Laplace Approximation Research Articles

Analysis on driving factors of microbial community succession in Jiuyao of Shaoxing Huangjiu (Chinese yellow rice wine)

The microbial ecosystem of fermented food is greatly disturbed by human activities.Jiuyao is important saccharification starter for brewing huangjiu. The interaction between environmental factors and microorganisms significantly affected the microbial community structure at different stages of Jiuyao manufacturing. This study combined environmental factor analysis and high-throughput sequencing technology to comprehensively analyze the specific changes of microbial community and environmental factors in each fermentation stage of Jiuyao production and their correlation. The results showed that the activities of liquefaction enzyme, glycosylation enzyme and acid protease reached the highest value on the 8 th day (192 h) after the beginning of fermentation, and the cellulase activity reached the highest value at the end of fermentation. Pediococcus（37.5 %-58.2 %）, Weissella（9.2 %-27.0 %） and Pelomonas（0.1 %-12.1 %） were the main microbial genera in the genus bacteria, and Saccharomycopsis（37.1 %-52.0 %）, Rhizopus（12.5 %-31.0 %） and Saccharomyces（4.0 %-20.5 %） were the main microbial genera in the genus fungi. The results of correlation analysis showed that the microbial communities in Jiuyao were closely related to environmental factors. Most microbial communities were positively correlated with temperature, but negatively correlated with ambient humidity, CO2 concentration, acidity and water content of Jiuyao. In addition, the transcription levels of enzymes related to microbial glucose metabolism in Jiuyao were higher in the late stage of Jiuyao fermentation. Interestingly, these enzymes had high transcription levels in fungi such as Saccharomycopsis, Rhizopus and Saccharomyces, as well as in bacteria such as Pediococcus and Lactobacillus. This study provides a reference for revealing the succession rule of microbial community structure caused by environmental factors during the preparation of Jiuyao in Shaoxing Huangjiu.

Does the exponential Wells-Riley model provide a good fit for human coronavirus and rhinovirus? A comparison of four dose-response models based on human challenge data.

The risk assessments during the COVID-19 pandemic were primarily based on dose-response models derived from the pooled datasets for infection of animals susceptible to SARS-CoV. Despite similarities, differences in susceptibility between animals and humans exist for respiratory viruses. The two most commonly used dose-response models for calculating the infection risk of respiratory viruses are the exponential and the Stirling approximated β-Poisson (BP) models. The modified version of the one-parameter exponential model or the Wells-Riley model was almost solely used for infection risk assessments during the pandemic. Still, the two-parameter (α and β) Stirling approximated BP model is often recommended compared to the exponential dose-response model due to its flexibility. However, the Stirling approximation restricts this model to the general rules of β≫1 and α≪β, and these conditions are very often violated. To refrain from these requirements, we tested a novel BP model by using the Laplace approximation of the Kummer hypergeometric function instead of the conservative Stirling approximation. The datasets of human respiratory airborne viruses available in the literature for human coronavirus (HCoV-229E) and human rhinovirus (HRV-16 and HRV-39) are used to compare the four dose-response models. Based on goodness-of-fit criteria, the exponential model was the best fitting model for the HCoV-229E (k=0.054) and for HRV-39 datasets (k=1.0), whereas the Laplace approximated BP model followed by the exact and Stirling approximated BP models are preferred for both the HRV-16 (α=0.152 and β=0.021 for Laplace BP) and the HRV-16 and HRV-39 pooled datasets (α=0.2247 and β=0.0215 for Laplace BP).

Corrigendum to "On the 1/ H -flow by p -Laplace approximation: new estimates via fake distances under Ricci lower bounds [ Amer. J. Math . 144 (2022), no. 3, 779–849

We correct a mistake in our proof of Lemma~2.17. Although we have to strengthen the assumptions therein and, accordingly, in Theorem~2.22, all of the results on the existence and properties of the IMCF are not affected. Minor changes, with no influence elsewhere in the paper, regard Lemma~3.3, Proposition~4.3 and Lemma~5.3.

