It has been widelydocumented that the sampling and resampling steps in particle filters cannot be differentiated. The reparameterisation trick was introduced to allow the sampling step to be reformulated into a differentiable function. We extend the reparameterisation trick to include the stochastic input to resampling therefore limiting the discontinuities in the gradient calculation after this step. Knowing the gradients of the prior and likelihood allows us to run particle Markov Chain Monte Carlo (p-MCMC) and use the No-U-Turn Sampler (NUTS) as the proposal when estimating parameters. We compare the Metropolis-adjusted Langevin algorithm (MALA), Hamiltonian Monte Carlo with different number of steps and NUTS. We consider three state-space models and show that NUTS improves the mixing of the Markov chain and can produce more accurate results in less computational time.

中文翻译：

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在粒子滤波器中使用可微分重采样有效学习非线性模型的参数

已经广泛证明，粒子滤波器中的采样和重采样步骤无法区分。引入了重新参数化技巧，以允许将采样步骤重新表述为可微分函数。我们扩展了重新参数化技巧包括重新采样的随机输入，因此限制了此步骤之后梯度计算中的不连续性。知道先验和似然的梯度允许我们运行粒子马尔可夫链蒙特卡罗（p-MCMC）并在估计参数时使用不掉头采样器（NUTS）作为提议。我们比较了 Metropolis-adjusted Langevin 算法 (MALA)、不同步数的 Hamiltonian Monte Carlo 和 NUTS。我们考虑了三个状态空间模型，并表明 NUTS 改进了马尔可夫链的混合，并且可以在更少的计算时间内产生更准确的结果。