The Fisher matrix allows us to estimate the errors on parameters without having to cover the whole parameter space (but of course will only be appropriate so long as the derivatives are roughly constant throughout the space). So, a Fisher matrix analysis is equivalent to the assumption of a Gaussian distribution about the peak of the likelihood (e.g. Bond et al. 1998). It also makes the calculations easier. For example, if we are only interested in a subset of parame- ters, then marginalising over unwanted parameters is just the same as inverting the Fisher matrix, taking only the rows and columns of the wanted parameters and inverting the smaller matrix back. It is also very straightforward to combine constraints from different independent parameters: we just sum over the Fisher matrices of the experiments (re- member Fisher matrix is the log of the likelihood function). We further note, as in all uses of the Fisher matrix, that any results thus obtained must be taken with the caveat that these relations only map onto realistic error bars in the case of a Gaussian distribution, usually most appropriate in the limit of high signal-to-noise ratio and/or relatively small scales, so that the conditions of the central limit theo- rem obtain. As long as we do not find extremely degenerate parameter directions, we expect that our results will cer- tainly be indicative of a full analysis, using simulations and techniques such as **Bayesian** **Experimental** **Design** (Trotta 2007c).

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Chapter 6
Conclusions and future work
In this thesis, we studied goal-oriented optimal **Bayesian** **experimental** **design**. We reviewed the background of the problem and introduced the information theoretical characterization of the **design** criterion. Using mutual information, the problem is then formulated as a combinatorial optimization problem. We then introduced three algorithms, Greedy, Minorize-Maximize, and Generalized Leverage Score for finding the approximate solutions. The classical analysis using (approximate) submodularity breaks in the goal-oriented setting due to the forward operator of the transformed problem being rank deficient under the assumption that n > m > d. We studied the computational cost and test the performance of these algorithms on both synthetic and real data sets. We concluded that although iterative algorithms have better performance, the computational cost is much larger than GLS. The performance of GLS is similar to that of Greedy and MM when the noise is uncorrelated or slightly correlated. However, in the case when the noise is highly correlated, the performance of GLS could be as poor as the random selections. Due to the difficulty in obtaining theoretical guarantees of the GLS algorithm, we obtain a lower bound for any k-set selections.

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In this thesis, we have demonstrated the use of Bayesian inference and Bayesian experimental design in a model film/substrate inference problem. To make inference an[r]

LTCI, CNRS, Telecom ParisTech Université Paris-Saclay, Paris, France 2 LRI, Univ. Paris-Sud, CNRS, Inria, Université Paris-Saclay, Orsay, France 3 Applied Mathematics, University of Campinas, Campinas, San Paulo, Brazil
Contact: Wanyu Liu (wanyu.liu@telecom-paristech.fr) Website: http://perso.telecom-paristech.fr/wliu/
A new information-theoretic approach based on
**Bayesian** **Experimental** **Design** (BED) is applied to

For example, one can initially start from a low po and low nquad for the DASQ, solve the inference problem at a particular fixed experimental condition using the result[r]

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corresponds to c-optimum **design**, that is, to L-optimum **design** with H given by the rank-one matrix cc ⊤ . Note that the dependence of c in θ
makes the problem nonlinear. A **Bayesian** approach is used in [3,6], based on a **design** criterion of the type E{c ⊤ M −1 k c}, where E{·} denotes the expectation with respect to θ for a given prior. Sequential approaches are considered in [14,22]. One can also refer to [2] for the use of c-optimal **design** in the context of **Bayesian** estimation and to [5] for a survey on **Bayesian** **experimental** **design**. Following (10), a penalty function related to c-optimal **design** is thus

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The CMDO framework is built on a large set of low fidelity modules representing the aircraft disciplines. All these modules include their own set of **design** variables, which increases the number of dimensions of the optimization problem. Consequently, it makes the thorough exploration of the **design** space expensive in terms of function calls and CPU time, in the order of days. Similarly, the PMDO framework also includes a large number of **design** variables required to define the wing geometry and the aero-structural models are time consuming to converge, in the order of weeks. The motivation of this research is then to apply **Bayesian** Optimization (BO) methods [3] to reduce the number of functions calls and accelerate the convergence time for both MDO frameworks. To do so, the SEGOMOE python tool-box is investigate against historical optimizers used at Bombardier aviation. The main objective of this paper is thus to demonstrate that all the optimizers of the tool-box has good convergence properties and performs well on an industrial test case.

