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The detrimental impacts of climate variability on water, agriculture, and food resources in East Africa underscore the importance of reliable seasonal climate prediction. To overcome this difficulty RARIMAE method were evolved. Applications RARIMAE in the literature shows that amalgamating different methods can be an efficient and effective way to improve the forecasts of time series under consideration. With these motivations, attempt have been made to develop a multiple linear regression model (MLR) and a RARIMAE models for forecasting seasonal rainfall in east Africa under the following objectives: 1. To develop MLR model for seasonal rainfall prediction in East Africa. 2. To develop a RARIMAE model for seasonal rainfall prediction in East Africa. 3. Comparison of model's efficiency under consideration In order to achieve the above objectives, the monthly precipitation data covering the period from 1949 to 2000 was obtained from Climate Research Unit (CRU). Next to that, the first differenced climate indices were used as predictors. In the first part of this study, the analyses of the rainfall fluctuation in whole Central- East Africa region which span over a longitude of 15 degrees East to 55 degrees East and a latitude of 15 degrees South to 15 degrees North was done by the help of maps. For models’ comparison, the R-squared values for the MLR model are subtracted from the R-squared values of RARIMAE model. The results show positive values which indicates that R-squared is improved by RARIMAE model. On the other side, the root mean square errors (RMSE) values of the RARIMAE model are subtracted from the RMSE values of the MLR model and the results show negative value which indicates that RMSE is reduced by RARIMAE model for training and testing datasets. For the second part of this study, the area which is considered covers a longitude of 31.5 degrees East to 41 degrees East and a latitude of 3.5 degrees South to 0.5 degrees South. This region covers Central-East of the Democratic Republic of Congo (DRC), north of Burundi, south of Uganda, Rwanda, north of Tanzania and south of Kenya. Considering a model constructed based on the average rainfall time series in this region, the long rainfall season counts the nine months lead of the first principal component of Indian sea level pressure (SLP_PC19) and the nine months lead of Dipole Mode Index (DMI_LR9) as selected predictors for both statistical and predictive model. On the other side, the short rainfall season counts the three months lead of the first principal component of Indian sea surface temperature (SST_PC13) and the three months lead of Southern Oscillation Index (SOI_SR3) as predictors for predictive model. For short rainfall season statistical model SAOD current time series (SAOD_SR0) was added on the two predictors in predictive model. By applying a MLR model it is shown that the forecast can explain 27.4% of the total variation and has a RMSE of 74.2mm/season for long rainfall season while for the RARIMAE the forecast explains 53.6% of the total variation and has a RMSE of 59.4mm/season. By applying a MLR model it is shown that the forecast can explain 22.8% of the total variation and has a RMSE of 106.1 mm/season for short rainfall season predictive model while for the RARIMAE the forecast explains 55.1% of the total variation and has a RMSE of 81.1 mm/season. From such comparison, a significant rise in R-squared, a decrease of RMSE values were observed in RARIMAE models for both short rainfall and long rainfall season averaged time series. In terms of reliability, RARIMAE outperformed its MLR counterparts with better efficiency and accuracy. Therefore, whenever the data suffer from autocorrelation, we can go for MLR with ARIMA error, the ARIMA error part is more to correct the autocorrelation thereby improving the variance and productiveness of the model. / Die nachteiligen Auswirkungen der Klimavariabilität auf Wasser, Landwirtschaft und Nahrungsressourcen in Ostafrika unterstreichen die Bedeutung einer zuverlässigen saisonalen Klimavorhersage. Um diese Schwierigkeit zu überwinden, wurden die Regression mit ARIMA-Fehlern (RARIMAE)-Methoden entwickelt. Die Anwendungen RARIMAE in der Literatur zeigen, dass die Zusammenführung verschiedener Methoden ein effizienter und effektiver Weg sein kann, um die Vorhersagen der betrachteten Zeitreihen zu verbessern. Aus dieser Motivation heraus wurde versucht, ein multiples lineares Regressionsmodell (MLR) und ein RARIMAE-Modell zur Vorhersage saisonaler Niederschläge in Ostafrika unter folgenden Zielsetzungen zu entwickeln: 1. Entwicklung eines MLR-Modells für die Vorhersage der saisonalen Regenfälle in Ostafrika. 