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The purpose of the current study is to apply the delay and probability discounting in the areas of parent training and probability of success of treatment. There was a total of 31 participants that completed one demographic questionnaire and two probability and delay discounting surveys either via computer or with paper and pencil. Participants had two options in the surveys: one was an immediate reward, and one with a probability delay. The first survey gave scenarios of hours of parent training, the second was a monetary probability discounting survey.

Den här uppsatsen inleds med att studera de moment som används för multinomial logistisk regression och hur resultaten mäts. Teorin tar sin avsats i den binomiala logistiska regression, för att stegvis ta sig vidare till den multinomiala logistiska regressionen. Begreppen logit, oddskvoten och sannolikheterna förtydligas, effekterna av de oberoende variablerna diskuteras och kopplingen till vanlig linjär regression åskådliggörs. Det blir även en fördjupning av matematiken bakom den logistiska funktionen. Därefter tillämpas den multinomial logistisk regressionsanalysen med ett praktiskt exempel. Analysmodellen är användbar inom flertalet områden och den här uppsatsen ligger inom ramen för sportanalys. Matchstatistik från ishockey och närmare bestämt Örebro Hockeys matcher från säsongerna 2012/13 till 2017/18 nyttjas och den slutgiltiga modellen använder sig av tre förklarande variabler. Resultatet visar att utfallet efter ordinarie tid kan förklaras till 60,9% med hjälp av matchstatistiken, vilket tyder på att den multinomiala regressionsmodellen presterar likvärdigt med andra metoder som tillämpar kategorisk dataanalys inom sportanalys. / This thesis starts by studying the multinomial logistic regression and its moments and how the results are measured. The theory begins with the binomial logistics regression and gradually moves on towards the multinomial logistics regression. Concepts as logit, odds ratio and probabilities are explained, the effects of the independent variables discussed and the link to ordinary linear regression is illustrated. There will also be a deeper, mathematical look at the function of logistic growth. Thereafter the multinomial logistic regression model will be applied. The model is useful within several domains and this thesis lies within sportsanalytics. For this thesis matchstatistics from ice hockey, that is Örebro Hockey’s matches from season 2012/13 to 2017/18, has been used and the final model has three exploratory variables. The outcome of the result performs equivalent to other methods, which applies categorical data analysis within sportsanalytics.

Financial markets have been crucial in driving capital investments across the world. Anessential piece of these markets is the presence of risk takers, or market speculators, who will hold financial portfolios in hopes of profit. Portfolios with cash flowsgenerated from floating interest rate derivatives will often be subjected to fixing risk, also called second-order basis risk, stemming from a discrepancy in time with the hedge and the original position. Using data from a fixing risk mitigation service, named RESET, this thesis aims todeepen the understanding of accumulation of fixing risk on the the USD dollar market for 3-month interest rate swaps. This is done by modeling customer behavior using machine learning methods. Macroeconomic factors such as market volatility and the January effect amongst others were incorporated as variables into the set. The two models explored are logistic regression and neural networks, the first one chosen for interoperability and the latter for its generality. Neither of the two models could accurately predict customer behavior, with a balanced accuracy short of 70 percent. The strongest influence of the final prediction turned out to be previous behavior, the January effect and how many of their financial positions the customer previously put into the service.

Statistics of met-ocean conditions including wind, current and wave at the location between west and central Gulf of Mexico (GOM) are derived based on about three year of field measurements. Two-parameter Weibull distribution has been employed to fit wind speed at 10m over sea level and current speed in various depth. The joint probability contour was derived based on First-Order Reliability Method. In addition, the joint distribution of wind speed and direction was visualized by wind-rose diagram. The results provided in this study may provide essential information to the probability distribution of met-ocean condition in the particular location and can be used as a reference in the future designs.

This work presents an enhancement to the classification tree algorithm which forms the basis for Random Forests. Differently from the classical tree-based methods that focus on one variable at a time to separate the observations, the new algorithm performs the search for the best split in two-dimensional space using a linear combination of variables. Besides the classification, the method can be used to determine variables interaction and perform feature extraction. Theoretical investigations and numerical simulations were used to analyze the properties and performance of the new approach. Comparison with other popular classification methods was performed using simulated and real data examples. The algorithm was implemented as an extension package for the statistical computing environment R and is available for free download under the GNU General Public License.

