L'insula a longtemps été considérée essentiellement comme une partie du « cerveau viscéral » du fait de son rôle dans le traitement des réponses physiologiques et viscérales. Or, depuis l’avènement de l’imagerie cérébrale fonctionnelle, son implication dans divers aspects du fonctionnement neuropsychologique est devenue bien établie. De plus en plus d’études suggèrent que le cortex insulaire joue un rôle clé dans les circuits responsables de la prise de décision risquée. L’hypothèse des marqueurs somatiques suggère que les émotions influencent nos décisions aux moyens de changements physiologiques internes et viscéraux. Il a été proposé que l'insula participe à la prise de décision risquée en représentant les états somatiques de la situation chargée émotionnellement et en projetant ces informations au cortex préfrontal ventro-médian, constituant ainsi une structure clé dans les circuits responsables de la prise de décision. Les théories actuelles avancent que l’insula serait davantage impliquée dans la prise de risque lorsque l’individu fait face à une perte potentielle plutôt qu'à un gain. Toutefois, bien que plusieurs études supportent un rôle dans le processus décisionnel, la contribution spécifique du cortex insulaire demeure énigmatique. Les études qui composent cette thèse visent à mieux comprendre la façon dont l'insula participe à la prise de risque aux moyens de tâches neuropsychologiques de gambling qui permettent de simuler des situations de prise de décision de la vie quotidienne. La première étude neurocomportementale examine les conséquences d’une résection au cortex insulaire sur la capacité à prendre des décisions face à un risque potentiel, chez des patients épileptiques réfractaires à la médication qui ont subi une résection unilatérale de cette région. Leurs performances à deux tâches de gambling sont comparées à celles d’un groupe de patients ayant subi une chirurgie de l'épilepsie du lobe temporal (épargnant l’insula) et d’un groupe d’individus contrôles en santé. Les résultats mettent en évidence une altération du patron de prise de risque chez les patients avec résection insulaire, qui se traduit par une difficulté à ajuster leur choix en fonction de la valeur attendue (EV) (c’est-à-dire le ratio entre la magnitude et les probabilités des résultats possibles) de l’option risquée en condition de perte. Cette étude appuie l’idée selon laquelle la prise de décision risquée implique différents processus neuronaux selon si le risque implique un gain ou une perte potentielle. La seconde visée de cette thèse porte sur l’évaluation spécifique de la valence, de l’ampleur, de la probabilité et de l’EV de l’option risquée à l’activité insulaire au cours d’une prise de décision. Au moyen de l’imagerie par résonnance magnétique fonctionnelle, l’activité cérébrale d’individus en santé a été enregistrée, alors qu’ils complétaient une tâche de jeu de hasard. Les résultats de l’étude suggèrent un rôle prédominant de l’insula dans l’ajustement des décisions risquées en fonction de l’EV. De plus, l’activité de l’insula pendant la prise de décision était influencée par la sensibilité à la punition des participants. En somme, les données de cette thèse contribuent à une meilleure compréhension du rôle spécifique de l’insula à la prise de décision risquée et conduisent à une réflexion sur l’évaluation neuropsychologique des atteintes insulaires. / The insula has long been considered primarily as part of the « visceral brain » because of its role in the treatment of physiological and visceral responses. However, since the advent of functional brain imaging, its involvement in various aspects of neuropsychological functioning has become well established. More and more studies suggest that the insular cortex plays a key role in the circuits responsible for risky decision-making. The somatic marker hypothesis suggests that emotions influence our decisions by means of internal and visceral physiological changes. It has been proposed that the insula participates in risky decision-making by representing the somatic states of the emotionally charged situation and projecting this information to the ventromedian prefrontal cortex, thus constituting a key structure in the circuits responsible for decision. Current theories argue that the insula would be more involved in risk taking when the individual faces a potential loss rather than a gain. However, although several studies support a role in the decision-making process, the specific contribution of the insular cortex remains enigmatic. The studies that make up this thesis aim to better understand how the insula participates in risk taking with neuropsychological tasks of gambling that can simulate decision-making situations of everyday life. The first neurobehavioral study examines the consequences of insular cortex resections on the ability to make decisions about potential risk in drug-refractory epileptic patients who have undergone unilateral resection of this region. Their performance in two gambling tasks is compared to a group of patients who had surgery for temporal lobe epilepsy (sparing the insula) and a group of healthy control. The results highlight an alteration of risk taking in patients with insular resection, which results in difficulty in adjusting their choice according to the expected value (EV) (i.e. the ratio between the magnitude and probabilities of possible outcomes) of the risky option in the loss condition. This study supports the idea that risky decision making involves different neural processes depending on whether the risk involves a potential gain or loss. The second aim of this thesis deals with the specific assessment of the valence, magnitude, probability and EV of the risky option to insula activity during a decision-making process. Using functional magnetic resonance imaging, the brain activity of healthy individuals was recorded as they completed a gambling task. The results of the study suggest a predominant role of the insula in adjusting risky decisions based on EV. In addition, the activity of the insular cortex during decision-making was influenced by the participants' sensitivity to punishment. In sum, the data from this thesis contribute to a better understanding of the specific role of the insula in risky decision-making and lead to a reflection on the neuropsychological evaluation of insular lesions.