2. Entwicklung eines RARIMAE-Modells für die saisonale Niederschlagsvorhersage in Ostafrika. 3. Vergleich der betrachteten Modelleffizienz Um die oben genannten Ziele zu erreichen, wurden die monatlichen Niederschlagsdaten für den Zeitraum von 1949 bis 2000 von der Climate Research Unit (CRU) bezogen. Daneben wurden die ersten differenzierten Klimaindizes als Prädiktoren verwendet. Im ersten Teil dieser Studie wurden die Niederschlagsschwankungen in der gesamten Region Zentral-Ostafrika, die sich über einen Längengrad von 15 Grad Ost bis 55 Grad Ost und einen Breitengrad von 15 Grad Süd bis 15 Grad Nord erstrecken, analysiert mit Hilfe von Karten gemacht. Für den Modellvergleich werden die Erklärte Varianz-Werte für das MLR-Modell von den R-Quadrat-Werten des RARIMAE-Modells abgezogen. Die Ergebnisse zeigen positive Werte, was darauf hinweist, die Erklärte Varianz durch das RARIMAE-Modell verbessert wird. Auf der anderen Seite werden die Root-Mean-Square-Error-Werte (RMSE) des RARIMAE-Modells von den RMSE-Werten des MLR-Modells subtrahiert und die Ergebnisse zeigen einen negativen Wert, der darauf hinweist, dass der RMSE durch das RARIMAE-Modell für Trainings- und Testdatensätze reduziert wird. Für den zweiten Teil dieser Studie umfasst das betrachtete Gebiet einen Längengrad von 31,5 Grad Ost bis 41 Grad Ost und einen Breitengrad von 3,5 Grad Süd bis 0,5 Grad Süd. Diese Region umfasst den Zentral-Osten der Demokratischen Republik Kongo (DRC), nördlich von Burundi, südlich von Uganda, Ruanda, nördlich von Tansania und südlich von Kenia. Betrachtet man ein Modell, das auf der Grundlage der durchschnittlichen Niederschlagszeitreihen in dieser Region erstellt wurde, zählt die lange Regensaison den neunmonatigen Vorsprung der ersten Hauptkomponente des indischen Meeresspiegeldrucks (SLP_PC19) und den neunmonatigen Vorsprung des Dipolmodus-Index (DMI_LR9) als ausgewählte Prädiktoren für statistische und prädiktive Modelle. Auf der anderen Seite zählt die kurze Regenzeit den dreimonatigen Vorsprung der ersten Hauptkomponente der indischen Meeresoberflächentemperatur (SST_PC13) und den dreimonatigen Vorsprung des Southern Oscillation Index (SOI_SR3) als Prädiktoren für das Vorhersagemodell. Für das statistische Modell der kurzen Regenzeit wurde die aktuelle SAOD-Zeitreihe (SAOD_SR0) zu den beiden Prädiktoren im Vorhersagemodell hinzugefügt. Durch die Anwendung eines MLR-Modells wird gezeigt, dass die Vorhersage 27,4 % der Gesamtvariation erklären kann und einen RMSE von 74,2 mm/Saison für eine lange Regenzeit hat, während die Vorhersage für RARIMAE 53,6% der Gesamtvariation erklärt und einen RMSE von 59,4 mm/Saison hat. Durch die Anwendung eines MLR-Modells wird gezeigt, dass die Vorhersage 22,8% der Gesamtvariation erklären kann und einen RMSE von 106,1 mm/Saison für das Vorhersagemodell für kurze Regenzeiten hat, während die Vorhersage für RARIMAE 55,1% der Gesamtvariation erklärt und a RMSE von 81,1 mm/Saison. Aus einem solchen Vergleich wurde ein signifikanter Anstieg die Erklärte Varianz und eine Abnahme der RMSE-Werte in RARIMAE-Modellen sowohl für die gemittelten Zeitreihen für kurze Regenfälle als auch für lange Regenzeiten beobachtet. In Bezug auf die Zuverlässigkeit übertraf RARIMAE seine MLR-Pendants mit besserer Effizienz und Genauigkeit. Wenn die Daten unter Autokorrelation leiden, können wir uns daher für MLR mit ARIMA-Fehler entscheiden. Der ARIMA-Fehlerteil dient mehr dazu, die Autokorrelation zu korrigieren, wodurch die Varianz und Produktivität des Modells verbessert wird.

An ongoing debate in society is about the existence of a wage gap between genders, and society’s alleged preference to hire a man over an equally qualified woman. This debate extends from the commercial employment world into the funding of research grants. Given data collected at North Dakota State University between 2012 and 2018 have women who have sought federal funding for their research experienced a gender bias? To investigate, a logistic regression model is fit to determine whether gender affects funding probability. Other characteristics such as the primary investigator’s college, requested amount, and the research team’s make up of tenured and Caucasian members is also investigated. It was found that there is not a gender bias towards faculty at NDSU. Naturally, there was a bias towards researchers from different colleges and towards proposals requesting less funding. Surprisingly, a bias towards higher-proportion Caucasian research projects was found.

