奖)(岭南版六年级上册)_T129830
- 苏科版数学 八年级下册 第八章第二节 可能性的大小
- 化学九年级下册全册同步 人教版 第25集 生活中常见的盐(二)
- 沪教版牛津小学英语(深圳用) 四年级下册 Unit 12
- 冀教版小学数学二年级下册第二单元《有余数除法的竖式计算》
- 沪教版八年级下册数学练习册21.4(1)无理方程P18
- 苏科版数学八年级下册9.2《中心对称和中心对称图形》
- 【获奖】科粤版初三九年级化学下册第七章7.3浓稀的表示
- 青岛版教材五年级下册第四单元(走进军营——方向与位置)用数对确定位置(一等奖)
- 飞翔英语—冀教版(三起)英语三年级下册Lesson 2 Cats and Dogs
- 冀教版小学数学二年级下册第二单元《租船问题》
- 外研版英语三起6年级下册(14版)Module3 Unit2
- 沪教版牛津小学英语(深圳用) 五年级下册 Unit 7
- 第8课 对称剪纸_第一课时(二等奖)(沪书画版二年级上册)_T3784187
- 北师大版小学数学四年级下册第15课小数乘小数一
- 沪教版八年级下册数学练习册21.3(3)分式方程P17
- 【部编】人教版语文七年级下册《过松源晨炊漆公店(其五)》优质课教学视频+PPT课件+教案,辽宁省
- 【部编】人教版语文七年级下册《逢入京使》优质课教学视频+PPT课件+教案,安徽省
精品推荐
- 2016-2017学年高一语文人教版必修一+模块学业水平检测试题(含答案)
- 广西钦州市高新区2017届高三11月月考政治试卷
- 浙江省湖州市2016-2017学年高一上学期期中考试政治试卷
- 浙江省湖州市2016-2017学年高二上学期期中考试政治试卷
- 辽宁省铁岭市协作体2017届高三上学期第三次联考政治试卷
- 广西钦州市钦州港区2016-2017学年高二11月月考政治试卷
- 广西钦州市钦州港区2017届高三11月月考政治试卷
- 广西钦州市钦州港区2016-2017学年高一11月月考政治试卷
- 广西钦州市高新区2016-2017学年高二11月月考政治试卷
- 广西钦州市高新区2016-2017学年高一11月月考政治试卷
分类导航
- 互联网
- 电脑基础知识
- 计算机软件及应用
- 计算机硬件及网络
- 计算机应用/办公自动化
- .NET
- 数据结构与算法
- Java
- SEO
- C/C++资料
- linux/Unix相关
- 手机开发
- UML理论/建模
- 并行计算/云计算
- 嵌入式开发
- windows相关
- 软件工程
- 管理信息系统
- 开发文档
- 图形图像
- 网络与通信
- 网络信息安全
- 电子支付
- Labview
- matlab
- 网络资源
- Python
- Delphi/Perl
- 评测
- Flash/Flex
- CSS/Script
- 计算机原理
- PHP资料
- 数据挖掘与模式识别
- Web服务
- 数据库
- Visual Basic
- 电子商务
- 服务器
- 搜索引擎优化
- 存储
- 架构
- 行业软件
- 人工智能
- 计算机辅助设计
- 多媒体
- 软件测试
- 计算机硬件与维护
- 网站策划/UE
- 网页设计/UI
- 网吧管理