This paper aims to extend the Besag model, a widely used Bayesian spatial model in disease mapping, to a non-stationary spatial model for irregular lattice-type data. The goal is to improve the model\'s ability to capture complex spatial dependence patterns and increase interpretability. The proposed model uses multiple precision parameters, accounting for different intensities of spatial dependence in different sub-regions. We derive a joint penalized complexity prior to the flexible local precision parameters to prevent overfitting and ensure contraction to the stationary model at a user-defined rate. The proposed methodology can be used as a basis for the development of various other non-stationary effects over other domains such as time. An accompanying R package fbesag equips the reader with the necessary tools for immediate use and application. We illustrate the novelty of the proposal by modeling the risk of dengue in Brazil, where the stationary spatial assumption fails and interesting risk profiles are estimated when accounting for spatial non-stationary. Additionally, we model different causes of death in Brazil, where we use the new model to investigate the spatial stationarity of these causes.

Despite a decrease in the prevalence of low birth weight (LBW) over time, its ongoing significance as a public health concern in Bangladesh remains evident. Low birth weight is believed to be a contributing factor to infant mortality, prolonged health complications, and vulnerability to non-communicable diseases. This study utilizes nationally representative data from the Multiple Indicator Cluster Surveys (MICS) conducted in 2012-2013 and 2019 to explore factors associated with birth weight. Modeling birth weight data considers interactions among factors, clustering in data, and spatial correlation. District-level maps are generated to identify high-risk areas for LBW. The average birth weight has shown a modest increase, rising from 2.93 kg in 2012-2013 to 2.96 kg in 2019. The study employs a regression tree, a popular machine learning algorithm, to discern essential interactions among potential determinants of birth weight. Findings from various models, including fixed effect, mixed effect, and spatial dependence models, highlight the significance of factors such as maternal age, household head\'s education, antenatal care, and few data-driven interactions influencing birth weight. District-specific maps reveal lower average birth weights in the southwestern region and selected northern districts, persisting across the two survey periods. Accounting for hierarchical structure and spatial autocorrelation improves model performance, particularly when fitting the most recent round of survey data. The study aims to inform policy formulation and targeted interventions at the district level by utilizing a machine learning technique and regression models to identify vulnerable groups of children requiring heightened attention.

The novel coronavirus disease (COVID-19) has spread rapidly across the world in a short period of time and with a heterogeneous pattern. Understanding the underlying temporal and spatial dynamics in the spread of COVID-19 can result in informed and timely public health policies. In this paper, we use a spatio-temporal stochastic model to explain the temporal and spatial variations in the daily number of new confirmed cases in Spain, Italy and Germany from late February 2020 to mid January 2021. Using a hierarchical Bayesian framework, we found that the temporal trends of the epidemic in the three countries rapidly reached their peaks and slowly started to decline at the beginning of April and then increased and reached their second maximum in the middle of November. However decline and increase of the temporal trend seems to show different patterns in Spain, Italy and Germany.