Estimation and Model Building M. H. Faber. Yovisto Academic Video Search. Model evaluation by statistical testing, Chi-square goodness of fit test, Kolmogorov- Smirnov goodness of fit test, Model comparison Testing Statistical Evaluation Model goo Mode Summary Small Short Lecture good Estimation Building Previous Overview ETH Zurich til exercis consid having sampl spac with only possibl stat choos randomly outcom that what corresponding likelihood function swiss federal institut technology model evaluation statistical testing comparison different hypothesis both fall positiv model plausibl compar goodness eith comparing sampl statistics directly could misleading inconclusiv numb degre likelihood swiss federal institut technology test shows hypothesis cannot rejected must rememb oth model could faact oft cag several pass should does mean necessary evidenc strong show with littl data swiss federal institut technology model evaluation statistical testing comparison giv that significanc mod evaluation statistical testing model comparison verification significanc used quantify plausibility giv relativ data evidenc cas hav considered what information actually contained thes swiss federal institut leas model evaluation statistical testing comparison verification significanc used quantify plausibility giv relativ data evidenc cas hav considered that call what information actually contained thes swiss federal institut model evaluation statistical testing kolmogorov-smirnov goodness test statistic tabulated slim dkss m484 swiss federal institut technology model evaluation statistical testing goodness test kolmogorov-smirnov statistic swiss federal institut technology model evaluation statistical testing kolmogorov-smirnov goodness test statistic tabulated meal hiss buys swiss federal institut technology avwa mod evaluation statistical testing kolmogorov-smirnov goodness test statistic swiss federal institut technology calculated from following statistic been proposed swiss federal institut technology mod evaluation statistical testing kolmogorov-smirnov goodness test observed cumulativ distribution function model evaluation statistical testing kolmogorov-smirnov goodness test idea behind that postulated cumulativ distribution function accordanc with observed data then maximal differenc betwe predicted function should small swiss federal institut technology exercis which equation correspond method moment swiss federal institut technology mod evaluation statistical testing goodness test assuming postulated normal distribution with following calculation sheet observed significanc level freedom yield small than hypothesis cannot rejected swiss federal institut technology model evaluation statistical testing goodness test assuming postulated normal distribution with following calculation sheet maim swiss federal institut technology goodness test mor paramet postulated distribution function been assessed using sam data used must reduc numb degre freedom accordingly assuming that estimated varianc from mean valu would hav swiss federal institut technology model evaluation statistical testing model evaluation statistical testing goodness test consid exampl that assum normal distribution with paramet estimated from availabl data meant standard deviation continuous probability density function easily discretized swiss federal institut technology model evaluation statistical testing goodness test postulated probability density function discretized total numb gull swiss federal institut technology model evaluation statistical testing goodness test observed predicted histogram numb sampl low interval interval lumped swiss federal institut technology mod evaluation statistical testing goodness test following calculation sheet produced numb predicted probability sampl stati significanc level distribution with degre freedom yield small than hypothesis cannot rejected swiss federal institut technology model evaluation statistical testing goodness test observed predicted histogram compared jidd swiss federal institut technology goodness test postulated probability density function discretized gull swiss federal institut technology model evaluation statistical testing model evaluation statistical testing goodness test consid exampl that assum normal distribution with paramet estimated from availabl data meal standard deviation continuous probability density function easily discretized swiss federal institut technology mod evaluation statistical testing goodness test postulated probability density function discretized jill swiss federal institut technology model evaluation statistical testing goodness test consid exampl that assum normal distribution with paramet estimated from availabl data meant standard deviation continuous probability density function easily discretized swiss federal institut technology model evaluation statistical testing goodness test postulated probability density function discretized gull swiss federal institut technology model evaluation statistical testing goodness test consid exampl that assum normal distribution with paramet estimated from availabl data meant standard deviation continuous probability density function easily discretized swiss federal institut technology technology model evaluation statistical testing goodness test idea then giv significanc level observed squared differenc plausibl postulating hypothesis that assumed distribution function gross contradiction with data formulating operating rul alternat less informativ becaus consid oth function than swiss federal institut model evaluation statistical testing goodness test summing squared differenc betwe observed predicted histogram distributed degre freedom swiss federal institut technology limp model evaluation statistical testing goodness test assuming that sampl discret random variabl tim numb realization binomial distributed with expected valu varianc giv predicted occurenc postulated correct larg enough central limit theor differenc standard normal swiss federal institut technology mod evaluation statistical testing goodness test assuming that sampl discret random variabl tim numb realization binomial distributed with expected valu varianc giv swiss federal institut technology probability density function swiss federal institut technology model evaluation statistical testing goodness test rememb that discret cumulativ distribution giv model evaluation statistical testing goodness test idea behind that differenc betwe predicted observed sampl histogram should small gong swiss federal institut model evaluation statistical testing goodness test idea behind that differenc betwe predicted observed sampl histogram should small swiss federal technology mod evaluation statistical testing considered namely verification gait discret distribution function test continuous kolmogorov smirnov swiss federal institut technology model evaluation statistical testing assum that hav selected distribution function describ uncertain quantity swiss federal institut technology exercise1 maxima log-likelihood function been found valu then likelihood swiss federal institut technology maximum likelihood swiss federal institut technology short summary previous lectur considered probl assessing paramet distribution based observation data what learn learned that estimated using method moment content todays lectur short summary previous overview estimation model building evaluation statistical testing goodness test kolmogorov-smirnov comparison swiss federal institut technology exercise1 maxima log-likelihood function been found valu then likelihood swiss federal institut technology statistics pap distribution family confidenc moment probabilistic statistical maximum likelihood method swiss federal institut technology overview estimation model building different typ information used when developing engineering model subiectiv subjectiv physical judgement sampl overview estimation model building different typ information used when developing engineering model subjectiv physical understanding judgement data sampl statistics confidenc interval statistical pap distribution family met swiss federal institut probabilistic overview estimation model building different typ information used when developing engineering model swiss federal institut technology short summary previous lectur method maximum likelihood full distribution estimat principl behind that estimat paramet observation data maximized provid extremely strong statistical tool swiss federal institut technology short summary previous lectur method moment point estimat principl behind that estimat paramet calculat based analytical expression becom equal sampl this lead equation which hav solved simultaneously wher numb swiss federal institut technology 111s