8 papers
A simple algorithm for global sensitivity analysis with Shapley effects
Takashi Goda
Global sensitivity analysis aims at measuring the relative importance of different variables or groups of variables for the variability of a quantity of interest. Among several sen…
Toeplitz Monte Carlo
Josef Dick, Takashi Goda, Hiroya Murata
Motivated mainly by applications to partial differential equations with random coefficients, we introduce a new class of Monte Carlo estimators, called Toeplitz Monte Carlo (TMC) e…
Efficient Debiased Evidence Estimation by Multilevel Monte Carlo Sampling
Kei Ishikawa, Takashi Goda
In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators o…
Multilevel Monte Carlo estimation of log marginal likelihood
Takashi Goda, Kei Ishikawa
In this short note we provide an unbiased multilevel Monte Carlo estimator of the log marginal likelihood and discuss its application to variational Bayes.
Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm
Josef Dick, Takashi Goda
We study quasi-Monte Carlo (QMC) methods for numerical integration of multivariate functions defined over the high-dimensional unit cube. Lattice rules and polynomial lattice rules…
Multilevel Monte Carlo estimation of the expected value of sample information
Tomohiko Hironaka, Michael B. Giles, Takashi Goda +1
We study Monte Carlo estimation of the expected value of sample information (EVSI) which measures the expected benefit of gaining additional information for decision making under u…