Bayesian Detectors for Wideband Radar Target With Range Walking in Compound Gaussian Clutter

In this paper, the problem of the wideband radar target detection with the range walking in compound Gaussian clutter without the secondary data is addressed. The wideband radar target return with the range walking is represented as a canonical linear model in the multi-rank subspace, and the clutter is modeled as a two-dimensional random process with separable complex inverse Wishart distributed random covariance matrices in the pulse and range-frequency domains. The generalized likelihood ratio test (GLRT), the Wald test and the Rao test based on the above target and clutter models are designed under the Bayesian framework. The Laplace approximation is adopted to compute the second-kind confluent hypergeometric function of matrix argument (SKCHFMA) in the proposed detectors. Finally, the performance of the detectors is validated by the simulations.

Alzheimer’s disease and other dementias in China: Secular trend in disease burden from 1990 to 2019 and projections to 2030

AbstractBackgroundAlzheimer’s disease and other dementias (ADOD) inflict substantial burden on the individual, family and society. China has the world’s highest number of people living with dementia, but the national‐level secular trends have not been well‐characterized.MethodDrawing on data from the Global Burden of Disease Study 2019, we explored the burden of ADOD in China from 1990 to 2019, including its prevalence, incidence, mortality, years of lost (YLLs), years of life lived with disability (YLDs), disability adjusted life years (DALYs), and attributable specific risk factors. Temporal trends in disease burden were calculated by average annual percentage changes (AAPCs) using log‐linear regression in age‐standardized rates. We utilized Bayesian age‐period‐cohort models with integrated nested Laplace approximations to predict the age‐sex‐specific number of new cases and deaths from 2020 to 2030.ResultThe age‐standardized prevalence, incidence, deaths, YLLs, YLDs and DALYs for ADOD were 788.28, 103.83, 23.32, 254.42, 114.07 and 368.49 per 100,000 population in 2019 respectively, with increasing trends observed (AAPC [95% Confidence Interval]: 0.66% [0.57 to 0.75], 0.33% [0.27 to 0.40], 0.15% [0.07 to 0.23], 0.10% [0.01 to 0.20], 0.65% [0.56 to 0.75], and 0.26% [0.21 to 0.31]) during the past three decades. Although ADOD is more prevalent in females, AAPCs in all indicators were more pronounced in males. More dementia cases were attributable to smoking in males than in females. Proportions of DALYs attributable to high BMI increased over time in both sexes, and the cases attributable to high fasting glucose were comparable in both sexes. Incidence and mortality from ADOD are projected to be 2,967,059 and 527,960 cases in 2030, representing a 1.65‐fold increase.ConclusionIncreasing incidence and mortality due to ADOD will continue in coming years due to population aging, although age‐standardized mortality rates showed a slight decrease. Further research on modifiable risk factors and targeted prevention strategies are warranted.

Spatially resolved self-consistent spectral modelling of jellyfish galaxies from MUSE with FADO: trends with mass and stripping intensity

ABSTRACT We present a spatially resolved stellar population analysis of 61 jellyfish galaxies and 47 control galaxies observed with ESO/MUSE attempting to understand the general trends of the stellar populations as a function of the stripping intensity and mass. This is the public sample from the GASP programme, with 0.01 < z < 0.15 and 8.9 < log (M⋆/M⊙) < 12.0. We apply the spectral population synthesis code fado to fit self-consistently both the stellar and nebular contributions to the spectra of the sources. We present 2D morphological maps for mean stellar ages, metallicities, gas-phase oxygen abundances, and star formation rates for the galaxies with Integrated Nested Laplace Approximation (inla), which is efficient in reconstructing spatial data of extended sources. We find that ‘extreme stripping’ and ‘stripping’ galaxies are typically younger than the other types. Regarding stellar and nebular metallicities, the ‘stripping’ and ‘control passive’ galaxies are the most metal-poor. Based on the phase space for jellyfish cluster members we find trends in ages, metallicities, and abundances with different regions of the diagram. We also compute radial profiles for the same quantities. We find that both the stripping and the stellar masses seem to influence the profiles, and we see differences between various groups and distinct mass bins. The radial profiles for different mass bins present relations already shown in the literature for undisturbed galaxies, i.e. profiles of ages and metallicities tend to increase with mass. However, beyond ∼0.75 effective radius, the ages of the most massive galaxies become similar to or lower than the ages of the lower mass ones.

