In this work we provide analytical and closed-form expressions for the exact computation of the score and the observed Fisher information matrix in a Gaussian random walk observed through Gaussian noise. Our method is based on the Oakes' identity and, as for the computation of the log-likelihood, its complexity in time is linear in the length of the sequence with the forward-backward (or Baum-Welch) algorithm. We illustrate the method over various simulation studies and provide parameter estimates computed with the Newton-Raphson algorithm along with confidence intervals.

翻译：本文针对通过高斯噪声观测的高斯随机游走模型，给出了得分函数和观测Fisher信息矩阵精确计算的解析闭式表达式。该方法基于Oakes恒等式，与对数似然计算类似，其时间复杂度通过前向-后向（或Baum-Welch）算法实现序列长度的线性增长。我们通过多种模拟研究验证了该方法，并利用Newton-Raphson算法计算参数估计值及其置信区间。