Research Article
Spatio-Temporal Random Effects Modeling of Malaria Incidence and Mortality in Kenya
Issue:
Volume 15, Issue 1, February 2026
Pages:
1-11
Received:
22 October 2025
Accepted:
5 December 2025
Published:
16 January 2026
DOI:
10.11648/j.ajtas.20261501.11
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Abstract: Malaria is a major public health challenge in sub-Saharan Africa, with transmission patterns that vary significantly across space and time due to environmental, socioeconomic, and epidemiological factors. These variations complicate efforts to design effective and targeted interventions, making it crucial to understand the dynamics of disease spread. This study employed Bayesian spatio-temporal random effects modeling framework to analyze malaria incidence and mortality ratio across Kenya. The approach incorporated spatial and temporal dependencies to provide a detailed understanding of malaria incidence and mortality risk patterns. Spatial random effects were modeled using conditional autoregressive (CAR) priors to account for correlations among neighboring counties, while temporal dependence was captured using autoregressive processes of order two (AR2), reflecting trends over multiple time periods. An evaluation was on the performance of Spatio-Temporal Poisson Linear Trend Model (STPLM), Spatio-Temporal Poisson ANOVA Model (STPAM), Spatio-Temporal Poisson Separable Model (STPSM) and Poisson Temporal Model for Spatio-Temporal Effects (PTSTN)using the Deviance Information Criterion (DIC), the effective number of parameters (p.d) and the Log Marginal Pseudo-Likelihood (LMPL). The Spatio-Temporal Poisson ANOVA Model (STPAM) was found as the best Poissson Spatial-Temporal Model and was used to develop a multivariate spatio-temporal model for the joint modeling of malaria incidence and mortality. Using the developed model, the study identified significant spatial clustering of malaria, with persistent high-risk zones in western and coastal counties. Temporal trends indicated an overall decline in transmission, though progress was uneven across counties, reflecting differences in intervention coverage, healthcare access, and local epidemiology. These findings underscored the value of multivariate spatio-temporal modeling of malaria incidence and mortality for guiding malaria control strategies. This study thus demonstrates that Bayesian Spatial-Temporal modeling is essential for understanding heterogeneous malaria incidence and mortality risk and informing strategies aimed at reducing disease burden and advancing toward malaria elimination in Kenya.
Abstract: Malaria is a major public health challenge in sub-Saharan Africa, with transmission patterns that vary significantly across space and time due to environmental, socioeconomic, and epidemiological factors. These variations complicate efforts to design effective and targeted interventions, making it crucial to understand the dynamics of disease sprea...
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Research Article
Second Order Properties of Nearest Neighbor Regression with Uniform Weighting Function for Strongly Mixing Processes
Patrick Rakotomarolahy*
Issue:
Volume 15, Issue 1, February 2026
Pages:
12-18
Received:
24 November 2025
Accepted:
11 December 2025
Published:
16 January 2026
DOI:
10.11648/j.ajtas.20261501.12
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Abstract: We examine the statistical properties of nearest neighbor regression function estimation beyond the classical i.i.d assumption. Second-order properties of this estimator for uniformly mixing processes have been derived in previous studies. Nevertheless, uniform mixing is a very strong form of dependence that is difficult to achieve. In contrast, strong mixing conditions are satisfied by a broad class of stochastic processes commonly encountered in theoretical and applied time series modeling. This paper focuses on the analysis of the second-order properties of the nearest neighbor regression estimator under strong mixing dependence measure. Under appropriate regularity conditions, including strong mixing assumptions and smoothness of the underlying density functions, we derive expressions for both the bias and the quadratic mean squared error (QMSE) of the nearest neighbor regression estimator with a uniform weighting scheme for estimating the unknown conditional mean function. Our results demonstrate that the QMSE of the nearest neighbor estimator attains the minimax-optimal rate for estimating a p-smooth regression function in a d-dimensional embedding space. The theoretical analysis integrates the dependence structure specific to strongly mixing processes with the geometric characteristics of k-nearest neighborhoods. This combination enables the identification of an optimal choice for the number of nearest neighbors that effectively balances the trade-off between bias and variance. Overall, these findings provide a rigorous theoretical foundation for the application of nearest neighbor regression methods to short-range dependent data. Furthermore, the explicit bias and variance characterizations lay the groundwork for establishing asymptotic normality, thereby enabling the construction of valid confidence intervals and supporting reliable statistical inference in dependent data settings.
Abstract: We examine the statistical properties of nearest neighbor regression function estimation beyond the classical i.i.d assumption. Second-order properties of this estimator for uniformly mixing processes have been derived in previous studies. Nevertheless, uniform mixing is a very strong form of dependence that is difficult to achieve. In contrast, st...
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