Hidden Markov models (HMMs) are general purpose models for time-series data widely used across the sciences because of their flexibility and elegance. Fitting HMMs can often be computationally demanding and time consuming, particularly when the number of hidden states is large or the Markov chain itself is long. Here we introduce a new Graphical Processing Unit (GPU)-based algorithm designed to fit long-chain HMMs, applying our approach to a model for low-frequency tremor events. Even on a modest GPU, our implementation resulted in an increase in speed of several orders of magnitude compared to the standard single processor algorithm. This permitted a full Bayesian inference of uncertainty related to model parameters and forecasts based on posterior predictive distributions. Similar improvements would be expected for HMM models given large number of observations and moderate state spaces ($<80$ states with current hardware). We discuss the model, general GPU architecture and algorithms and report performance of the method on a tremor dataset from the Shikoku region, Japan. The new approach led to improvements in both computational performance and forecast accuracy, compared to existing frequentist methodology.

隐马尔可夫模型 (HMM) 是时间序列数据的通用模型，因其灵活性和优雅性而被广泛应用于各个科学领域。拟合 HMM 通常需要大量计算和耗时，特别是当隐藏状态的数量很大或马尔可夫链本身很长时。在这里，我们介绍了一种新的基于图形处理单元 (GPU) 的算法，旨在适合长链 HMM，将我们的方法应用于低频震颤事件的模型。即使在适度的 GPU 上，与标准的单处理器算法相比，我们的实现也使速度提高了几个数量级。这允许基于后验预测分布对与模型参数和预测相关的不确定性进行完整的贝叶斯推断。$<80$当前硬件的状态）。我们讨论了模型、通用 GPU 架构和算法，并报告了该方法在日本四国地区的震颤数据集上的性能。与现有的频率论方法相比，新方法提高了计算性能和预测准确性。