The Swedish Transport Agency has for a long time collected data on a monthly basis for different variables that are used to make predictions, short projections as well as longer projections. They have used SAS for producing statistical models in air transport. The model with the largest value of coefficient of determination is the method that has been used for a long time. The Swedish Transport Agency felt it was time for an evaluation of their models and methods of how projections is estimated, they would also explore the possibilities to use different, completely new models for forecasting air travel. This Bachelor thesis examines how the Holt-Winters method does compare with SARIMA, error terms such as RMSE, MAPE, R2, AIC and BIC  will be compared between the methods.  The results which have been produced showing that there may be a risk that the Holt-Winters models adepts a bit too well in a few variables in which Holt-Winters method has been adapted. But overall the Holt-Winters method generates better forecasts . / <p>Avbryt / Spara utkast</p>

Prevalence is a valuable epidemiological measure about the burden of disease in a community for planning health services; however, true prevalence is typically underestimated and there exists no reliable method of confirming the estimate of this prevalence in question. This thesis studies imprecise priors for the development of a statistical reasoning framework regarding this epidemiological decision making problem. The concept of imprecise probabilities introduced by Walley (1991) is adopted for the construction of this inferential framework in order to model prior ignorance and quantify the degree of imprecision associated with the inferential process. The study is restricted to the standard and zero-truncated Poisson sampling models that give an exponential family with a canonical log-link function because of the mechanism involved with the estimation of population size. A three-parameter exponential family of posteriors which includes the normal and log-gamma as limiting cases is introduced by applying normal priors on the canonical parameter of the Poisson sampling models. The canonical parameters simplify dealing with families of priors as Bayesian updating corresponds to a translation of the family in the canonical hyperparameter space. The canonical link function creates a linear relationship between regression coefficients of explanatory variables and the canonical parameters of the sampling distribution. Thus, normal priors on the regression coefficients induce normal priors on the canonical parameters leading to a higher-dimensional exponential family of posteriors whose limiting cases are again normal or log-gamma. All of these implementations are synthesized to build the ipeglim package (Lee, 2013) that provides a convenient method for characterizing imprecise probabilities and visualizing their translation, soft-linearity, and focusing behaviours. A characterization strategy for imprecise priors is introduced for instances when there exists a state of complete ignorance. The learning process of an individual intentional unit, the agreement process between several intentional units, and situations concerning prior-data conflict are graphically illustrated. Finally, the methodology is applied for re-analyzing the data collected from the epidemiological disease surveillance of three specific cases – Cholera epidemic (Dahiya, 1973), Down’s syndrome (Zelterman, 1988), and the female users of methamphetamine and heroin (B ̈ ohning, 2009).

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Model selection is an important part of classification. In this thesis we study the two classification models logistic regression and random forest. They are compared and evaluated based on prediction accuracy and metadata analysis. The models were trained on 25 diverse datasets. We calculated the prediction accuracy of both models using RapidMiner. We also collected metadata for the datasets concerning number of observations, number of predictor variables and number of classes in the response variable.     There is a correlation between performance of logistic regression and random forest with significant correlation of 0.60 and confidence interval [0.29 0.79]. The models appear to perform similarly across the datasets with performance more influenced by choice of dataset rather than model selection.     Random forest with an average prediction accuracy of 81.66% performed better on these datasets than logistic regression with an average prediction accuracy of 73.07%. The difference is however not statistically significant with a p-value of 0.088 for Student's t-test.     Multiple linear regression analysis reveals none of the analysed metadata have a significant linear relationship with logistic regression performance. The regression of logistic regression performance on metadata has a p-value of 0.66. We get similar results with random forest performance. The regression of random forest performance on metadata has a p-value of 0.89. None of the analysed metadata have a significant linear relationship with random forest performance.     We conclude that the prediction accuracies of logistic regression and random forest are correlated. Random forest performed slightly better on the studied datasets but the difference is not statistically significant. The studied metadata does not appear to have a significant effect on prediction accuracy of either model.

