اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBayesian Non-Parametric Inference for Infectious Disease Data
143
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We propose a framework for Bayesian non-parametric estimation of the rate at which new infections occur assuming that the epidemic is partially observed. The developed methodology relies on modelling the rate at which new infections occur as a function which only depends on time. Two different types of prior distributions are proposed namely using step-functions and B-splines. The methodology is illustrated using both simulated and real datasets and we show that certain aspects of the epidemic such as seasonality and super-spreading events are picked up without having to explicitly incorporate them into a parametric model.
قيم البحث
اقرأ أيضاً
Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard tool to mode
l e.g. financial, neuronal and population growth dynamics. However inference for multidimensional SDE models is still very challenging, both computationally and theoretically. Approximate Bayesian computation (ABC) allow to perform Bayesian inference for models which are sufficiently complex that the likelihood function is either analytically unavailable or computationally prohibitive to evaluate. A computationally efficient ABC-MCMC algorithm is proposed, halving the running time in our simulations. Focus is on the case where the SDE describes latent dynamics in state-space models; however the methodology is not limited to the state-space framework. Simulation studies for a pharmacokinetics/pharmacodynamics model and for stochastic chemical reactions are considered and a MATLAB package implementing our ABC-MCMC algorithm is provided.
In spatial statistics, it is often assumed that the spatial field of interest is stationary and its covariance has a simple parametric form, but these assumptions are not appropriate in many applications. Given replicate observations of a Gaussian sp
atial field, we propose nonstationary and nonparametric Bayesian inference on the spatial dependence. Instead of estimating the quadratic (in the number of spatial locations) entries of the covariance matrix, the idea is to infer a near-linear number of nonzero entries in a sparse Cholesky factor of the precision matrix. Our prior assumptions are motivated by recent results on the exponential decay of the entries of this Cholesky factor for Matern-type covariances under a specific ordering scheme. Our methods are highly scalable and parallelizable. We conduct numerical comparisons and apply our methodology to climate-model output, enabling statistical emulation of an expensive physical model.
We introduce a numerically tractable formulation of Bayesian joint models for longitudinal and survival data. The longitudinal process is modelled using generalised linear mixed models, while the survival process is modelled using a parametric genera
l hazard structure. The two processes are linked by sharing fixed and random effects, separating the effects that play a role at the time scale from those that affect the hazard scale. This strategy allows for the inclusion of non-linear and time-dependent effects while avoiding the need for numerical integration, which facilitates the implementation of the proposed joint model. We explore the use of flexible parametric distributions for modelling the baseline hazard function which can capture the basic shapes of interest in practice. We discuss prior elicitation based on the interpretation of the parameters. We present an extensive simulation study, where we analyse the inferential properties of the proposed models, and illustrate the trade-off between flexibility, sample size, and censoring. We also apply our proposal to two real data applications in order to demonstrate the adaptability of our formulation both in univariate time-to-event data and in a competing risks framework. The methodology is implemented in rstan.
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using Gaussian pro
cesses. This enables regularization and accounting for uncertainty in the map estimation, while still resulting in a closed-form and invertible posterior map. We then focus on inferring the distribution of a nonstationary spatial field from a small number of replicates. We develop specific transport-map priors that are highly flexible and are motivated by the behavior of a large class of stochastic processes. Our approach is scalable to high-dimensional fields due to data-dependent sparsity and parallel computations. We also discuss extensions, including Dirichlet process mixtures for marginal non-Gaussianity. We present numerical results to demonstrate the accuracy, scalability, and usefulness of our methods, including statistical emulation of non-Gaussian climate-model output.
We consider inference from non-random samples in data-rich settings where high-dimensional auxiliary information is available both in the sample and the target population, with survey inference being a special case. We propose a regularized predictio
n approach that predicts the outcomes in the population using a large number of auxiliary variables such that the ignorability assumption is reasonable while the Bayesian framework is straightforward for quantification of uncertainty. Besides the auxiliary variables, inspired by Little & An (2004), we also extend the approach by estimating the propensity score for a unit to be included in the sample and also including it as a predictor in the machine learning models. We show through simulation studies that the regularized predictions using soft Bayesian additive regression trees yield valid inference for the population means and coverage rates close to the nominal levels. We demonstrate the application of the proposed methods using two different real data applications, one in a survey and one in an epidemiology study.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
