Rare-event Simulation and Efficient Discretization for the Supremum of Gaussian Random Fields

In this paper, we consider a classic problem concerning the high excursion probabilities of a Gaussian random field $f$ living on a compact set $T$. We develop efficient computational methods for the tail probabilities $P(\sup_T f(t) > b)$ and the conditional expectations $E(\Gamma(f) | \sup_T f(t) > b)$ as $b\rightarrow \infty$. For each $\varepsilon$ positive, we present Monte Carlo algorithms that run in \emph{constant} time and compute the interesting quantities with $\varepsilon$ relative error for arbitrarily large $b$. The efficiency results are applicable to a large class of H\"older continuous Gaussian random fields. Besides computations, the proposed change of measure and its analysis techniques have several theoretical and practical indications in the asymptotic analysis of extremes of Gaussian random fields

Zaozao Xu’s case: Chinese women’s appeal for the right to freeze their eggs

China’s regulatory framework on assisted reproductive technologies (henceforth ARTs) has remained unchanged and unchallenged for over two decades, prohibiting unmarried women from accessing any form of ARTs. Section 1 Article 4(1) of the Ethical Principles for Human Reproductive Technologies and Human Sperm Banks explicitly stipulates that ‘couples who do not comply with national population and family planning laws and regulations and single women’ are prohibited from accessing ARTs. However, unmarried men are allowed to freeze sperm regardless of their marital status, constituting direct discrimination against women. Furthermore, significant legislative conflicts exist between local regulations and departmental rules in this area, hindering the consistent application of ART norms in China and substantially limiting the reproductive rights of Chinese women. Zaozao Xu’s case is the first case in China directly challenging the current prohibitive regulations on egg freezing and may signify a crucial turning point in China’s reform of ARTs legislation. This commentary provides an overview of the case and examines various issues associated with the existing regulatory framework, including the vagueness of the legislation and regulation, legislative conflicts in the current framework, deeply rooted discrimination against women, and the regulator’s problematic conception of ARTs. This commentary emphasises the urgent need for China to re-evaluate and reform its ARTs regulatory framework to allow unmarried women to access ARTs, or at least egg-freezing services as the first step