Climate variability, socio-economic conditions and vulnerability to malaria infections in Mozambique 2016-2018: a spatial temporal analysis.

Temperature, precipitation, relative humidity (RH), and Normalized Different Vegetation Index (NDVI), influence malaria transmission dynamics. However, an understanding of interactions between socioeconomic indicators, environmental factors and malaria incidence can help design interventions to alleviate the high burden of malaria infections on vulnerable populations. Our study thus aimed to investigate the socioeconomic and climatological factors influencing spatial and temporal variability of malaria infections in Mozambique. We used monthly malaria cases from 2016 to 2018 at the district level. We developed an hierarchical spatial-temporal model in a Bayesian framework. Monthly malaria cases were assumed to follow a negative binomial distribution. We used integrated nested Laplace approximation (INLA) in R for Bayesian inference and distributed lag nonlinear modeling (DLNM) framework to explore exposure-response relationships between climate variables and risk of malaria infection in Mozambique, while adjusting for socioeconomic factors. A total of 19,948,295 malaria cases were reported between 2016 and 2018 in Mozambique. Malaria risk increased with higher monthly mean temperatures between 20 and 29°C, at mean temperature of 25°C, the risk of malaria was 3.45 times higher (RR 3.45 [95%CI: 2.37-5.03]). Malaria risk was greatest for NDVI above 0.22. The risk of malaria was 1.34 times higher (1.34 [1.01-1.79]) at monthly RH of 55%. Malaria risk reduced by 26.1%, for total monthly precipitation of 480 mm (0.739 [95%CI: 0.61-0.90]) at lag 2 months, while for lower total monthly precipitation of 10 mm, the risk of malaria was 1.87 times higher (1.87 [1.30-2.69]). After adjusting for climate variables, having lower level of education significantly increased malaria risk (1.034 [1.014-1.054]) and having electricity (0.979 [0.967-0.992]) and sharing toilet facilities (0.957 [0.924-0.991]) significantly reduced malaria risk. Our current study identified lag patterns and association between climate variables and malaria incidence in Mozambique. Extremes in climate variables were associated with an increased risk of malaria transmission, peaks in transmission were varied. Our findings provide insights for designing early warning, prevention, and control strategies to minimize seasonal malaria surges and associated infections in Mozambique a region where Malaria causes substantial burden from illness and deaths.

Spatial age-period-cohort analysis of hepatitis B risk in Xinjiang from 2006 to 2019.

The objective of this study was to investigate the spatio-temporal distribution and epidemiological characteristics of hepatitis B in 96 districts and counties of Xinjiang and to give useful information for hepatitis B prevention and treatment. Based on the incidence data of hepatitis B in 96 districts and counties of Xinjiang from 2006 to 2019, the global trend analysis method was used to characterize the spatial variability of the disease, and the spatial autocorrelation and spatio-temporal aggregation analysis were used to explore the spatial clustering of hepatitis B and to identify high-risk areas and periods. The Integrated Nested Laplace Approximation (INLA)-based spatial age-period-cohort model was established to further explore the influence of age, period, birth queue effect, and spatial distribution on the incidence risk of hepatitis B, and sum-to-zero constraint was adopted to avoid the issue of model unrecognition. The risk of hepatitis B in Xinjiang is increasing from west to east and from north to south, with spatial heterogeneity and spatio-temporal scanning statistics yielding five clustering areas. The spatial age-period-cohort model showed two peaks in the average risk of hepatitis B, at [25,30) years old and [50,55) years old, respectively. The mean risk of hepatitis B incidence fluctuated up and down around 1 with time, and the average risk of disease by birth cohort displayed an increasing-decreasing-stabilizing trend. Taking age, period, and cohort effect into consideration, it was found that the areas with a high risk of hepatitis B are Tianshan District, Xinshi District, Shuimogou District, Changji City, Aksu City, Kashi City, Korla City, Qiemo County and Yopurga County in Xinjiang. According to the spatio-temporal effect item, it was found that there are unobserved variables affecting the incidence of hepatitis B in some districts and counties of Xinjiang. The spatio-temporal characteristics of hepatitis B and the high-risk population needed to be taken into attention. It is suggested that the relevant disease prevention and control centers should strengthen the prevention and control of hepatitis B among young people while paying attention to middle-aged and older adult people, and strengthening the prevention and monitoring of high-risk areas.

