Search results for "Laplace's method"
showing 10 items of 10 documents
Efficient estimation of generalized linear latent variable models.
2019
Generalized linear latent variable models (GLLVM) are popular tools for modeling multivariate, correlated responses. Such data are often encountered, for instance, in ecological studies, where presence-absences, counts, or biomass of interacting species are collected from a set of sites. Until very recently, the main challenge in fitting GLLVMs has been the lack of computationally efficient estimation methods. For likelihood based estimation, several closed form approximations for the marginal likelihood of GLLVMs have been proposed, but their efficient implementations have been lacking in the literature. To fill this gap, we show in this paper how to obtain computationally convenient estim…
Hierarchical log Gaussian Cox process for regeneration in uneven-aged forests
2021
We propose a hierarchical log Gaussian Cox process (LGCP) for point patterns, where a set of points x affects another set of points y but not vice versa. We use the model to investigate the effect of large trees to the locations of seedlings. In the model, every point in x has a parametric influence kernel or signal, which together form an influence field. Conditionally on the parameters, the influence field acts as a spatial covariate in the intensity of the model, and the intensity itself is a non-linear function of the parameters. Points outside the observation window may affect the influence field inside the window. We propose an edge correction to account for this missing data. The par…
Statistical methods for spatial cluster detection in childhood cancer incidence : A simulation study
2021
BACKGROUND AND OBJECTIVE: The potential existence of spatial clusters in childhood cancer incidence is a debated topic. Identification of such clusters may help to better understand etiology and develop preventive strategies. We evaluated widely used statistical approaches to cluster detection in this context.; METHODS: Incidence of newly diagnosed childhood cancer (140/1,000,000 children under 15 years) and nephroblastoma (7/1,000,000) was simulated. Clusters of defined size (1-50) were randomly assembled on the district level in Germany. Each cluster was simulated with different relative risk levels (1-100). For each combination 2000 iterations were done. Simulated data was then analyzed …
Path Integral approach via Laplace’s method of integration for nonstationary response of nonlinear systems
2019
In this paper the nonstationary response of a class of nonlinear systems subject to broad-band stochastic excitations is examined. A version of the Path Integral (PI) approach is developed for determining the evolution of the response probability density function (PDF). Specifically, the PI approach, utilized for evaluating the response PDF in short time steps based on the Chapman–Kolmogorov equation, is here employed in conjunction with the Laplace’s method of integration. In this manner, an approximate analytical solution of the integral involved in this equation is obtained, thus circumventing the repetitive integrations generally required in the conventional numerical implementation of …
Modelling the presence of disease under spatial misalignment using Bayesian latent Gaussian models.
2015
Modelling patterns of the spatial incidence of diseases using local environmental factors has been a growing problem in the last few years. Geostatistical models have become popular lately because they allow estimating and predicting the underlying disease risk and relating it with possible risk factors. Our approach to these models is based on the fact that the presence/absence of a disease can be expressed with a hierarchical Bayesian spatial model that incorporates the information provided by the geographical and environmental characteristics of the region of interest. Nevertheless, our main interest here is to tackle the misalignment problem arising when information about possible covar…
Statistical Properties of Double Hoyt Fading With Applications to the Performance Analysis of Wireless Communication Systems
2018
In this paper, we investigate the statistical properties of double Hoyt fading channels, where the overall received signal is determined by the product of two statistically independent but not necessarily identically distributed single Hoyt processes. Finite-range integral expressions are first derived for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades of the envelope fading process. A closed-form approximate solution is also deduced for the LCR by making use of the Laplace approximation theorem. Applying the derived PDF of the double Hoyt channel, we then provide analytical expressions for the average…
Laplace’s Method of Integration in the Path Integral Approach for the Probabilistic Response of Nonlinear Systems
2020
In this paper the response of nonlinear systems under stationary Gaussian white noise excitation is studied. The Path Integral (PI) approach, generally employed for evaluating the response Probability Density Function (PDF) of systems in short time steps based on the Chapman-Kolmogorov equation, is here used in conjunction with the Laplace’s method of integration. This yields an approximate analytical solution of the integral involved in the Chapman-Kolmogorov equation. Further, in this manner the repetitive integrations, generally required in the conventional numerical implementation of the procedure, can be circumvented. Application to a nonlinear system is considered, and pertinent compa…
Methods of spatial cluster detection in rare childhood cancers: Benchmarking data and results from a simulation study on nephroblastoma
2021
Abstract The potential existence of spatial clusters in childhood cancer incidence is a debated topic. Identification of rare disease clusters in general may help to better understand disease etiology and develop preventive strategies against such entities. The incidence of newly diagnosed childhood malignancies under 15 years of age is 140/1,000,000. In this context, the subgroup of nephroblastoma represents an extremely rare entity with an annual incidence of 7/1,000,000. We evaluated widely used statistical approaches for spatial cluster detection in childhood cancer (Ref. [22] Schundeln et al., 2021, Cancer Epidemiology). For the simulation study, random high risk clusters of 1 to 50 ad…
Prior-based Bayesian information criterion
2019
We present a new approach to model selection and Bayes factor determination, based on Laplace expansions (as in BIC), which we call Prior-based Bayes Information Criterion (PBIC). In this approach, the Laplace expansion is only done with the likelihood function, and then a suitable prior distribution is chosen to allow exact computation of the (approximate) marginal likelihood arising from the Laplace approximation and the prior. The result is a closed-form expression similar to BIC, but now involves a term arising from the prior distribution (which BIC ignores) and also incorporates the idea that different parameters can have different effective sample sizes (whereas BIC only allows one ov…
Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit
2011
In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [S. Herrmann and J. Tugaut. Electron. J. Probab. 15 (2010) 2087–2116], the authors proved that, for linear interaction and under suitable conditions, there exists a unique symmetric limit measure associated to the set of invariant measures in the small-noise limit. The aim of this study is essentially to point out that this statement leads to the existence, as the noise intensity is small, of one unique…