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Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from high-dimensional distributions in Statistics and Machine learning. HMC is known to run very efficiently in practice and its popular second-order "leapfrog" implementation has long bee ...
How many samples are sufficient to guarantee that the eigenvectors and eigenvalues of the sample covariance matrix are close to those of the actual covariance matrix? For a wide family of distributions, including distributions with finite second moment and ...
We investigate the effect of limiting the number of reserve prices on the revenue in a probabilistic single item auction. In the model considered, bidders compete for an impression drawn from a known distribution of possible types. The auction mechanism se ...
Dynamic optimization problems affected by uncertainty are ubiquitous in many application domains. Decision makers typically model the uncertainty through random variables governed by a probability distribution. If the distribution is precisely known, then ...
The currently adopted practice for uncertainty quantification of thermal-hydraulics code predictions is done through statistical sampling where the code is evaluated multiple times using different values of input parameters that are randomly generated acco ...
The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and mai ...
We consider the stochastic wave equation on the real line driven by space time white noise and with irregular initial data. We give bounds on higher moments and, for the hyperbolic Anderson model, explicit formulas for second moments. These bounds imply we ...
We present a risk-averse multi-dimensional newsvendor model for a class of products whose demands are strongly correlated and subject to fashion trends that are not fully understood at the time when orders are placed. The demand distribution is known to be ...
There have been many studies on the spatial configuration of cities, but few attempts to quantify the difference in building patterns between the old and new parts of cities. This may be partly attributable to lack of suitable study methods. This paper pre ...
We adopt an innovation-driven framework and investigate the sparse/compressible distributions obtained by linearly measuring or expanding continuous-domain stochastic models. Starting from the first principles, we show that all such distributions are neces ...
