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- W3012491516 abstract "This paper concerns the use of a particular class of determinantal point processes (DPP), a class of repulsive spatial point processes, for Monte Carlo integration.Let $dge 1$, $Isubseteq overline d={1,dots,d}$ with $iota=|I|$. Using a single set of $N$ quadrature points ${u_1,dots,u_N}$ defined, once for all, in dimension $d$ from the realization of the DPP model, we investigate ``minimal'' assumptions on the integrand in order to obtain unbiased Monte Carlo estimates of $mu(f_I)=int_{[0,1]^iota} f_I(u) de u$ for any known $iota$-dimensional integrable function on $[0,1]^iota$. In particular, we show that the resulting estimator has variance with order $N^{-1-(2swedge 1)/d}$ when the integrand belongs to some Sobolev space with regularity $s > 0$. When $s>1/2$ (which includes a large class of non-differentiable functions), the variance is asymptotically explicit and the estimator is shown to satisfy a Central Limit Theorem." @default.
- W3012491516 created "2020-03-23" @default.
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- W3012491516 date "2021-01-01" @default.
- W3012491516 modified "2023-10-18" @default.
- W3012491516 title "Monte Carlo integration of non-differentiable functions on $[0,1]^iota$, $iota=1,dots,d$ , using a single determinantal point pattern defined on $[0,1]^d$" @default.
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- W3012491516 doi "https://doi.org/10.1214/21-ejs1929" @default.
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