In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a ...flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys' priors, are designed to support Occam's razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations.
In recent years, disease mapping studies have become a routine application within geographical epidemiology and are typically analysed within a Bayesian hierarchical model formulation. A variety of ...model formulations for the latent level have been proposed but all come with inherent issues. In the classical BYM (Besag, York and Mollié) model, the spatially structured component cannot be seen independently from the unstructured component. This makes prior definitions for the hyperparameters of the two random effects challenging. There are alternative model formulations that address this confounding; however, the issue on how to choose interpretable hyperpriors is still unsolved. Here, we discuss a recently proposed parameterisation of the BYM model that leads to improved parameter control as the hyperparameters can be seen independently from each other. Furthermore, the need for a scaled spatial component is addressed, which facilitates assignment of interpretable hyperpriors and make these transferable between spatial applications with different graph structures. The hyperparameters themselves are used to define flexible extensions of simple base models. Consequently, penalised complexity priors for these parameters can be derived based on the information-theoretic distance from the flexible model to the base model, giving priors with clear interpretation. We provide implementation details for the new model formulation which preserve sparsity properties, and we investigate systematically the model performance and compare it to existing parameterisations. Through a simulation study, we show that the new model performs well, both showing good learning abilities and good shrinkage behaviour. In terms of model choice criteria, the proposed model performs at least equally well as existing parameterisations, but only the new formulation offers parameters that are interpretable and hyperpriors that have a clear meaning.
Bayesian Computing with INLA: A Review Rue, Håvard; Riebler, Andrea; Sørbye, Sigrunn H ...
Annual review of statistics and its application,
03/2017, Letnik:
4, Številka:
1
Journal Article
Recenzirano
Odprti dostop
The key operation in Bayesian inference is to compute high-dimensional integrals. An old approximate technique is the Laplace method or approximation, which dates back to Pierre-Simon Laplace (1774). ...This simple idea approximates the integrand with a second-order Taylor expansion around the mode and computes the integral analytically. By developing a nested version of this classical idea, combined with modern numerical techniques for sparse matrices, we obtain the approach of integrated nested Laplace approximations (INLA) to do approximate Bayesian inference for latent Gaussian models (LGMs). LGMs represent an important model abstraction for Bayesian inference and include a large proportion of the statistical models used today. In this review, we discuss the reasons for the success of the INLA approach, the
R-INLA
package, why it is so accurate, why the approximations are very quick to compute, and why LGMs make such a useful concept for Bayesian computing.
This paper develops methodology that provides a toolbox for routinely fitting complex models to realistic spatial point pattern data. We consider models that are based on log-Gaussian Cox processes ...and include local interaction in these by considering constructed covariates. This enables us to use integrated nested Laplace approximation and to considerably speed up the inferential task. In addition, methods for model comparison and model assessment facilitate the modelling process. The performance of the approach is assessed in a simulation study. To demonstrate the versatility of the approach, models are fitted to two rather different examples, a large rainforest data set with covariates and a point pattern with multiple marks.
Studies of spatial population synchrony constitute a central approach for understanding the drivers of ecological dynamics. Recently, identifying the ecological impacts of climate change has emerged ...as a new important focus in population synchrony studies. However, while it is well known that climatic seasonality and sequential density dependence influences local population dynamics, the role of season-specific density dependence in shaping large-scale population synchrony has not received attention. Here, we present a widely applicable analytical protocol that allows us to account for both season and geographic context-specific density dependence to better elucidate the relative roles of deterministic and stochastic sources of population synchrony, including the renowned Moran effect. We exemplify our protocol by analyzing time series of seasonal (spring and fall) abundance estimates of cyclic rodent populations, revealing that season-specific density dependence is a major component of population synchrony. By accounting for deterministic sources of synchrony (in particular season-specific density dependence), we are able to identify stochastic components. These stochastic components include mild winter weather events, which are expected to increase in frequency under climate warming in boreal and Arctic ecosystems. Interestingly, these weather effects act both directly and delayed on the vole populations, thus enhancing the Moran effect. Our study demonstrates how different drivers of population synchrony, presently altered by climate warming, can be disentangled based on seasonally sampled population time-series data and adequate population models.
Metabolic syndrome (MetS) defines important risk factors in the development of cardiovascular diseases and other serious health conditions. This study aims to investigate the influence of different ...dietary patterns on MetS and its components, examining both associations and predictive performance.
The study sample included 10,750 participants from the seventh survey of the cross-sectional, population-based Tromsø Study in Norway. Diet intake scores were used as covariates in logistic regression models, controlling for age, educational level and other lifestyle variables, with MetS and its components as response variables. A diet high in meat and sweets was positively associated with increased odds of MetS and elevated waist circumference, while a plant-based diet was associated with decreased odds of hypertension in women and elevated levels of triglycerides in men. The predictive power of dietary patterns derived by different dimensionality reduction techniques was investigated by randomly partitioning the study sample into training and test sets. On average, the diet score variables demonstrated the highest predictive power in predicting MetS and elevated waist circumference. The predictive power was robust to the dimensionality reduction technique used and comparable to using a data-driven prediction method on individual food variables.
The strongest associations and highest predictive power of dietary patterns were observed for MetS and its single component, elevated waist circumference.