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which typically have two features: the measures are re-weighted in some way and the moments play an important role. Both features arise, as we have seen, in the above algorithms.
In classical optimal **design** theory for polynomial regression (see, e.g., Fe- dorov (1972)) one is interested in functionals of the moment (information) matrix M (ξ) of a **design** measure ξ:

Model Validation
Previous studies have modeled realistic batch RO systems, accounting for factors including membrane permeability, frictional losses, pump and ERD efficiencies, and concentration polarization (Swaminathan et al., 2017). We compared the energy consumption of our batch RO prototype to the predictions of a batch RO model over a range of recovery ratios, fluxes, and feed salinities. The **experimental** results agree well with the model predictions. This is the first time that models of batch RO energy consumption have been validated with **experimental** results, greatly increasing the utility of previous models. While our batch RO prototype is currently limited to operating pressures under 10 bar, we anticipate that the validated model can be used to predict batch RO performance over a wider range of operating conditions.

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The optical **design** may require one or several dia- phragm layers to provide the pupil of the system and
to solve the problem of crosstalk between adjacent channels (a description of the issues linked to cross- talk in the specific case of our system will be dis- cussed in Subsection 4.C ). The diaphragm layers can be made either of independent metallic arrays of pinholes or of a metallization on the surfaces of the lenses. From a practical point of view, an inde- pendent metallic pinhole array would be supported using the same hybridization techniques as the mi- crolenses. However, in order to avoid stacking too many elements, we prefer using a metallization on the surfaces of the lenses.

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One of the most critical components in the **experimental** test stand was the motor. We obtained an off-the-shelf permanent magnet low-inertia dc motor (the 4N63–100 from Pacific Sci- entific, Rockford, IL, USA) with adequate characteristics—a large torque-to-rotor inertia ratio (2.543 · 10 5 (1/s 2 )), high rated power output (321 W), appropriate rated speed (3440 rpm), appropriate rated rms (14.2 A) and pulse (48 A) current, ap- propriate rated voltage (42 V), and appropriate electrical (0.11 ms) and mechanical (0.6 ms) time constants—for the proposed EMVD. Unfortunately, this motor is large in size—too large to be easily implemented in an actuation system on an IC engine head. Smaller motors will be required to implement the proposed EMVD on an engine cylinder head [30]. To this end, a very small off-the-shelf dc motor (the B1118-050-A from Portescap, West Chester, PA, USA) capable of actuating engine intake valves and small enough to be implemented on an IC engine head was more recently obtained. **Design** considerations and experimen- tal results obtained using this motor will be presented in a future publication.

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4.8. Performances of the sequential designs with different computational costs
Figure 9 shows the prediction mean accuracy with a best I-optimal sequential **design** when the costs of the two codes are different. It can be seen that at a given total computational cost the accuracy of prediction is better when the cost of the first code is lower. In other words the prediction mean accuracy is better at a given computational budget when more observation points can be added to the first code for the same computational budget. These results are consistent with those of figure 8.

Abstract
Earth reentry and recovering of a small space probe (typical of a students’ project satellite) set questions related to guidance and control. If the probe is asked to reach a target point with constraints on the landing precision, then other questions related to the foil and to the complete system performance arise. In this frame, the aim of the present work is to **design**, to build and to operate a decelerator system that is automatically controlled by the satellite probe in the objective to reach an a priori chosen landing point with a required precision. This multiphysics project involves at the same time **design** and fabrication of the decelerator (parafoil and suspension lines), flight mechanics of the deformable decelerator, guidance and control development, system engineering of the probe development. The project is divided in two similar but distinct projects. The first one called ”small probe" (33 cL / up to 350 g, International Class) aims to improve the complete system global performance with the goal of precise landing and in-flight missions, for a low altitude release configuration. The ”small probe" students’ project aims the French CanSat challenge, an international competition organised in France by CNES and Planète Sciences Association. The second one is to launch a ”big probe" (1 L / up to 1 kg) from a 1/25th scale replica of the Soyouz Rocket developed by a partner student’s team of Samara State Aerospace University (Russia). The latter case aims to test previous developments in more complex and severe release and descent conditions.