High levels of toxic heavy metals in the environment are a major concern and our knowledge about their adverse impacts and distribution patterns is improving. To mitigate human exposure for large regions, understanding the spatial distribution of metals in soil is key. Several types of models are available to predict the concentration levels, but they are often complex and data-intensive. The objective of this research is to explore the application of a simple method that produces geographically referenced predictions of surface soil concentrations of heavy metals. The approach uses publicly-available Canadian soil sample data, Geographic Information Science, statistical correlation and regression analyses. Geographically Weighted Regression (GWR) was used to investigate the spatial variability of the relationship between surface and the subsurface soil metal concentrations. Correlation analysis (Pearson’s) between the log of concentration levels of the two layers shows relationships of 0.51 for arsenic (As), and 0.23 for lead (Pb). Although the correlation results showed levels in the two layers are related, GWR analysis illustrates that the degree of this relation varies geographically. This study suggests that factors (natural and anthropogenic) other than the subsurface concentration itself are contributing to the concentration surface levels for all of the studied metals in this dataset. Based on the above findings, two linear regression models were developed to predict As and Pb levels in surface soil. Independent variables in the models were developed using geographic data on factors hypothesized to influence surface levels, an approach that has been extensively used for modelling air pollution and known as Land Use Regression (LUR). For the LUR analysis, the results show that industrial activities account for more than 70% of the variation of Pb concentrations in surface soil. Interestingly, the LUR model for As suggests that the bedrock geology and the total length of road at a location are the main factors. Both variables account for more than 40% of the variations of the As levels in surface soil in BC. The LUR results suggest that regional scale modeling of As and Pb surface soil concentrations can provide information about their spatial patterns that may be useful for understanding potential human exposure and the conduct of environmental epidemiological studies. / Graduate / 768 / 573 / 481 / steeved@uvic.ca

Den rapport du just ska till att läsa är ett kandidatarbete i matematisk statistik skrivet vid matematiska instutitionen, Linköpings Universitet. Det område som undersöks är att om man med hjälp av P/E-tal kan förutsäga kraftiga börsnedgångar (börskrascher) på OMXS30. För att definiera en börskrasch har vi använt måttet Value at Risk (VaR). Detta mått är vedertaget hos finansiella instutitioner som ett riskmått men i denna rapport används det som sagt för att definiera nivån for en börskrasch. VaR har beräknats med diverse olika metoder som presenteras i rapporten.   Efter att en börskrasch definierats har vi använt logistisk regression med P/E-tal som förklaringsvariabel för att undersöka om dessa nedgångar har ett samband med höga P/E-tal. Denna undersökning har lett fram till ett starkt resultat som säger att om en börsnedgång definieras med ett V aR mått som bygger på normalfördelningsantagande där volatiliteten är simulerad med GARCH(1,1) så kan vi konstatera att det finns ett säkerställt samband mellan höga P/E-tal och börskrascher.   Slutsatserna som dragit från undersökningen är att man genom att inkorporera en logistisk regression mot P/E-talet kan forstärka sitt VaR mått givet de antaganden som presenterats. Författarna uppmuntrar vidare forskning på området för att se om resultatet kan generaliseras till olika börsindex och även till specifika bolag.

