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

Assessing the Competitiveness of Matrix-Free Block Likelihood Estimation in Spatial Models