8 problems

Let $I^+(\theta,t)$ denote the active information of a stochastic algorithm that starts randomly according to the null distribution of a non-guided algorithm and then performs $t$…

The expected squared jump distance scaling constant $h(\ell)$ is defined by … where $\Phi$ is the standard Normal cumulative distribution function and $\ell$ is the limiting rescal…

Convergence-rate conjecture. The convergence rate of MTM-IS($k$) without replacement is faster than

Let $P$ be the target measure on spanning forests and linking edges. A state has the form $S=(T,L)$, where $T$ is a multi-scale hierarchical forest and $L$ is a linking edge set; p…

The paper considers rough target densities and the anomalous scaling behavior of Metropolis–Hastings chains exhibited by its examples. Typicality conjecture. Despite the examples b…

Let $(X_n,Y_n)_{n\in\mathbb{N}}$ be an augmented Metropolis-Hastings Markov chain with stationary initial distribution, so that $X_1\sim\mu$, and let $f\colon G\to\mathbb{R}$ be bo…

Let $P_s$ and $P_m$ be pseudo-marginal Metropolis--Hastings kernels formed by averaging $s\leq m$ estimators, and let $\mathrm{V}(\varphi,P_k)$ denote the asymptotic variance of an…

Spectral-radius conjecture. For $q\leq q_0$, where $q_0\approx 0.35$, one has