Spatial analysis of thunderstorms and lightning casualties in Bangladesh

Considering the adverse outcomes of thunderstorm‐mediated lightning in recent years, this study aimed to identify the most thunderstorm‐and‐casualty prone regions and seasons in Bangladesh, via geospatial mapping. We attempted to forecast the number of yearly thunderstorm (TS) days for each meteorological station and district‐level lightning casualties by using TS days as a proxy variable. Data on TS days and lightning casualties were collected from Bangladesh Meteorological Department and Network for Information, Response And Preparedness Activities on Disaster respectively. This study analysed 629 fatalities and 232 injuries. The Integrated Nested Laplace Approximation with Matern covariance function was employed to assess the spatial pattern of TS days. Polynomial regressions were used to forecast the number of TS days and the single clustered Generalized Estimating Equations method was employed to explore the relationship between the number of TS days and lightning casualties. The results indicated that the mean number of TS days per station increased in recent years, particularly in February, March, April, and September. We found the months of April, May, June, and September to be the most threatening months due to TS events and related casualties. The northeast region was identified as the most TS‐prone region with the highest number of casualties in Bangladesh. Our analysis suggests that it might remain the most hazardous region in coming years.

Random Effects Multinomial Processing Tree Models: A Maximum Likelihood Approach

The present article proposes and evaluates marginal maximum likelihood (ML) estimation methods for hierarchical multinomial processing tree (MPT) models with random and fixed effects. We assume that an identifiable MPT model with S parameters holds for each participant. Of these S parameters, R parameters are assumed to vary randomly between participants, and the remaining S-R parameters are assumed to be fixed. We also propose an extended version of the model that includes effects of covariates on MPT model parameters. Because the likelihood functions of both versions of the model are too complex to be tractable, we propose three numerical methods to approximate the integrals that occur in the likelihood function, namely, the Laplace approximation (LA), adaptive Gauss–Hermite quadrature (AGHQ), and Quasi Monte Carlo (QMC) integration. We compare these three methods in a simulation study and show that AGHQ performs well in terms of both bias and coverage rate. QMC also performs well but the number of responses per participant must be sufficiently large. In contrast, LA fails quite often due to undefined standard errors. We also suggest ML-based methods to test the goodness of fit and to compare models taking model complexity into account. The article closes with an illustrative empirical application and an outlook on possible extensions and future applications of the proposed ML approach.

Mapping the risk of Rift Valley fever in Uganda using national seroprevalence data from cattle, sheep and goats.

Uganda has had repeated outbreaks of Rift Valley fever (RVF) since March 2016 when human and livestock cases were reported in Kabale after a long interval. The disease has a complex and poorly described transmission patterns which involves several mosquito vectors and mammalian hosts (including humans). We conducted a national serosurvey in livestock to determine RVF virus (RVFV) seroprevalence, risk factors, and to develop a risk map that could be used to guide risk-based surveillance and control measures. A total of 3,253 animals from 175 herds were sampled. Serum samples collected were screened at the National Animal Disease Diagnostics and Epidemiology Centre (NADDEC) using a competition multispecies anti-RVF IgG ELISA kit. Data obtained were analyzed using a Bayesian model that utilizes integrated nested Laplace approximation (INLA) and stochastic partial differential equation (SPDE) approaches to estimate posterior distributions of model parameters, and account for spatial autocorrelation. Variables considered included animal level factors (age, sex, species) and multiple environmental data including meteorological factors, soil types, and altitude. A risk map was generated by projecting fitted (mean) values, from a final model that had environmental factors onto a spatial grid that covered the entire domain. The overall RVFV seroprevalence was 11.3% (95% confidence interval: 10.2-12.3%). Higher RVFV seroprevalences were observed in older animals compared to the young, and cattle compared to sheep and goats. RVFV seroprevalence was also higher in areas that had (i) lower precipitation seasonality, (ii) haplic planosols, and (iii) lower cattle density. The risk map generated demonstrated that RVF virus was endemic in several regions including those that have not reported clinical outbreaks in the northeastern part of the country. This work has improved our understanding on spatial distribution of RVFV risk in the country as well as the expected burden of the disease in livestock.

