When a hidden Markov model permits the conditional likelihood of an observation given the hidden process to be zero, all particle simulations from one observation time to the next could produce zeros. If so, the filtering distribution cannot be estimated and the estimated parameter likelihood is zero. The alive particle filter addresses this by simulating a random number of particles for each inter-observation interval, stopping after a target number of non-zero conditional likelihoods. For outlying observations or poor parameter values, a non-zero result can be extremely unlikely, and computational costs prohibitive. We introduce the Frankenfilter, a principled, partially alive particle filter that targets a user-defined amount of success whilst fixing lower and upper bounds on the number of simulations. The Frankenfilter produces unbiased estimators of the likelihood, suitable for pseudo-marginal Metropolis--Hastings (PMMH). We demonstrate that PMMH with the Frankenfilter is more robust to outliers and mis-specified initial parameter values than PMMH using standard particle filters, and is typically at least 2-3 times more efficient. We also provide advice for choosing the amount of success. In the case of n exact observations, this is particularly simple: target n successes.

翻译：当隐马尔可夫模型允许给定隐过程的观测条件似然为零时，从一个观测时刻到下一个时刻的所有粒子模拟都可能产生零值。若如此，则无法估计滤波分布，且估计的参数似然为零。存活粒子滤波器通过为每个观测间隔模拟随机数量的粒子来解决此问题，在达到目标数量的非零条件似然后停止。对于异常观测或较差的参数值，获得非零结果的可能性极低，且计算成本过高。我们提出了Frankenfilter，一种基于原则的、部分存活的粒子滤波器，它在固定模拟次数上下限的同时，以用户定义的成功量为目标。Frankenfilter产生无偏的似然估计量，适用于伪边际Metropolis-Hastings（PMMH）算法。我们证明，与使用标准粒子滤波器的PMMH相比，采用Frankenfilter的PMMH对异常值和初始参数值设定错误具有更强的鲁棒性，且通常效率至少提高2-3倍。我们还提供了关于如何选择成功量的建议。在n次精确观测的情况下，这尤其简单：以n次成功为目标。