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In parasitological surveillance of livestock, prevalence surveys are conducted on a sample of farms using several sampling designs. For example, opportunistic surveys or informative sampling designs are very common. Preferential sampling refers to any situation in which the spatial process and the sampling locations are not independent. Most examples of preferential sampling in the spatial statistics literature are in environmental statistics with focus on pollutant monitors, and it has been shown that, if preferential sampling is present and is not accounted for in the statistical modelling and data analysis, statistical inference can be misleading. In this paper, working in the context of veterinary parasitology, we propose and use geostatistical models to predict the continuous and spatially-varying risk of a parasite infection. Specifically, breaking with the common practice in veterinary parasitological surveillance to ignore preferential sampling even though informative or opportunistic samples are very common, we specify a two-stage hierarchical Bayesian model that adjusts for preferential sampling and we apply it to data on Fasciola hepatica infection in sheep farms in Campania region (Southern Italy) in the years 2013-2014.

In this paper the focus is on environmental statistics, with the aim of estimating the concentration surface and related uncertainty of an air pollutant. We used air quality data recorded by a network of monitoring stations within a Bayesian framework to overcome difficulties in accounting for prediction uncertainty and to integrate information provided by deterministic models based on emissions meteorology and chemico-physical characteristics of the atmosphere. Several authors have proposed such integration, but all the proposed approaches rely on representativeness and completeness of existing air pollution monitoring networks. We considered the situation in which the spatial process of interest and the sampling locations are not independent. This is known in the literature as the preferential sampling problem, which if ignored in the analysis, can bias geostatistical inferences. We developed a Bayesian geostatistical model to account for preferential sampling with the main interest in statistical integration and uncertainty. We used PM10 data arising from the air quality network of the Environmental Protection Agency of Lombardy Region (Italy) and numerical outputs from the deterministic model. We specified an inhomogeneous Poisson process for the sampling locations intensities and a shared spatial random component model for the dependence between the spatial location of monitors and the pollution surface. We found greater predicted standard deviation differences in areas not properly covered by the air quality network. In conclusion, in this context inferences on prediction uncertainty may be misleading when geostatistical modelling does not take into account preferential sampling.

Fasciola hepatica infection challenges health, welfare and productivity of small ruminants throughout the world. The distribution of F. hepatica in sheep in Europe is usually scattered and studies are generally concerned with a single area making it difficult to compare results from different environments, climates and management regimes. In order to elucidate the current scenario in terms of prevalence and intensity of F. hepatica infection in sheep farms across Europe, a standardized cross-sectional survey was conducted in three pilot areas in Ireland, Switzerland and Italy, all part of the EU funded GLOWORM project. Two consecutive field surveys (in 2012 and 2013) were conducted in the three countries in the same period (August-October) in 361 sheep farms in total. Harmonized procedures (from farm to laboratory) based on pooled samples and the highly sensitive and accurate, diagnostic FLOTAC technique were used. The georeferenced parasitological results were modelled (at the pilot area level) following a Bayesian geostatistical approach with correction for preferential sampling and accounting for climatic and environmental covariates. The observed F. hepatica prevalence rates did not differ between the two study years in any of the three pilot areas, but they did vary between the countries showing high values in Ireland (61.6%) compared to Italy (7.9%) and Switzerland (4.0%). Spatial patterns of F. hepatica distribution were detected by the Bayesian geostatistical approach in Ireland with a high risk of infection in the south-western part of the pilot area there. The latent factor analysis highlighted the importance of year-to-year variation of mean temperature, rainfall and seasonality within a country, while long-term trends of temperature and rainfall dominated between countries with respect to prevalence of infection.

A core challenge in epidemiological analysis of the impact of exposure to air pollution on health is assessment of the individual exposure for subjects at risk. Geographical information systems (GIS)-based pollution mapping, such as kriging, has become one of the main tools for evaluating individual exposure to ambient pollutants. We applied universal Bayesian kriging to estimate the residential exposure to gaseous air pollutants for children living in a high-risk area (Milazzo- Valle del Mela in Sicily, Italy). Ad hoc air quality monitoring campaigns were carried out: 12 weekly measurements for sulphur dioxide (SO2) and nitrogen dioxide (NO2) were obtained from 21 passive dosimeters located at each school yard of the study area from November 2007 to April 2008. Universal Bayesian kriging was performed to predict individual exposure levels at each residential address for all 6- to 12-years-old children attending primary school at various locations in the study area. Land use, altitude, distance to main roads and population density were included as covariates in the models. A large geographical heterogeneity in air quality was recorded suggesting complex exposure patterns. We obtained a predicted mean level of 25.78 (± 10.61) µg/m(3) of NO2 and 4.10 (± 2.71) µg/m(3) of SO2 at 1,682 children's residential addresses, with a normalised root mean squared error of 28% and 25%, respectively. We conclude that universal Bayesian kriging approach is a useful tool for the assessment of realistic exposure estimates with regard to ambient pollutants at home addresses. Its prediction uncertainty is highly informative and can be used for both designing subsequent campaigns and for improved modelling of epidemiological associations.