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Question What is an effective way for sampling from $P_\epsilon$ given that sampling from $P$ is easy ? …

Generalization: Given two distributions $\pi_0$ and $\pi_1$ on the states, prescribe a procedure for sampling a path $x =: s_0 \rightarrow s_1 \rightarrow \ldots \rightarrow s_T = y$, such that $x$ is … N.B.: If $\pi_0 := \delta_x$ and $\pi_1 = \delta_y$, then this problem reduces to the first part, i.e it demands just the sampling of a random path between $x$ and $y$ If $\pi_0 = \pi_1$, then the computed …

Is there an efficient way to compute $e_j^\mu(T)$ which is "cheaper" (in the sense faster convergence / lower variance of estimates) than just sampling $x_1,\ldots, x_M \sim \mu$ and computing the empirical …

the most popular way to sample from a polytope (in H-representation) \begin{equation} \mathcal{P} := \{z \in \mathbb{R}^n | (Az)_j \le b_j\; \forall j=1,2,\ldots,m\} \end{equation} is to do rejection-sampling … So, in this limiting case, rejection-sampling using $\mathcal{B}$, is very ineffective (almost all drawn points will be rejected). …

N.B.: Sorry for cross-posting from https://stats.stackexchange.com/posts/347804/edit (I realized it was the wrong venue for the question, but couldn't find an easy way to transfer the question here). …

Let $(X,Y)$ be a pair of random variables on a measure space $\mathcal T \subseteq \text{"subsets of }\mathbb R^2\text{"}$, with joint probability distribution $P$. We don't assume $X$ and $Y$ are in …