Trade-Offs in Statistical and Machine-Learning-Based Imputation for Algal Time-Series: A Multi-Criteria Evaluation on Optical Density Data Without Ground Truth

Abstract

Missing values are pervasive in algal cultivation monitoring, where instrument failure and transmission loss remove whole runs of consecutive observations, and the repair method chosen silently shapes every downstream analysis. This study asks which repair method should be used, and on what evidence, when no complete reference series exists. Twelve methods are compared on optical density and ten covariates recorded across 30 open-pond production cycles at five geographically distinct sites: four interpolation schemes, a propagation scheme, two nearest-neighbour schemes, three chained-equation variants, a random-forest ensemble and a mechanistic growth-curve fit. The principal contribution is a validation framework organised in two clearly separate tiers. The first tier needs no ground truth and applies to the naturally missing values, comparing central tendency, dispersion, distributional shape, autocorrelation structure and coverage between observed and repaired series. The second tier withholds values that were in fact recorded and rebuilds them, so reconstruction error can be measured directly; it is replicated over ten random seeds, three masking proportions and four contiguous outage lengths, giving 25,200 paired evaluations in which every method sees an identical pattern of withhold cells. Key findings found that no method dominates. Ensemble and chained-equation learners rebuild individual values most accurately, with a normalised error of 0.1927 against 0.2645 for linear interpolation, but they compress dispersion and distort distributional shape, whereas shape-preserving interpolation and propagation protect those properties and rebuild less accurately. Gap structure matters: interpolation loses accuracy when gaps are contiguous rather than scattered, while multivariate learners gain. Regularising the chained equations removes a convergence failure that left one pond unrepaired. An aggregated decision analysis turns these trade-offs into a weight-dependent selection rule, giving practitioners an auditable basis for matching method to analytical objective instead of a single universal default.