<p>Stochastic microlensing is a central tool in probing dark matter on galactic scales. From first principles, we initiate the development of a mathematical theory </p><p>of stochastic microlensing. We first construct a natural probability space for stochastic microlensing and characterize the general behaviour of the random time </p><p>delay functions' random critical sets. Next we study stochastic microlensing in two distinct random microlensing scenarios: The uniform stars' distribution with</p><p> constant mass spectrum and the spatial stars' distribution with general mass spectrum. For each scenario, we determine exact and asymptotic (in the large number</p><p> of point masses limit) stochastic properties of the random time delay functions and associated random lensing maps and random shear tensors, including their </p><p>moments and asymptotic density functions. We use these results to study certain random observables, such as random fixed lensed images, random bending angles, </p><p>and random magnifications. These results are relevant to the theory of random </p><p>fields and provide a platform for further generalizations as well as analytical limits for checking astrophysical studies of stochastic microlensing.</p><p>Continuing our development of a mathematical theory of stochastic microlensing, we study the stochastic version of the Image Counting Problem, first considered </p><p>in the non-random setting by Einstein and generalized by Petters. In particular, we employ the Kac-Rice formula and Morse theory to deduce general formulas for </p><p>the expected total number of images and the expected number of saddle images for a general random lensing scenario. We further </p><p>generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of</p><p> global expected number of positive parity images due to a general lensing map. Applying the result to the uniform stars' distribution random microlensing </p><p>scenario, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars. This global expectation is bounded, </p><p>while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars.</p><p>Finally, we outline a framework for the study of stochastic microlensing in the neighbourhood of lensed images. This framework is related to the study of the </p><p>local geometry of a random surface. In our case, the surface is non-Gaussian, and therefore standard literature on the subject does not apply. We explore the case</p><p> of a random gravitational field caused by a random star.</p> / Dissertation

¡@¡@This paper studies the MNE¡¦s choice of the optimal transfer price with the consideration of the possibility of transfer pricing penalty. Because the transfer prices are determined in-house, there are opportunities for MNE to manipulate the prices and evade corporate income tax and trade taxes. To reduce these opportunities, most governments have implemented transfer pricing regulations based on the OECD guidelines. If the MNE¡¦s manipulation of transfer prices is too flagrant, an extra tax will be levied to penalize the MNE. As long as the tax rates are different in different jurisdictions, the MNE will pick transfer prices that balance between the gain from profit shifting and the loss coming from the possible penalty. ¡@¡@Three forms of probability are introduced to capture the possibility of being penalized when the MNE tries to manipulate the transfer prices. We find close form solutions under the linear and quadratic forms of probability. And numerical simulation is used to get the optimal transfer price under the exponential form of probability.

This dissertation consists of three more or less independent projects. In the first project, we find the microstates free entropy dimension of a large class of L1[0; 1]{ circular operators, in the presence of a generator of the diagonal subalgebra. In the second one, for each sequence {cn}n in l1(N), we de fine an operator A in the hyper finite II1-factor R. We prove that these operators are quasinilpotent and they generate the whole hyper finite II1-factor. We show that they have non-trivial, closed, invariant subspaces affiliated to the von Neumann algebra, and we provide enough evidence to suggest that these operators are interesting for the hyperinvariant subspace problem. We also present some of their properties. In particular, we show that the real and imaginary part of A are equally distributed, and we find a combinatorial formula as well as an analytical way to compute their moments. We present a combinatorial way of computing the moments of A*A. Finally, let fTkg1k =1 be a family of *-free identically distributed operators in a finite von Neumann algebra. In this paper, we prove a multiplicative version of the Free Central Limit Theorem. More precisely, let Bn = T*1T*2...T*nTn...T2T1 then Bn is a positive operator and B1=2n n converges in distribution to an operator A. We completely determine the probability distribution v of A from the distribution u of jTj2. This gives us a natural map G : M M with u G(u) = v. We study how this map behaves with respect to additive and multiplicative free convolution. As an interesting consequence of our results, we illustrate the relation between the probability distribution v and the distribution of the Lyapunov exponents for the sequence fTkg1k=1 introduced by Vladismir Kargin.