Syftet med uppsatsen är undersöka huruvida utbildningsnivå och arbetssituation har ett samband med attityder till invandring i Sverige idag. I litteraturen finns det förklaringar som menar att lägre utbildade individer hyser mer negativa attityder mot invandrare och invandring jämfört med högre utbildade individer som genom sin utbildning får ett mer upplyst perspektiv som hämmar de negativa attityderna. Det förekommer även förklaringar som menar att arbetslöshet och en upplevd konkurrens från invandrare leder till negativa attityder mot invandrare och invandring. I den här uppsatsen används material från European Social Survey 2012 för att se hur attityderna mot invandring och invandrare ser ut i Sverige idag. Uppsatsen utgår från två hypoteser. Högutbildade individer förväntas ha mer positiva attityder mot invandrare jämfört med lågutbildade och individer som är sysselsatta förväntas ha mer positiva attityder mot invandrare jämfört med arbetslösa individer. Materialet analyseras med hjälp av två logistiska regressioner där utfallen är sannolikheten att anse att Sveriges kulturliv undergrävs av invandring samt sannolikheten att vilja tillåta få eller inga invandrare med annan hudfärg eller etnisk tillhörighet som majoriteten av Sveriges befolkning. Resultatet visar att den första hypotesen stämmer, högre utbildade individer har mer positiva attityder mot invandrare jämfört med lägre utbildade individer. Resultatet visar vidare att den andra hypotesen kan förkastas, det finns inget signifikant samband som visar att sysselsatta individer har mer positiva attityder mot invandrare jämfört med arbetslösa individer. Slutsatsen är att enbart utbildningsnivå förmodligen inte kan förklara orsakerna till negativa attityder till invandring och invandrare.

This thesis explores the practical use of kernel smoothing in three areas: binary regression, density estimation and Poisson regression sample size calculations. Both nonparametric and semiparametric binary regression estimators are examined in detail, and extended to two bandwidth cases. The asymptotic behaviour of these estimators is presented in a unified way, and the practical performance is assessed using a simulation experiment. It is shown that, when using the ideal bandwidth, the two bandwidth estimators often lead to dramatically improved estimation. These benefits are not reproduced, however, when two general bandwidth selection procedures described briefly in the literature are applied to the estimators in question. Only in certain circumstances does the two bandwidth estimator prove superior to the one bandwidth semiparametric estimator, and a simple rule-of-thumb based on robust scale estimation is suggested. The second part summarises and compares many different approaches to improving upon the standard kernel method for density estimation. These estimators all have asymptotically 'better' behaviour than the standard estimator, but a small-sample simulation experiment is used to examine which, if any, can give important practical benefits. Very simple bandwidth selection rules which rely on robust estimates of scale are then constructed for the most promising estimators. It is shown that a particular multiplicative bias-correcting estimator is in many cases superior to the standard estimator, both asymptotically and in practice using a data-dependent bandwidth. The final part shows how the sample size or power for Poisson regression can be calculated, using knowledge about the distribution of covariates. This knowledge is encapsulated in the moment generating function, and it is demonstrated that, in most circumstances, the use of the empirical moment generating function and related functions is superior to kernel smoothed estimates.

This Thesis focuses on the study of multivariate statistical regression techniques which have been used to produce non-linear empirical models of chemical processes, and on the development of a novel approach to non-linear Projection to Latent Structures regression. Empirical modelling relies on the availability of process data and sound empirical regression techniques which can handle variable collinearities, measurement noise, unknown variable and noise distributions and high data set dimensionality. Projection based techniques, such as Principal Component Analysis (PCA) and Projection to Latent Structures (PLS), have been shown to be appropriate for handling such data sets. The multivariate statistical projection based techniques of PCA and linear PLS are described in detail, highlighting the benefits which can be gained by using these approaches. However, many chemical processes exhibit severely nonlinear behaviour and non-linear regression techniques are required to develop empirical models. The derivation of an existing quadratic PLS algorithm is described in detail. The procedure for updating the model parameters which is required by the quadratic PLS algorithms is explored and modified. A new procedure for updating the model parameters is presented and is shown to perform better the existing algorithm. The two procedures have been evaluated on the basis of the performance of the corresponding quadratic PLS algorithms in modelling data generated with a strongly non-linear mathematical function and data generated with a mechanistic model of a benchmark pH neutralisation system. Finally a novel approach to non-linear PLS modelling is then presented combining the general approximation properties of sigmoid neural networks and radial basis function networks with the new weights updating procedure within the PLS framework. These algorithms are shown to outperform existing neural network PLS algorithms and the quadratic PLS approaches. The new neural network PLS algorithms have been evaluated on the basis of their performance in modelling the same data used to compare the quadratic PLS approaches.

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