Master of Science / Department of Psychology / Gary L. Brase / In 2006, the Center for Disease Control and Prevention recommended the revision of state HIV testing laws. With these recommendations, more low-risk individuals are tested regardless of their risk group. However, there is a greater chance of a false positive test result for low-risk individuals than for high-risk individuals. Additionally, previous research found that doctors and HIV counselors in Germany did not accurately communicate the relationship between risk factors and false positive tests (Gigerenzer, Hoffrage, & Ebert, 1998). This study aimed to (1) compare the findings of the 1998 German sample to HIV hotline counselors in the United States in 2011; and (2) to investigate the ability of students to calculate the conditional probability of HIV for a low-risk individual after receiving a positive test, based on idealized transcripts of conversations with HIV hotline counselors. The first study found that HIV hotline counselors use both verbal expressions of risk and percentages to communicate HIV testing statistics. Additionally, 2011 American counselors were more aware of the chance of false positives and false negatives than compared to the 1998 German sample. However, no 2011 American counselors were able to provide an accurate positive predictive value for a low-risk woman. The second study found low performance among students in the calculation of the positive predictive value. Performance was facilitated by a natural frequency format for high numerate individuals. There were different patterns of results for the General Numeracy Scale and the Subjective Numeracy Scale. This would suggest that these two scales might be measuring different constructs. These findings are consistent with the two theories supporting the Frequency Effect, namely the Frequentist Hypothesis and the Nested Sets Hypothesis. Additionally, this research suggests computation of the conditional risk of HIV is facilitated by a natural frequency format. Teaching techniques have been developed and demonstrate long lasting improvement in health related computations. If a few hours of training is all that it takes to communicate these life and death statistics in a manner that is consistent with reasoning, health practitioners and students should be required to have more education in communicating and computing probabilities.

La méthode d'optimisation d'un portefeuille issue de la minimisation du DownSide Risk a été mise au point pour suppléer les carences de la méthode classique de Markowitz dont l'hypothèse de la normalité de la distribution des rendements se trouve défaillante très souvent. Dans cette thèse, nous proposons d'introduire des estimateurs non paramétriques de la moyenne ou de la médiane conditionnelle pour remplacer les rendements observés d'un portefeuille ou des actifs constituant un portefeuille dans le cas du DownSide Risk. Ces estimateurs nous permettent d'obtenir des frontières efficientes lisses et facilement interprétables. Nous développons des algorithmes itératifs pour résoudre les différents problèmes d'optimisation permettant d'obtenir des portefeuilles optimaux. Nous proposons aussi une nouvelle mesure de risque dit risque conditionnel qui tient compte des anticipations des valeurs futures des différents rendements. Pour le définir nous avons fait appel aux prédicteurs non paramétriques basés sur l'estimation de la moyenne conditionnelle. Enfin, nous avons testé et validé toutes nos méthodes sur des données issues de différents marchés et nous avons montré leur performance et leur efficacité comparées aux méthodes classiques / The DownSide Risk (DSR) model for portfolio optimization allows to overcome the drawbacks of the classical Mean-Variance model concerning the asymmetry of returns and the risk perception of investors. This optimization model deals with a positive definite matrix that is endogenous with respect to the portfolio weights and hence leads to a non standard optimization problem. To bypass this hurdle, we developed a new recursive minimization procedure that ensures the convergence to the solution and gives a smooth portfolio efficient frontier. Our method consists in replacing all the returns by their nonparametric estimators counterpart using kernel mean or median regressions. This technique provides an effect similar to the case where an infinite number of observations is available. We also develop a new portfolio optimization model where the risks are measured through conditional variance or semivariance. This strategy allows us to take advantage from returns prediction which are obtained by nonparametric univariate methods. The prediction step uses kernel estimation of the conditional mean. Data from different markets are used to test and validate the proposed approaches, and results indicate better overall performance