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StatisticalThoughtEnglishEditionCoursewareIntroductionDescriptivestatisticsFundamentalsofProbabilityTheoryInferentialstatisticsBayesianstatisticsTimeseriesanalysisNonparametricstatisticsIntroduction01Learningmethods:Thecourseoptionsacombinationoftheoreticalknowledgeandpracticalexercises,allowinglearnerstogainadeepunderstandingofstatisticalthinkinganditsapplicationsthroughhands-onexperienceCoursecontent:Thiscourseprovidesanintroductiontostatisticalthinking,includingbasicstatisticalconcepts,methods,andapplicationsItcoversawiderangeoftopics,suchasdescriptivestatistics,probabilitytheory,inferentialstatistics,andstatisticalmodelingLearningobjectives:Thecourseaimstocultivatestudents'statisticalthinkingability,improvetheirdataanalysisandproblem-solvingskills,andenablethemtoapplystatisticalmethodstorealworldproblemseffectivelyCourseIntroductionTheimportanceofstatisticalthinkingProblemsolvingskills:Statisticalthinkingisanessentialskillforproblemsolvinginthemodernworld,asithelpsindividualsanalyzecomplexdata,identifypatternsandtrends,andmakeinformeddecisionsbasedonevidenceDatadrivendecisionmaking:Withtheincreasingavailabilityofdatainvariousfields,theabilitytousestatisticalthinkingtointerpretandanalyzedatahasbecomecrucialforeffectivedecisionmakingStatisticalthinkinghelpsindividualsmakedatadrivendecisionsthatareevidencebasedandrelatedScientificresearch:Statisticalthinkingisessentialinthefieldofscientificresearch,whereitisusedtodesignexperiments,collectandanalyzedata,anddrawconclusionsbasedonevidenceItplaysacriticalroleinthedevelopmentofnewknowledgeandtheoriesindifferentfields,includingthenaturalsciences,socialsciences,andhumanitiesDescriptivestatistics02

CollectionandorganizationofdataCollectdataGatherinformationthroughsurveys,experiences,ordatabasesEnsureaccuracyUsereliableandvalidmethodstocollectdatatominimizeerrorsandbiasesOrganizedataArrangeandstructurethecollecteddatainameaningfulwayforanalysisCalculatemeasuresofcentraltensionCalculatemean,media,andmodetodescribethecenterofthedatadistributionDeterminemeasuresofspreadCalculaterange,variance,andstandarddeviationtodescribethedispersionofthedataIdentifyoutliersIdentifyandhandledatapointsthataresignificantlydifferentfromtherestofthedataMethodofdescribingdataUsehistoriestovisualizethefrequencydistributionofdataCreatehistoriesBarchartsareusefulforcomparingcategoricalvariablesMakebarchartsScatterplotsareusedtovisualizetherelationshipbetweentwocontinuousvariablesDrawscatterplotsBoxplotsprovideavisualsummaryofnumericaldata,showingtherange,quarters,andmediaProduceboxplotsVisualizationofdataFundamentalsofProbabilityTheory03ThebasicconceptofprobabilityThebasicconceptofprobabilitydefinesthelifestyleofaneventhappeningSummaryProbabilityisameasureofthelikelihoodofaneventoccurring,expressedasanumberbetween0and1Aprobabilityof0meanstheeventcannothappen,whileaprobabilityof1meanstheeventwillhappenProbabilitytheoryisthefoundationforstatisticalinferenceanddecisionmakingDetailsRandomvariablesarequantitiesthatcantakedifferentvalues,andtheirdistributionsdescribethelifestyleofeachvalueSummaryRandomvariablescanbediscrete,takingafixedsetofvalues,orcontinuous,takinganyvaluewithinarangeDistributionsdescribethelikelihoodofeachvalue,suchasthebinarydistributionfordistinctvariablesorthenormaldistributionforcontinuousvariablesDetailsRandomvariablesandtheirdistributionsSummaryParameterestimationistheprocessofinferringunknownparametersofadistribution,whilehypothesistestingisusedtoevaluatewhereagivenhypothesisistrueorfalse要点一要点二DetailsParameterestimationtechniquesincludemaximumlikelihoodestimationandBayesianestimationHypothesistestingusesstatisticalteststodeterminewhichgivenhypothesisissupportedbythedataornotCommonlyusedhypothesistestsincludethet-test,chisquaretest,andANOVAtestParameterestimationandhypothesistestingInferentialstatistics04ItisastatisticalmethodthatexaminestherelationshipbetweenonedependentvariableandoneormoreindependentvariablesIthelpsinpredictingthedependentvariablesbasedontheindependentvariablesItextendsthelinearregressionbyincludingmultipleindependentvariablestopredictthedependentvariablesIthelpsinunderstandingtherelativeimportanceofdifferentindependentvariablesinpredictingthedependentvariablesItisusedtopredictbinaryoutcomesbymodelingtheprobabilityoftheeventoccurringusingalogisticfunctionItiscommonlyusedinareaslikemarketing,finance,andmedicalresearchLinearregressionMultipleregressionLogisticregressionRegressionanalysisANOVA(AnalysisofVariance)ItisastatisticaltechniqueusedtocomparethemeansoftwoormoregroupsIttestswhicharesignificantlydifferentfromeachother,indicatingapossibleeffectofatreatmentorotherfactoronthegroupsANCOVA(AnalysisofCovariance)ItisanextensionofANOVAthatallowsfortheinclusionofadditionalvariablesthatmayaffectthedependentvariables,beyondthegroupsIthelpsincontrollingforconsolidatingvariablesandprovidingamoreaccurateestimateoftheeffectofthetreatmentVarianceanalysisDecisionTreeandRandomForestDecisionTree:ItisagraphicalrepresentationofadecisionmakingprocessthatleadstoaconclusionItiscommonlyusedinmachinelearningalgorithmstoclassifyorpredictoutputsbasedoninputfeaturesAdecisiontreeconsistencyofnodesandbranchesthatrepresentsdifferentdecisionsandoutcomesRandomForest:ItisanensemblelearningmethodthatcombinesthepredictionsofmultipledecisiontreestoimproveaccuracyandreduceoverfittingEachtreeintherandomforestisbuiltonasubsetofthedataandusesarandomsubsetoffeaturesateachnodeformakingdecisionsThefinalpredictionismadebyaggregatingthepredictionsofallthetreesintheforestRandomforestsareknownfortheiraccuracy,robustness,andabilitytohandlelargedatasetseffectivelyBayesianstatistics05TheBayesiantheoryisafundamentaltheoryinBayesianstatistics,whichprovidesamathematicalexpressionfortheconditionalprobabilityofeventsItisakeytoolinupdatingbeliefsinthelightofnewevidenceBayesiantheoryTheBayesiantheoryhasbeenwidelyusedinvariousfieldsofscientificresearch,suchasmedicaldiagnosis,signalprocessing,andnaturallanguageprocessingItallowsresearcherstoincorporatepriorknowledgeintotheiranalysisandmakemoreaccurateconsultationsApplicationsinScientificResearchBayesiantheoryanditsapplicationsDefinitionABayesiannetworkisaprobabilisticgraphicalmodelthatreportsthejointprobabilitydistributionofasetofrandomvariablesItusesadirectedacidicgraphtoreportconditionalindependencerelationshipsamongvariablesApplicationsindecisionmakingBayesiannetworkshavebeenusedinvariousdecisionmakingproblems,suchasmedicaldiagnosis,financialriskassessment,andmilitarydecisionmakingTheyprovideastructuredwaytoreportuncertaintyandmakedecisionsunderuncertaintyBayesiannetworkIntroductionBayesiandecisionanalysisisaframeworkformakingdecisionsunderuncertaintyusingBayesianprobabilitytheoryItintegratestheprinciplesofdecisiontheorywithBayesianstatisticstoprovideasystematicapproachfordecisionmakingApplicationsinrealworldproblemsBayesiandecisionanalysishasbeenappliedtosolverealworldproblems,suchasmedicaltreatmentdecisions,inventorymanagement,andfinancialportfoliomanagementItallowsdecisionmakerstotakeintoaccountboththeuncertaintyofoutcomesandthevalueofinformationintheirdecisionsBayesiandecisionanalysisTimeseriesanalysis06010203DefinitionThestationarityofatimeseriesreferstoitsstatisticalcharacteristicsthatdonotchangeovertime.TestingmethodThestationarityofthetimeseriesistestedbyobservingthemean,variance,andautocorrelationplotofthetimeseries,aswellasconductingstatisticaltestssuchasADFandPPtests.ImportanceStationarityisaprerequisitefortimeseriesanalysis,asmanytimeseriesanalysismethodsassumethatthedataisstationary.TestingthestationoftimeseriesDefinitionARIMAmodelisastatisticalmodelusedforanalyzingandpredictingtimeseriesdata,whichincludesthreeparts:autoregressive(AR),difference(I),andmovingaverage(MA).ModelingstepsFirst,performdifferentialanalysisonthedatatoeliminatenonstationarity,thenidentifyandestimatetheparametersofthemodel,andfinallymakepredictions.ApplicationscenarioWidelyusedintimeseriesforecastinginfieldssuchasfinance,economy,andmeteorology.ARIMAmodel要点三DefinitionSeasonaltimeseriesreferstoatimeserieswithperiodicchanges,suchasmonthly,quarterly,orannualdata.要点一要点二AnalysismethodAnalyzeseasonaltimeseriesbyobservingtheseasonalchartandseasonalindexofthetimeseries,andusingmodelssuchasseasonalautoregressiveintegralmovingaverage(SARIMA).ApplicationscenarioSuitablefordatawithobviousseasonalcharacteristics,suchassalesdata,climatedata,etc.要点三SeasonaltimeseriesanalysisNonparametricstatistics07Kerneldensityestimationisanonparametricstatisticalmethodusedtoestimateunknownpr