•A diet high in meat and sweets was positively associated with increased odds of MetS and elevated waist circumference (WC).•A plant-based diet was positively associated with decreased odds of hypertension in women and high triglycerides in men.•The predictive power of diet score variables was highest in predicting MetS and elevated WC.•Dietary patterns and predictive power were robust to the dimensionality techniques used.
Finite-sample properties of estimators for first and second order autoregressive processes Sørbye, Sigrunn H.; Nicolau, Pedro G.; Rue, Håvard
Statistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems,
10/2022, Letnik:
25, Številka:
3
Journal Article
Odprti dostop
The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available ...statistical software like R. A potential problem is that commonly applied estimators for the coefficients of AR processes are severely biased when the time series are short. This paper studies the finite-sample properties of well-known estimators for the coefficients of stationary AR(1) and AR(2) processes and provides bias-corrected versions of these estimators which are quick and easy to apply. The new estimators are constructed by modeling the relationship between the true and originally estimated AR coefficients using weighted orthogonal polynomial regression, taking the sampling distribution of the original estimators into account. The finite-sample distributions of the new bias-corrected estimators are approximated using transformations of skew-normal densities, combined with a Gaussian copula approximation in the AR(2) case. The properties of the new estimators are demonstrated by simulations and in the analysis of a real ecological data set. The estimators are easily available in our accompanying R-package for AR(1) and AR(2) processes of length 10–50, both giving bias-corrected coefficient estimates and corresponding confidence intervals.
The treatment of open lower limb fractures represents a major challenge for any trauma surgeon, and this even more so in resource-limited areas. The aim of the study is to describe the intervention, ...report the treatment plan, and observe the effectiveness of the Norwegian Open Fracture Management System in saving lower limbs in rural settings.
A retrospective and prospective interventional study was carried out in the period 2011 through 2017 in six rural hospitals in Cambodia. The fractures were managed with locally produced external fixators and orthosis developed in 2007. Based on skills and living locations, two local surgeons and one paramedic without reconstructive surgery experience were selected to reach the top of the reconstructive ladder and perform limb salvage surgeries. This study evaluated 56 fractures using the Ganga Hospital Open Injury Score (GHOIS) for Gustilo-Anderson Type IIIA and Type IIIB open fracture classification groups.
The primary success rate in open tibia fractures was 64.3% (95% CI, 50.3 - 76.3). The average treatment time to complete healing for all of the patients was 39.6 weeks (95% CI, 34.8 - 44.4). A percentage of 23.2% (95% CI, 13.4 - 36.7) experienced a deep infection. Fifteen of the patients had to undergo soft tissue reconstruction and 22 flaps were performed. Due to non-union, a total of 15 bone grafts were performed. All of the 56 patients in the study gained limb salvage and went back to work.
The given fracture management program proves that low-resource countries are able to produce essential surgical tools at high quality and low price. Treatment with external fixation and functional bracing, combined with high-level training of local surgeons, demonstrates that a skilled surgical team can perform advanced limb salvage surgery in low-resource settings.
Fractional Gaussian noise (fGn) is a stationary time series model with long-memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting ...an fGn model of length
n
using a likelihood-based approach is
O
(
n
2
)
, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to
O
(
n
3
)
. This paper presents an approximate fGn model of
O
(
n
)
computational cost, both with direct and indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive (AR) processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four AR components. Specifically, the given approximate fGn model is incorporated within the class of latent Gaussian models in which Bayesian inference is obtained using the methodology of integrated nested Laplace approximation. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.
Abstract
Background
A healthy diet can decrease the risk of several lifestyle diseases. From studying the health effects of single foods, research now focuses on examining complete diets and dietary ...patterns reflecting the combined intake of different foods. The main goals of the current study were to identify dietary patterns and then investigate how these differ in terms of sex, age, educational level and physical activity level (PAL) in a general Nordic population.
Methods
We used data from the seventh survey of the population-based Tromsø Study in Norway, conducted in 2015-2016. The study included 21,083 participants aged
$$40-99$$
40
-
99
years, of which
$$72\%$$
72
%
completed a comprehensive food frequency questionnaire (FFQ). After exclusion, the study sample included 10,899 participants with valid FFQ data. First, to cluster food variables, the participants were partitioned in homogeneous cohorts according to sex, age, educational level and PAL. Non-overlapping diet groups were then identified using repeated hierarchical cluster analysis on the food variables. Second, average standardized diet intake scores were calculated for all individuals for each diet group. The individual diet (intake) scores were then modelled in terms of age, education and PAL using regression models. Differences in diet scores according to education and PAL were investigated by pairwise hypothesis tests, controlling the nominal significance level using Tukey’s method.
Results
The cluster analysis revealed three dietary patterns, here named the Meat and Sweets diet, the Traditional diet, and the Plant-based- and Tea diet. Women had a lower intake of the Traditional diet and a higher preference for the Plant-based- and Tea diet compared to men. Preference for the Meat and Sweets diet and Traditional diet showed significant negative and positive trends as function of age, respectively. Adjusting for age, the group having high education and high PAL compared favourably with the group having low education and low PAL, having a significant lower intake of the Meat and Sweets and the Traditional diets and a significant higher intake of the Plant-based- and Tea diet.
Conclusions
Three dietary patterns (Meat and Sweets, Traditional, and Plant-based- and Tea) were found by repeated clustering of randomly sampled homogeneous cohorts of individuals. Diet preferences depended significantly on sex, age, education and PAL, showing a more unhealthy dietary pattern with lower age, low education and low PAL.
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