<p>With the advance of technology, the collection and storage of data has become routine. Huge amount of data are increasingly produced from biological experiments. the advent of DNA microarray technologies has enabled scientists to measure expressions of tens of thousands of genes simultaneously. Single nucleotide polymorphism (SNP) are being used in genetic association with a wide range of phenotypes, for example, complex diseases. These high-dimensional problems are becoming more and more common. The "large p, small n" problem, in which there are more variables than samples, currently a challenge that many statisticians face. The penalized variable selection method is an effective method to deal with "large p, small n" problem. In particular, The Lasso (least absolute selection and shrinkage operator) proposed by Tibshirani has become an effective method to deal with this type of problem. the Lasso works well for the covariates which can be treated individually. When the covariates are grouped, it does not work well. Elastic net, group lasso, group MCP and group bridge are extensions of the Lasso. Group lasso enforces sparsity at the group level, rather than at the level of the individual covariates. Group bridge, group MCP produces sparse solutions both at the group level and at the level of the individual covariates within a group. Our simulation study shows that the group lasso forces complete grouping, group MCP encourages grouping to a rather slight extent, and group bridge is somewhere in between. If one expects that the proportion of nonzero group members to be greater than one-half, group lasso maybe a good choice; otherwise group MCP would be preferred. If one expects this proportion to be close to one-half, one may wish to use group bridge. A real data analysis example is also conducted for genetic variation (SNPs) data to find out the associations between SNPs and West Nile disease.</p> / Master of Science (MSc)

Estimating the variables of importance in inferentialmodelling is of significant interest in many fields of science,engineering, biology, medicine, finance and marketing. However,variable selection in high-dimensional data, where the number ofvariables is relatively large compared to the observed data points,is a major challenge and requires more research in order toenhance reliability and accuracy. In this bachelor thesis project,several known methods of variable selection, namely orthogonalmatching pursuit (OMP), ridge regression, lasso, adaptive lasso,elastic net, adaptive elastic net and multivariate adaptive regressionsplines (MARS) were implemented on a high-dimensional dataset.The aim of this bachelor thesis project was to analyze andcompare these variable selection methods. Furthermore theirperformance on the same data set but extended, with the numberof variables and observations being of similar size, were analyzedand compared as well. This was done by generating models forthe different variable selection methods using built-in packagesin R and coding in MATLAB. The models were then used topredict the observations, and these estimations were compared tothe real observations. The performances of the different variableselection methods were analyzed utilizing different evaluationmethods. It could be concluded that some of the variable selectionmethods provided more accurate models for the implementedhigh-dimensional data set than others. Elastic net, for example,was one of the methods that performed better. Additionally, thecombination of final models could provide further insight in whatvariables that are crucial for the observations in the given dataset, where, for example, variable 112 and 23 appeared to be ofimportance. / Att skatta vilka variabler som är viktigai inferentiell modellering är av stort intresse inom mångaforskningsområden, industrier, biologi, medicin, ekonomi ochmarknadsföring. Variabel-selektion i högdimensionella data, därantalet variabler är relativt stort jämfört med antalet observeradedatapunkter, är emellertid en stor utmaning och krävermer forskning för att öka trovärdigheten och noggrannheteni resultaten. I detta projekt implementerades ett flertal kändavariabel-selektions-metoder, nämligen orthogonal matching pursuit(OMP), ridge regression, lasso, elastic net, adaptive lasso,adaptive elastic net och multivariate adaptive regression splines(MARS), på ett högdimensionellt data-set. Syftet med dettakandidat-examensarbete var att analysera och jämföra resultatenav dessa metoder. Vidare analyserades och jämfördes metodernasresultat på samma data-set, fast utökat, med antalet variableroch observationer ungefär lika stora. Detta gjordes genom attgenerera modeller för de olika variabel-selektions-metodernavia inbygga paket i R och programmering i MATLAB. Dessamodeller användes sedan för att prediktera observationer, ochestimeringarna jämfördes därefter med de verkliga observationerna.Resultaten av de olika variabel-selektions-metodernaanalyserades sedan med hjälp av ett flertal evaluerings-metoder.Det kunde fastställas att vissa av de implementerade variabelselektions-metoderna gav mer relevanta modeller för datanän andra. Exempelvis var elastic net en av metoderna sompresterade bättre. Dessutom drogs slutsatsen att kombineringav resultaten av de slutgiltiga modellerna kunde ge en djupareinsikt i vilka variabler som är viktiga för observationerna, där,till exempel, variabel 112 och 23 tycktes ha betydelse. / Kandidatexjobb i elektroteknik 2021, KTH, Stockholm

MSc (Statistics) / Department of Statistics / Selection of variables is vital in high dimensional statistical modelling as it aims to identify the right subset model. However, variable selection for discrete survival analysis poses many challenges due to a complicated data structure. Survival data might have unobserved heterogeneity leading to biased estimates when not taken into account. Conventional variable selection methods have stability problems. A simulation approach was used to assess and compare the performance of Least Absolute Shrinkage and Selection Operator (Lasso) and gradient boosting on discrete survival data. Parameter related mean squared errors (MSEs) and false positive rates suggest Lasso performs better than gradient boosting. Frailty models outperform discrete survival models that do not account for unobserved heterogeneity. The two methods were also applied on Zimbabwe Demographic Health Survey (ZDHS) 2016 data on age at first marriage and did not select exactly the same variables. Gradient boosting retained more variables into the model. Place of residence, highest educational level attained and age cohort are the major influential factors of age at first marriage in Zimbabwe based on Lasso. / NRF