Impaired reproduction studies with Poisson responses are among a growing class of toxicity studies in the biological and medical realm. In recent years, little effort has been focused on the development of efficient experimental designs for impaired reproduction studies. This research concentrates on two areas: 1) the use of Bayesian techniques to make single regressor designs robust to parameter misspecification and 2) the extension of design optimality methods to the k-regressor model. The standard Poisson model with log link is used. Bayesian designs with priors on the parameters are explored using both the D and F-optimality criteria for the single regressor Poisson exponential model. Since these designs are found via numeric optimization techniques, Bayesian equivalence theory functions are derived to verify the optimality of these designs. Efficient Bayesian designs which provide for lack-of-fit testing are discussed. Characterizations of D, D_s, and interaction optimal designs which are factorial in nature are demonstrated for models involving interaction through k factors. The optimality of these designs is verified using equivalence theory. In addition, augmentations of these designs that result in desirable lack of fit properties are discussed. Also, a structure for fractional factorials is given in which specific points are added one at a time to the main effect design in order to gain estimability of the desired interactions. Robustness properties are addressed as well. Finally, this entire line of research is extended to industrial exponential models where different regressors work to increase and/or decrease a count data response produced by a process. / Ph. D.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24265号 / 情博第809号 / 新制||情||136(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 梅野 健, 教授 山下 信雄, 准教授 加嶋 健司 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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Priority based scheduling disciplines are widely used by existing computer operating systems. However, the mathematical analysis and modelling of these systems present great difficulties since priority schedulling is not compatible with exact product form solutions of queueing network models (QNM's). It is therefore, necessary to employ credible approximate techniques for solving QNM's with priority classes. The principle of maximum entropy (ME) is a method of inference for estimating a probability distribution given prior information in the form of expected values. This principle is applied, based on marginal utilisation, mean queue length and idle state probability constraints, to characterise new product-form approximations for general open and closed QNM's with priority (preemptive-resume, non-preemtive head-of-line) and non-priority (first-come-first-served, processor-sharing, last-come-first-served with, or without preemtion) servers. The ME solutions are interpreted in terms of a decomposition of the original network into individual stable GIG11 queueing stations with assumed renewal arrival processes. These solutions are implemented by making use of the generalised exponential (GE) distributional model to approximate the interarrival-time and service-time distributions in the network. As a consequence the ME queue length distribution of the stable GE/GEzl priority queue, subject to mean value constraints obtained via classical queueing theory on bulk queues, is used as a 'building block' together with corresponding universal approximate flow formulae for the analysis of general QNM's with priorities. The credibility of the ME method is demonstrated with illustrative numerical examples and favourable comparisons against exact, simulation and other approximate methods are made. / Algerian government

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Humans have difficulties grasping the notion of exponential growth and often underestimate the accumulated final value, a phenomenon called exponential growth bias (EGB). During the COVID-19 pandemic, this tendency led to the inaccurate judgment of the virus spread, ultimately making safety measures seem less important. In prospect theory, loss aversion refers to the tendency of perceiving loss as more severe than a gain of the same magnitude is perceived as good. The question addressed was whether loss aversion through the valence of framing influences the judgments of exponential changes within the context of COVID-19. Furthermore, the association between EGB and the individual characteristic Need for Cognition (NFC) was investigated. Participants (n=129) were randomized into one of the two framing conditions (Recovery or Infection) and were presented with six EGB problems with different change rates and the six-item version of the Need for Cognition Scale. The results confirmed the existence of EGB at all growth rates (+5%, +15%, +25%), while the effect of EGB was mixed for exponential decline. The framing did not show a considerable effect on the accuracy of judgments. Simple linear regression analyses indicated that NFC moderates the effect of EGB at higher growth rates (i.e., at +15% and +25%). Overall, the results were more consistent and clearer for exponential growth than for exponential decline. The underestimation of exponential growth in the context of COVID-19 is quite alarming as it entails the risk of insufficient behavioral changes, which can lead to serious consequences for both the individual and society.