论文标题
连续时间隐藏的马尔可夫模型，具有COX过程观察模型的脱偏粒子过滤
De-biasing particle filtering for a continuous time hidden Markov model with a Cox process observation model
论文作者
论文摘要
我们为特定类别的连续时间空间模型开发了一种（几乎）无偏的粒子过滤算法，因此（a）潜在过程$ x_t $是线性高斯扩散； （b）观察结果来自强度$λ（x_t）$的泊松过程。潜在过程的后验概率密度函数的可能性包括一个棘手的路径积分。我们的算法取决于泊松估计，该估计几乎是公正的。我们展示了如何调整这些泊松估计值，以确保算法产生的一些估计值以外的概率很大。然后将负估计替换为零会导致偏差要比通过离散化获得的偏差要小得多。我们量化了某些特殊情况下负估计的概率，并表明我们的粒子过滤器有效地公正。我们将我们的方法应用于具有出生和狼观察模型的具有挑战性的3D单分子跟踪示例。
We develop a (nearly) unbiased particle filtering algorithm for a specific class of continuous-time state-space models, such that (a) the latent process $X_t$ is a linear Gaussian diffusion; and (b) the observations arise from a Poisson process with intensity $λ(X_t)$. The likelihood of the posterior probability density function of the latent process includes an intractable path integral. Our algorithm relies on Poisson estimates which approximate unbiasedly this integral. We show how we can tune these Poisson estimates to ensure that, with large probability, all but a few of the estimates generated by the algorithm are positive. Then replacing the negative estimates by zero leads to a much smaller bias than what would obtain through discretisation. We quantify the probability of negative estimates for certain special cases and show that our particle filter is effectively unbiased. We apply our method to a challenging 3D single molecule tracking example with a Born and Wolf observation model.
