In geostatistics, block likelihood offers a balance between statistical accuracy and computational efficiency when estimating covariance functions. This balance is reached by dividing the sample into blocks and computing a weighted sum of (sub) log-likelihoods corresponding to pairs of blocks. Practitioners often choose block sizes ranging from hundreds to a few thousand observations, inherently involving matrix-based implementations. An alternative, residing at the opposite end of this methodological spectrum, treats each observation as a block, resulting in the matrix-free pairwise likelihood method. We propose an additional alternative within this broad methodological landscape, systematically constructing blocks of size two and merging pairs of blocks through conditioning. Importantly, our method strategically avoids large-sized blocks, facilitating explicit calculations that ultimately do not rely on matrix computations. Studies with both simulated and real data validate the effectiveness of our approach, on one hand demonstrating its superiority over pairwise likelihood, and on the other, challenging the intuitive notion that employing matrix-based versions universally lead to better statistical performance.

翻译：在地统计学中，当估计协方差函数时，块似然法在统计准确性与计算效率之间取得了平衡。该平衡通过将样本划分为多个块，并计算对应块对（子）对数似然的加权和来实现。实践中，研究者通常选择包含数百至数千个观测值的块大小，这本质上涉及基于矩阵的实现。另一种处于该方法论光谱对立端的替代方案，将每个观测值视为独立块，从而引出无矩阵的成对似然方法。我们在这一广阔方法论框架内提出另一替代方案：系统性地构建大小为二的块，并通过条件化合并块对。关键的是，我们的方法策略性地避免了大尺寸块，使得显式计算最终不依赖矩阵运算成为可能。基于模拟数据与真实数据的研究验证了该方法的有效性：一方面证明了其优于成对似然法，另一方面挑战了"采用基于矩阵版本必然带来更优统计性能"的直觉认知。