傳統迴歸分析是假設觀測值的不確定性來自於隨機現象，本文則應用模糊隨機變數概念於迴歸模式的架構，考慮將隨機現象和模糊認知並列研究。針對樣本模糊數(x_i, Y_i)，我們進行模糊迴歸參數估計，並稱此為模糊迴歸模式分析。模糊迴歸參數估計大都採用線性規劃，求出適當區間，將觀測模糊數Y_i的分佈範圍全部覆蓋。但是此結果並不能充分反映觀測樣本Y_i的特性。本研究提出一套模糊迴歸參數的估計方法，其結果對觀測樣本的解釋將更為合理，且具有模糊不偏的特性。在分析過程中，我們亦提出一些模糊統計量如模糊期望值、模糊變異數、模糊中位數的定義，以增加對這些參數的模糊理解。最後在本文中也針對台灣景氣指標與經濟成長率作實務分析，說明模糊迴歸模式的適用性。 / Conventional study on the regression analysis is based on the conception that the uncertainty of observed data comes from the random property. However, in this paper we consider both of the random property and the fuzzy perception to construct the regression model by using of fuzzy random variables. For the fuzzy sample (x_i,Y_i), we will process the parameters estimation of the fuzzy regression, and we call this process as fuzzy regression analysis. The parameters estimation for a fuzzy regression model is generally derived by the linear programming scheme. But it's result usually doesn't sufficiently reflect the characteristics of the observed samples. Hence in this paper we propose an alternative technique for parameters estimation in constructing the fuzzy regression model. The result will describe the observed data better than the conventional method did, moreover it will have the fuzzy unbiased properties. For the purpose of fuzzy perception on the fuzzy random variables, we also give definitions for certain important fuzzy statistics such as fuzzy expected value, fuzzy variance and fuzzy median. Finally, we give an example about the Taiwan Business Cycle and the Taiwan Economic Growth Rate for illustration.

自舒華特發明以管制圖監測製程以來，管制圖在工程的應用日趨重要。在特殊工程中，一個高效的管制圖方法尤為重要。基於此項事實，在文獻中各式各樣的管制圖層出不窮且技術日益完善。但傳統管制圖往往受制于常態分佈，因此在無母數管制圖研究方向仍有大量工作值得探討。於是本文在母體分佈未知情況下，推廣Yang (2015)的無母數平均值管制圖方法建立變動樣本指数加权移动平均管制圖，VSS EWMA-np control chart。新的管制圖將變動樣本大小（VSS）和指數加權移動平均（EWMA）方法結合建立一種新的管制圖方法，並用這種新型管制圖監測未知分佈母體的平均值是否發生變動。而為了監測平均數是否發生變化，也為了減少抽樣損失，本文評估管制圖監測效力的指標為管制圖偵測出異常訊息所需抽樣的樣本數期望值（EN）、平均連串長度（ARL）和平均觀測值總數（ANOS）。從本文的比較結果看出新的變動樣本指數加權移動平均管制圖擁有更好的失控偵測力。 / Since Shewhart invention control chart monitor the process, control charts are increasingly important in engineering applications. In special projects, an efficient control chart is especially important. Based on this fact, the various kinds of control charts in the literature are not poor and the technology is improving. However, traditional control charts are often subject to normal distribution, so there is still a lot of work to be discussed in the direction of the study of non-parametric control charts. So in this paper under unknown distribution in the matrix, Yang (2015) established on the basis of the theory of a non-parametric method of control chart - Exponentially Weighted Moving Average Control Chart with Variable Sampling Sizes (VSS EWMA - np control chart). New control chart will change the sample size (VSS) and exponential weighted moving average (EWMA) method to establish a new control chart, and use new control chart for monitoring the mean of unknown distribution matrix is changed. And whether to monitor the average changes in order to reduce the loss of sampling, this paper mainly evaluate control chart for monitoring the effectiveness of the statistics for the expected value of the sample size (EN), the average run length (ARL) and the average number of observations to signal (ANOS). From the comparison shown in this paper, the new control chart has better detection.