Modeling biomarker variability in joint analysis of longitudinal and time-to-event data.

The role of visit-to-visit variability of a biomarker in predicting related disease has been recognized in medical science. Existing measures of biological variability are criticized for being entangled with random variability resulted from measurement error or being unreliable due to limited measurements per individual. In this article, we propose a new measure to quantify the biological variability of a biomarker by evaluating the fluctuation of each individual-specific trajectory behind longitudinal measurements. Given a mixed-effects model for longitudinal data with the mean function over time specified by cubic splines, our proposed variability measure can be mathematically expressed as a quadratic form of random effects. A Cox model is assumed for time-to-event data by incorporating the defined variability as well as the current level of the underlying longitudinal trajectory as covariates, which, together with the longitudinal model, constitutes the joint modeling framework in this article. Asymptotic properties of maximum likelihood estimators are established for the present joint model. Estimation is implemented via an Expectation-Maximization (EM) algorithm with fully exponential Laplace approximation used in E-step to reduce the computation burden due to the increase of the random effects dimension. Simulation studies are conducted to reveal the advantage of the proposed method over the two-stage method, as well as a simpler joint modeling approach which does not take into account biomarker variability. Finally, we apply our model to investigate the effect of systolic blood pressure variability on cardiovascular events in the Medical Research Council elderly trial, which is also the motivating example for this article.

Does mobility restriction significantly control infectious disease transmission? Accounting for non-stationarity in the impact of COVID-19 based on Bayesian spatially varying coefficient models.

COVID-19 is the most severe health crisis of the 21st century. COVID-19 presents a threat to almost all countries worldwide. The restriction of human mobility is one of the strategies used to control the transmission of COVID-19. However, it has yet to be determined how effective this restriction is in controlling the rise in COVID-19 cases, particularly in small areas. Using Facebook's mobility data, our study explores the impact of restricting human mobility on COVID-19 cases in several small districts in Jakarta, Indonesia. Our main contribution is showing how the restriction of human mobility data can give important information about how COVID-19 spreads in different small areas. We proposed modifying a global regression model into a local regression model by accounting for the spatial and temporal interdependence of COVID-19 transmission across space and time. We applied Bayesian hierarchical Poisson spatiotemporal models with spatially varying regression coefficients to account for non-stationarity in human mobility. We estimated the regression parameters using an Integrated Nested Laplace Approximation. We found that the local regression model with spatially varying regression coefficients outperforms the global regression model based on DIC, WAIC, MPL, and R2 criteria for model selection. In Jakarta's 44 districts, the impact of human mobility varies significantly. The impacts of human mobility on the log relative risk of COVID-19 range from -4.445 to 2.353. The prevention strategy involving the restriction of human mobility may be beneficial in some districts but ineffective in others. Therefore, a cost-effective strategy had to be adopted.

An algorithmic approach based on generating trees for enumerating pattern-avoiding inversion sequences

We introduce an algorithmic approach based on a generating tree method for enumerating the inversion sequences with various pattern-avoidance restrictions. For a given set of patterns, we propose an algorithm that outputs either an accurate description of the succession rules of the corresponding generating tree or an ansatz. By using this approach, we determine the generating trees for the pattern classes In(000,021), In(100,021), In(110,021), In(102,021), In(100,012), In(011,201), In(011,210) and In(120,210). Then we use the kernel method, obtain generating functions of each class, and find enumerating formulas. Lin and Yan studied the classification of the Wilf-equivalences for inversion sequences avoiding pairs of length-three patterns and showed that there are 48 Wilf classes among 78 pairs. In this paper, we solve six open cases for such pattern classes. Moreover, we extend the algorithm to restricted growth sequences and apply it to several classes. In particular, we present explicit formulas for the generating functions of the restricted growth sequences that avoid either {12313,12323}, {12313,12323,12333}, or {123⋯ℓ1}.