This thesis applies the methods of previous work in aerial magnetic field mapping and use in state estimation to the Virginia Tech Swing Space motion capture indoor facility. State estimation with magnetic field data acquired from a quadrotor is comparatively performed with Gaussian process regression, a multiplicative extended Kalman filter, and a particle filter to estimate the position and attitude of an uncrewed aircraft system (UAS) at any point in the motion capture testing environment. Motion capture truth data is used in the analysis. The first experimental method utilized in this thesis is Gaussian process regression. This machine learning tool allows us to create three-dimensional magnetic field maps of the indoor test space by collecting magnetic field vector data with a small UAS. Here, the maps illustrate the 3D magnetic field strengths and directions in the Virginia Tech Swing Space motion capture lab. Also, the magnetic field spatial variation of the test space is analyzed, yielding higher magnetic field gradient at lower heights above the ground. Next, the multiplicative extended Kalman filter is used with our Gaussian process regression magnetic field maps to estimate the attitude of the quadrotor. The results indicate an increase in attitude estimation accuracy when magnetic field mapping is utilized compared to when it is not. Here, results show that the addition of aerial magnetic field mapping leads to enhanced attitude estimation. Finally, the particle filter is utilized with support from our magnetic field maps to estimate the position of a small quadrotor UAS. The magnetic field maps allow us to obtain UAS position vectors by tracking UAS movement through magnetic field data. The particle filter gives three-dimensional position estimates to within 0.2 meters for five out of our eight test flights. The root mean square error is within 0.1 meters for each test flight. The effects of magnetic field spatial variation are also analyzed. The accuracy of position estimation is higher for two out the four flights in the maximum magnetic gradient area, while the accuracy is similar in both minimum and maximum gradient regions for the remaining two flights. There is evidence to support an increase in accuracy for high magnetic variation areas, but further work is needed to confirm utility for practical applications. / Master of Science / This thesis investigates airborne magnetic field mapping for the Virginia Tech Swing Space motion capture indoor facility. Position and attitude estimation with magnetic field data acquired from a small uncrewed aircraft system (UAS) is comparatively performed with multiple estimation methods. Motion capture truth data is used in analyses. The first data processing method is called Gaussian process regression. This machine learning tool allows us to create magnetic field maps of the indoor test space by averaging or regressing field estimates over collected UAS data. The maps illustrate the magnetic field strengths and directions over a three dimensional volume in the Virginia Tech Swing Space motion capture lab. Next, a multiplicative extended Kalman filter is used with our Gaussian process regression magnetic field maps to estimate UAS attitude. Results show improvement in attitude estimation accuracy when magnetic field mapping is utilized compared to when it is not. Finally, a particle filter method is utilized with our magnetic field maps to estimate UAS position. The particle filter estimates three-dimensional UAS position estimates to within 0.2 meters for five out of our eight test flights. The effects of magnetic field spatial variation are also analyzed, indicating the need for future work before magnetic field based position estimation can be practically applied.

My research makes three contributions to the literature. The first contribution is to find supportive evidence for the augmented Taylor rule model with orthogonalized bond market variables I build to more accurately describe and forecast the behavior the Federal Reserve, with improved model’s fit both in and out-of-sample. The second contribution to the existing literature is that I find supportive evidence for a macro explanation of industrial firm behavior in the United States. The third contribution of this paper is that I provide a new aspect to understand the monetary policy and the monetary policy transmission mechanism for both monetary policy practitioners and researchers. This research proceeds as the following: Essay one provides a literature review for the research in this dissertation discussing background and theories for both the empirical and theoretical applications of the Taylor rule, a tool for the setting of the federal funds rate. The second essay is designed to understand the setting of monetary policy by the Federal Reserve. I show that augment a simple Taylor rule with bond market information can significantly improve the model’s fit, both in and out-of-sample. The improvement is enough to produce lower forecast errors than those of non-linear policy models. In addition, the inclusion of these bond market variables resolves the parameter instability of the Taylor rule documented in the literature, and implies that the lagged federal funds rate plays a much smaller role than that suggested in the previous studies. The third essay examines the impact of monetary shocks on corporate cash holdings. I find evidence that small industrial firms hold onto cash when monetary policy is too tight and large industrial firms do the reverse both in the short-run and in the long-run. Further tests examine whether the long lasting loose monetary policy results in the pileup of corporate cash holdings. The evidence supports the assumption that industrial firms take the “long lasting lower interest rate” environment to hoard cash to buffer the monetary policy effectiveness.

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<p> Protein sequences display replacement rate heterogeneity across sites. In an earlier work, half of the causal site-wise variation in replacement rates was explained by a simple linear regression model consisting of terms for the solvent exposure of each residue, distance from the active site, and glycines in unusual main-chain conformations. Replacement rates vary not only across sites, they may also vary over time. In this study, we apply the linear regression model to phylogenies divided into subtrees to see if lineage-specific rate shifts have a structural basis that can be detected by the model. This approach is applied to two different data sets. The first set consists of phylogenies containing two representative structures, divided into subtrees such that one structure is present in each subtree. These structures have little or no obvious functional divergence between them. The model is tested with permutations of subtrees and structures from each subtree. While there is a slight effect of the specific structure on the fit of the model, the specific subtree has a greater effect. The second data set involves homologous structure pairs where the quaternary structure has changed at some point in the phylogeny. These pairs are examined to see how the change in constraint on the new interface sites affect the replacement rate, and its relationship with other structural factors. We find that the unique interfaces are as conserved as the shared ones, and they exhibit a different relationship between replacement rates and indicators of constraint than the shared interfaces or other protein sites. We also find that the unique interfaces display characteristic amino acid preferences that may identify interfaces which are still in the process of stabilizing. </p> / Thesis / Master of Science (MSc)