[pt] No Brasil, grandes consumidores podem estabelecer seus contratos de energia elétrica em dois ambientes: Ambiente de Contratação Regulado e Ambiente de Contratação Livre. Grandes consumidores são aqueles que possuem carga igual ou superior a 2 MW e podem ser atendidos sob contratos firmados em quaisquer um desses ambientes. Já os consumidores com demanda contratada inferior a 2 MW e superior a 500 kW podem ter seu contrato de energia estabelecido no Ambiente de Contratação Livre proveniente de geração de energia renovável ou no Ambiente de Contratação Regulada através das distribuidoras de energia. A principal vantagem do Ambiente de Contratação Livre é a possibilidade de negociar contratos com diferentes parâmetros, como, por exemplo, preço, quantidade de energia e prazo. Eventuais diferenças entre a energia contratada e a consumida, são liquidadas ao preço de energia de curto prazo, que pode ser bastante volátil.Neste caso o desafio é estabelecer uma estratégia de contratação que minimize os riscos associados a este ambiente. Esta dissertação propõe uma metodologia que envolve a simulação estatística de cenários correlacionados de energia, demanda máxima e preço de curto prazo (também chamado de PLD – Preço de Liquidação das Diferenças) para serem inseridos em um modelo matemático de otimização estocástica, que define os parâmetros ótimos da contratação de energia e demanda. Na parte estatística, um modelo Box e Jenkins é usado para estimar os parâmetros das séries históricas de energia e demanda máxima com o objetivo de simular cenários correlacionados com o PLD. Na parte de otimização, emprega-se uma combinação convexa entre Valor Esperado (VE) e Conditional Value-at-Risk (CVaR) como medidas de risco para encontrar os valores ótimos dos parâmetros contratuais, como a demanda máxima contratada, o volume mensal de energia a ser contratado, além das flexibilidades inferior e superior da energia contratada. Para ilustrar a abordagem proposta, essa metodologia é aplicada a um estudo de caso real para um grande consumidor no Ambiente de Contratação Livre. Os resultados indicaram que a metodologia proposta pode ser uma ferramenta eficiente para consumidores no Ambiente de Contratação Livre e, dado à natureza do modelo, pode ser generalizado para diferentes contratos e mercados de energia. / [en] In Brazil, big consumers can choose their energy contract between two different energy environments: Regulated Contract Environment and Free Contract Environment. Big consumers are characterized by installed load capacity equal or greater than 2 MW and can firm an energy contract under any of these environments. For those consumers with installed load lower than 2 MW and higher than 500 kW, their energy contracts can be firmed in the Free Contract Environment using renewable energy generation or in the Regulated Contract Environment by local distribution companies. The main advantage of the Free Market Environment is the possibility of negotiating contracts with different parameters such as, for example, price, energy quantity and deadlines. Possible differences between contracted energy and consumed energy are settled by the spot price, which can be rather volatile. In this case, the challenge is to establish a contracting strategy that minimize the associated risks with this environment. This thesis proposes a methodology that involves statistical simulation of correlated energy, peak demand and Spot Price scenarios to be used in a stochastic optimization model that defines the optimal energy and demand contract parameters. In the statistical part, a Box and Jenkins model is used to estimate parameters for energy and peak demand in order to simulate scenarios correlated with Spot Price. In the optimization part, a convex combination of Expected Value (EV) and Conditional Value-at-Risk (CVaR) is used as risk measures to find the optimal contract parameters, such as the contracted peak demand, the seasonal energy contracted volumes, in addition to the upper and lower energy contracted bound. To illustrate this approach, this methodology is applied in a real case study for a big consumer with an active Free Market Environment contract. The results indicate that the proposed methodology can be a efficient tool for consumers in the Free Contract Environment and, due to the nature of the model, it can be generalized for different energy contracts and markets.

Many have used the principles of statistics and Bayesian decision theory to model specific learning problems. It is less common to see models of the processes of learning in general. One exception is the model of the supervised learning process known as the "Extended Bayesian Formalism" or EBF. This model is descriptive, in that it can describe and compare learning algorithms. Thus the EBF is capable of modeling both effective and ineffective learning algorithms. We extend the EBF to model un-supervised learning, semi-supervised learning, supervised learning, and empirical function optimization. We also generalize the utility model of the EBF to deal with non-deterministic outcomes, and with utility functions other than 0-1 loss. Finally, we modify the EBF to create a "prescriptive" learning model, meaning that, instead of describing existing algorithms, our model defines how learning should optimally take place. We call the resulting model the Unified Bayesian Decision Theoretical Model, or the UBDTM. WE show that this model can serve as a cohesive theory and framework in which a broad range of questions can be analyzed and studied. Such a broadly applicable unified theoretical framework is one of the major missing ingredients of machine learning theory. Using the UBDTM, we concentrate on supervised learning and empirical function optimization. We then use the UBDTM to reanalyze many important theoretical issues in Machine Learning, including No-Free-Lunch, utility implications, and active learning. We also point forward to future directions for using the UBDTM to model learnability, sample complexity, and ensembles. We also provide practical applications of the UBDTM by using the model to train a Bayesian variation to the CMAC supervised learner in closed form, to perform a practical empirical function optimization task, and as part of the guiding principles behind an ongoing project to create an electronic and print corpus of tagged ancient Syriac texts using active learning.