Matrix Whittaker processes

We study a discrete-time Markov process on triangular arrays of matrices of size dge 1, driven by inverse Wishart random matrices. The components of the right edge evolve as multiplicative random walks on positive definite matrices with one-sided interactions and can be viewed as a d-dimensional generalisation of log-gamma polymer partition functions. We establish intertwining relations to prove that, for suitable initial configurations of the triangular process, the bottom edge has an autonomous Markovian evolution with an explicit transition kernel. We then show that, for a special singular initial configuration, the fixed-time law of the bottom edge is a matrix Whittaker measure, which we define. To achieve this, we perform a Laplace approximation that requires solving a constrained minimisation problem for certain energy functions of matrix arguments on directed graphs.

Uncertainty quantification in three‐dimensional magnetohydrodynamic equilibrium reconstruction via surrogate‐assisted Bayesian inference

AbstractIn three‐dimensional (3D) equilibrium, reconstruction defining parameters of an ideal magneto‐hydrodynamic equilibrium are inferred from a set of plasma diagnostic measurements. For the reconstructed parameters, various forms of uncertainty estimates exist within common 3D reconstruction frameworks. These estimates often assume a Gaussian posterior distribution. The validity of this assumption is not obvious in such highly nonlinear inverse problems, and therefore the accuracy of the estimates cannot be guaranteed. In this work, we formulate the problem of 3D equilibrium reconstruction in a Bayesian sense and explore the posterior distribution of reconstruction parameters via Markov chain Monte Carlo (MCMC) sampling. The target reconstruction parameters, that is, shape and scaling factors of the pressure and toroidal current‐density profiles as well as the total toroidal flux, are taken from a reduced subspace of Wendelstein 7‐X equilibrium configurations. Since the corresponding forward model evaluations are computationally demanding, we replace the forward model via a polynomial chaos expansion surrogate. We compare the posterior distribution obtained via MCMC sampling to Laplace's approximation, which assumes a Gaussian posterior. We find that the two approaches provide similar results in regimes where the uncertainty on the plasma diagnostic signals is low. However, discrepancies between the posteriors are observed in cases of higher diagnostic signal uncertainty. Therefore, we provide further validation of the commonly used Laplace's approximation as a method of uncertainty quantification in 3D equilibrium reconstruction and showcase some of its limitations.

Strategies of property developers in the context of carbon tax.

China needs to guide property developers in actively reducing emissions to reach carbon emission reduction targets and respond to global climate change. A carbon tax is an important policy tool. Still, to establish successful rules to steer property developers' reasonable carbon emission reduction behavior, we must first explore property developers' decision-making mechanisms. This study develops an emission reduction and price game model for property developers under the constraint of a carbon tax. It then applies reverse order induction and optimization methods to identify the game equilibrium solution for property developers. Using the game equilibria, we explore the carbon tax mechanism on emission reduction and property developer pricing strategies. We can derive the following conclusions if the carbon tax policy is not implemented: 1.House prices are related to the substitutability of the two types of competitive property developers. 2.The greater the substitutability, the greater the cost of emission reduction paid by consumers. 3.The game equilibrium carbon emission intensity is the average carbon emission intensity of the housing business. In the situation of enacting a carbon tax, we arrive at the following conclusions: 1.The profits of real estate developers who do not have the advantage of emission reduction continue to decline with the increase of carbon tax. 2. For real estate developers who have the advantage of decreasing emissions, profits declined initially and then increased as the carbon tax rate increased, and only when the carbon tax rate reaches Tm1* can they fully leverage the cost advantage and obtain ever-increasing profits. 3.Low tax rates should be adopted by the government at the start of the implementation of the carbon tax policy to provide a buffer time for real estate developers who do not have the advantage of emission reduction costs.

Analysis of the space-time trends in open defecation in Nigeria.

