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利用 Laplace 近似进行随机微分方程推断：演示与实例AI 解读

Stochastic differential equations are a natural framework for dynamic systems and time series in ecology, because they allow for non-linear first-principle knowledge and uncertainty in the dynamics, and can be combined with measurement errors. However, estimation methods are often technically and computationally challenging. Here, we demonstrate that the Laplace approximation is useful for estimating states and parameters in these models, when done correctly. We give special…

利用稀疏性提升分层贝叶斯模型的No-U-Turn采样效率AI 解读

Analysts routinely use Bayesian hierarchical models to understand natural processes. The no-U-turn sampler (NUTS) is the most widely used algorithm to sample high-dimensional, continuously differentiable models. But NUTS is slowed by high correlations, especially in high dimensions, limiting the complexity of applied analyses. Here we introduce Sparse NUTS (SNUTS), which preconditions (decorrelates and descales) posteriors using a sparse precision matrix ($Q$). We use…