Calibration and improved prediction of computer models by universal Kriging

This paper addresses the use of experimental data for calibrating a computer model and improving its predictions of the underlying physical system. A global statistical approach is proposed in which the bias between the computer model and the physical system is modeled as a realization of a Gaussian process. The application of classical statistical inference to this statistical model yields a rigorous method for calibrating the computer model and for adding to its predictions a statistical correction based on experimental data. This statistical correction can substantially improve the calibrated computer model for predicting the physical system on new experimental conditions. Furthermore, a quantification of the uncertainty of this prediction is provided. Physical expertise on the calibration parameters can also be taken into account in a Bayesian framework. Finally, the method is applied to the thermal-hydraulic code FLICA 4, in a single phase friction model framework. It allows to improve the predictions of the thermal-hydraulic code FLICA 4 significantly

Real-time Planning as Decision-making Under Uncertainty

In real-time planning, an agent must select the next action to take within a fixed time bound. Many popular real-time heuristic search methods approach this by expanding nodes using time-limited A* and selecting the action leading toward the frontier node with the lowest f value. In this thesis, we reconsider real-time planning as a problem of decision-making under uncertainty. We treat heuristic values as uncertain evidence and we explore several backup methods for aggregating this evidence. We then propose a novel lookahead strategy that expands nodes to minimize risk, the expected regret in case a non-optimal action is chosen. We evaluate these methods in a simple synthetic benchmark and the sliding tile puzzle and find that they outperform previous methods. This work illustrates how uncertainty can arise even when solving deterministic planning problems, due to the inherent ignorance of time-limited search algorithms about those portions of the state space that they have not computed, and how an agent can benefit from explicitly meta-reasoning about this uncertainty

On statistics, computation and scalability

How should statistical procedures be designed so as to be scalable computationally to the massive datasets that are increasingly the norm? When coupled with the requirement that an answer to an inferential question be delivered within a certain time budget, this question has significant repercussions for the field of statistics. With the goal of identifying "time-data tradeoffs," we investigate some of the statistical consequences of computational perspectives on scability, in particular divide-and-conquer methodology and hierarchies of convex relaxations.Comment: Published in at http://dx.doi.org/10.3150/12-BEJSP17 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Nonasymptotic bounds on the mean square error for MCMC estimates via renewal techniques

The Nummellin’s split chain construction allows to decompose a Markov chain Monte Carlo (MCMC) trajectory into i.i.d. "excursions". Regenerative MCMC algorithms based on this technique use a random number of samples. They have been proposed as a promising alternative to usual fixed length simulation [25, 33, 14]. In this note we derive nonasymptotic bounds on the mean square error (MSE) of regenerative MCMC estimates via techniques of renewal theory and sequential statistics. These results are applied to costruct confidence intervals. We then focus on two cases of particular interest: chains satisfying the Doeblin condition and a geometric drift condition. Available explicit nonasymptotic results are compared for different schemes of MCMC simulation

The cost of using exact confidence intervals for a binomial proportion

When computing a confidence interval for a binomial proportion p one must choose between using an exact interval, which has a coverage probability of at least 1-{\alpha} for all values of p, and a shorter approximate interval, which may have lower coverage for some p but that on average has coverage equal to 1-\alpha. We investigate the cost of using the exact one and two-sided Clopper--Pearson confidence intervals rather than shorter approximate intervals, first in terms of increased expected length and then in terms of the increase in sample size required to obtain a desired expected length. Using asymptotic expansions, we also give a closed-form formula for determining the sample size for the exact Clopper--Pearson methods. For two-sided intervals, our investigation reveals an interesting connection between the frequentist Clopper--Pearson interval and Bayesian intervals based on noninformative priors