The practice of open defecation has persistently remained high in Nigeria despite the grave danger it poses to public and environmental health, and the several intervention programs put in place over the years to curtail the ugly practice. This study quantifies the space and time trends in open defecation practice in Nigeria with the aim of highlighting the changes that have taken place at various locations in Nigeria over a 15-year period. A Bayesian spatio-temporal model was applied to cross-section data obtained from the Nigeria Demographic and Health Survey conducted in 2003, 2008, 2013, and 2018, and inference was based on integrated nested Laplace approximation technique. The findings indicate a north-south spatio-temporal patterns that are similar among the rural and urban dwellers. States such as Kwara, Kogi, Oyo, Ondo, Osun, Ekiti, Enugu, and Ebonyi all of which are neighbors to each other are among those with persistent high prevalence of open defecation in the country. Given the diversity of the Nigerian population groups within the states, a more understanding of the socio-cultural standard of the different communities would be required to implement policies that recognize opportunities to explore, while being culturally responsive to community needs in ending open defecation in Nigeria.

Integrated species distribution models fitted in INLA are sensitive to mesh parameterisation

The ever‐growing popularity of citizen science, as well as recent technological and digital developments, have allowed the collection of data on species' distributions at an extraordinary rate. In order to take advantage of these data, information of varying quantity and quality needs to be integrated. Point process models have been proposed as an elegant way to achieve this for estimates of species distributions. These models can be fitted efficiently using Bayesian methods based on integrated nested Laplace approximations (INLA) with stochastic partial differential equations (SPDEs). This approach uses an efficient way to model spatial autocorrelation using a Gaussian random field and a triangular mesh over the spatial domain. The mesh is constructed by user‐defined variables, so effectively represents a free parameter in the model. However, there is a lack of understanding about how to set these mesh parameters, and their effect on model performance. Here, we assess how mesh parameters affect predictions and model fit to estimate the distribution of the serotine bat,Eptesicus serotinus, in Great Britain. A Bayesian INLA model was fitted using five meshes of varying densities to a dataset comprising both structured observations from a national monitoring programme and opportunistic records. We demonstrate that mesh density impacted spatial predictions with a general loss of accuracy with increasing mesh coarseness. However, we also show that the finest mesh was unable to overcome spatial biases in the data. In addition, the magnitude of the covariate effects differed markedly between meshes. This confirms that mesh parameterisation is an important and delicate process with implications for model inference. We discuss how species distribution modellers might adapt their use of INLA in the light of these findings.

Hospital admission risks and excess costs for neurological symptoms attributable to long-term exposure to fine particulate matter in New York State, USA

BackgroundAlthough emerging evidence suggests that PM2.5 is linked to neurological symptoms (NSs) via neuroinflammation, relevant studies are scarce. This study aimed to investigate the risks and excess costs of hospital admission for five NSs—fatigue, headache, dizziness, convulsion, and paralysis—attributable to long-term exposure to PM2.5 in New York State, USA. MethodsWe analyzed the New York Statewide Planning and Research Cooperative System (SPARCS) from 2010 to 2016. A Bayesian hierarchical model with integrated nested Laplace approximations was performed to estimate the risks and excess costs of hospital admission for NSs due to long-term exposure to PM2.5 at the county level. ResultsA 1 μg/m3 increase in lag 0–1 years PM2.5 was associated with an increased risk of headache and convulsion by 1.06 (95% CI: 1.01, 1.11) and 1.04 (95% CI: 1.01, 1.06), respectively. The excess hospital admission cost for five NSs attributable to lag 0–1 years PM2.5 above the new World Health Organization guideline (annual standard: 5 μg/m3) was $200.24 (95% CI: 6.00, 376.96) million during 2011–2016, recording the highest for convulsion ($153.73 [95% CI: 63.61, 244.19] million). ConclusionsThis study provides quantitative estimates of risks and excess costs for NSs attributable to long-term PM2.5 and suggests that policies that reduce long-term PM2.5 concentration in accordance with the new WHO air quality guidelines can yield substantial health and economic benefits related to NSs in the New York State population.