arXiv subjects

Anjana Wijayawardhana

Publications and source records attributed to Anjana Wijayawardhana.

3 recordsLinked to original sources

arXiv2025

Bayesian Inference for Non-Gaussian Simultaneous Autoregressive Models with Missing Data

Standard simultaneous autoregressive (SAR) models typically assume normally distributed errors, an assumption often violated in real-world datasets that frequently exhibit non-normal, skewed, or heavy-tailed characteristics. New SAR models are proposed to capture these non-Gaussian features. The spatial error model (SEM), a widely used SAR-type model, is considered. Three novel SEMs are introduced, extending the standard Gaussian SEM. These extensions incorporate Student's $t$-distributed errors to accommodate heavy-tailed behaviour, one-to-one transformations of the response variable to address skewness, or a combination of both. Variational Bayes (VB) estimation methods are developed for these models, and the framework is further extended to handle missing response data under the missing not at random (MNAR) mechanism. Standard VB methods perform well with complete datasets; however, handling missing data requires a hybrid VB (HVB) approach, which integrates a Markov chain Monte Carlo (MCMC) sampler to generate missing values. The proposed VB methods are evaluated using both simulated and real-world datasets, demonstrating their robustness and effectiveness in dealing with non-Gaussian data and missing data in spatial models. Although the method is demonstrated using SAR models, the proposed model specifications and estimation approaches are widely applicable to various types of models for handling non-Gaussian data with missing values.

stat.ME↗

arXiv2024

A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing Data

Efficient estimation methods for simultaneous autoregressive (SAR) models with missing data in the response variable have been well-explored in the literature. A common practice is to introduce measurement error into SAR models to separate the noise component from the spatial process. However, prior research has not considered incorporating measurement error into SAR models with missing data. Maximum likelihood estimation for such models, especially with large datasets, poses significant computational challenges. This paper proposes an efficient likelihood-based estimation method, the marginal maximum likelihood (ML), for estimating SAR models on large datasets with measurement errors and a high percentage of missing data in the response variable. The spatial error model (SEM) and the spatial autoregressive model (SAM), two popular SAR model types, are considered. The missing data mechanism is assumed to follow a missing at random (MAR) pattern. We propose a fast method for marginal ML estimation with a computational complexity of $O(n^{3/2})$, where $n$ is the total number of observations. This complexity applies when the spatial weight matrix is constructed based on a local neighbourhood structure. The effectiveness of the proposed methods is demonstrated through simulations and real-world data applications.

stat.ME↗

arXiv2024

Variational Bayes Inference for Spatial Error Models with Missing Data

The spatial error model (SEM) is a type of simultaneous autoregressive (SAR) model for analysing spatially correlated data. Markov chain Monte Carlo (MCMC) is one of the most widely used Bayesian methods for estimating SEM, but it has significant limitations when it comes to handling missing data in the response variable due to its high computational cost. Variational Bayes (VB) approximation offers an alternative solution to this problem. Two VB-based algorithms employing Gaussian variational approximation with factor covariance structure are presented, joint VB (JVB) and hybrid VB (HVB), suitable for both missing at random and not at random inference. When dealing with many missing values, the JVB is inaccurate, and the standard HVB algorithm struggles to achieve accurate inferences. Our modified versions of HVB enable accurate inference within a reasonable computational time, thus improving its performance. The performance of the VB methods is evaluated using simulated and real datasets.

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