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The importance of lightweight structures in many fields of engineering is well known since long time. The innovations in technological processes based on material addiction allow pushing the **design** towards challenging geometries and associated structural properties. Engineered materials like lattice structures can be theoretically used to modify the local material properties and strength with minimization of the mass of components; in practice, several issues are still to be solved in stabilization of additive processes and achieving repeatable structures able to pass qualification procedures. At this purpose, dedicated **experimental** and **design** methods like those reported in this paper are needed.

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Abstract
Earth reentry and recovering of a small space probe (typical of a students’ project satellite) set questions related to guidance and control. If the probe is asked to reach a target point with constraints on the landing precision, then other questions related to the foil and to the complete system performance arise. In this frame, the aim of the present work is to **design**, to build and to operate a decelerator system that is automatically controlled by the satellite probe in the objective to reach an a priori chosen landing point with a required precision. This multiphysics project involves at the same time **design** and fabrication of the decelerator (parafoil and suspension lines), flight mechanics of the deformable decelerator, guidance and control development, system engineering of the probe development. The project is divided in two similar but distinct projects. The first one called ”small probe" (33 cL / up to 350 g, International Class) aims to improve the complete system global performance with the goal of precise landing and in-flight missions, for a low altitude release configuration. The ”small probe" students’ project aims the French CanSat challenge, an international competition organised in France by CNES and Planète Sciences Association. The second one is to launch a ”big probe" (1 L / up to 1 kg) from a 1/25th scale replica of the Soyouz Rocket developed by a partner student’s team of Samara State Aerospace University (Russia). The latter case aims to test previous developments in more complex and severe release and descent conditions.

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Some follow up experiments might be designed primarily to explore the mechanisms by which fractional factorial designs apparently lead to blindness to mistakes in engineering models. The subjects in the fractional factorial condition may prefer to use paired comparisons between two individual **experimental** outcomes as a heuristic for forming expectations. However, since this heuristic is difficult to implement in the fractional factorial **design**, the subjects might be able to learn a different approach. For example, they might learn to form expectations for main effects instead. Perhaps the difficulty with forming an expectation for a main effect will persist even if training or suggestions were made regarding critical assessment of main effects. A main effect of a factor is conceptually very different from a conditional effect of a single factor. By its very definition, a main effect of a factor is a function of behavior in a model across a multi-dimensional domain of factor changes. Even if an experimenter is able to form an expectation, the certainty about that prediction would have to include an assessment of the reliability of that expectation in the face of all the possible interactions that might countermand that prediction. Therefore we suggest investigations into the conceptual differences between main effects and conditional effects. For example, experiments might focus on the ability of engineers to predict main effects and their confidence in those predictions.

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Optimisation of simulation parameters in event generators; Optimisation of compiler flags to maximize execution speed; Optimisation of hyper-parameters in machine learning for HEP; ... l[r]

What is **Bayesian** about **Bayesian** optimization?
• The **Bayesian** strategy treats the unknown objective function as a random function and place a prior over it.
The prior captures our beliefs about the behaviour of the function. It is here defined by a Gaussian process whose covariance function captures assumptions about the smoothness of the objective.

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there is an actual prior stage from which the players can update their beliefs) or be considered as a purely formal device (Gul 1998).
The rest of the paper is organised as follows. Section 1 presents the early developments of **Bayesian** game theory with Harsanyi’s initial work on games of incomplete information, and its progressive extension to the case of strategic uncertainty. Section 2 then presents the 1982 debate in Management Science between Kadane and Larkey on the one hand and Harsanyi on the other hand about the proper object of game theory, and especially the role of normative game theory. Section 3 discusses the emergence of modern **Bayesian** game theory in the 1980s and the equivalence between CBR and equilibrium play. Section 4 then highlights the interpretational difficulties of EGT, and the incoherence between the narrative of the theory and its formal structure. Section 5 concludes by discussing the possibility (and probably the necessity) of developing game theoretic models without assuming CBR.

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Unit´e de recherche INRIA Lorraine, Technopˆole de Nancy-Brabois, Campus scientifique, ` NANCY 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LES Unit´e de recherche INRIA Rennes, Ir[r]