Making good predictions of a physical system using a computer code requires the inputs to be carefully specified. Some of these inputs, called control variables, reproduce physical conditions whereas other inputs, called parameters, are specific to the computer code and most often uncertain. The goal of statistical calibration consists in reducing their uncertainty with the help of a statistical model which links the code outputs with the field measurements. In a Bayesian setting, the posterior distribution of these parameters is typically sampled using MCMC methods. However, they are impractical when the code runs are highly timeconsuming. A way to circumvent this issue consists of replacing the computer code with a Gaussian process emulator, then sampling a surrogate posterior distribution based on it. Doing so, calibration is subject to an error which strongly depends on the numerical design of experiments used to fit the emulator. Under the assumption that there is no code discrepancy, we aim to reduce this error by constructing a sequential design by means of the Expected Improvement criterion. Numerical illustrations in several dimensions assess the efficiency of such sequential strategies.

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International audienceWe consider a model for the risk-based design of a flood protection dike, and use probability distributions to represent aleatory uncertainty and possibility distributions to describe the epistemic uncertainty associated to the poorly known parameters of such probability distributions. A hybrid method is introduced to hierarchically propagate the two types of uncertainty, and the results are compared with those of a Monte Carlo-based Dempster-Shafer approach employing independent random sets and a purely probabilistic, two-level Monte Carlo approach: the risk estimates produced are similar to those of the Dempster-Shafer method and more conservative than those of the two-level Monte Carlo approach

The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a case, the estimation of transition probabilities is straightforwardly made by counting one-step moves from a given state to another. In many real-life problems, however, the inference is much more difficult as state sequences are not fully observed, namely the state of each individual is known only for some given values of the time variable. A review of the problem is given, focusing on Monte Carlo Markov Chain (MCMC) algorithms to perform Bayesian inference and evaluate posterior distributions of the transition probabilities in this missing-data framework. Leaning on the dependence between the rows of the transition matrix, an adaptive MCMC mechanism accelerating the classical Metropolis-Hastings algorithm is then proposed and empirically studied.

Complex physical systems are increasingly modeled by computer codes which aim at predicting the reality as accurately as possible. During the last decade, code validation has benefited from a large interest within the scientific community because of the requirement to assess the uncertainty affecting the code outputs. Inspiring from past contributions to this task, a testing procedure is proposed in this paper to decide either a pure code prediction or a discrepancy‐corrected one should be used to provide the best approximation of the physical system. In a particular case where the computer code depends on uncertain parameters, this problem of model selection can be carried out in a Bayesian setting. It requires the specification of proper prior distributions that are well known as having a strong impact on the results. Another way consists in specifying non‐informative priors. However, they are sometimes improper, which is a major barrier for computing the Bayes factor. A way to overcome this issue is to use the so‐called intrinsic Bayes factor (IBF) in order to replace the ill‐defined Bayes factor when improper priors are used. For computer codes which depend linearly on their parameters, the computation of the IBF is made easier, thanks to some explicit marginalization. In the paper, we present a special case where the IBF is equal to the standard Bayes factor when the right‐Haar prior is specified on the code parameters and the scale of the code discrepancy. On simulated data, the IBF has been computed for several prior distributions. A confounding effect between the code discrepancy and the linear code is pointed out. Finally, the IBF is computed for an industrial computer code used for monitoring power plant production. Copyright © 2016 John Wiley & Sons, Ltd.