scholarly journals Spatial Conditional Autoregressive Models in Stan

2021 ◽  
Author(s):  
Connor Donegan
Keyword(s):  
Monte Carlo ◽  
Bayesian Inference ◽  
Mortality Data ◽  
Computationally Efficient ◽  
Probability Models ◽  
Public Resource ◽  
Conditional Autoregressive ◽  
Modeling Data ◽  
Fully Bayesian ◽  
Conditional Autoregressive Models

Modeling data collected by areal units, such as counties or census tracts, is a core component of population health research and public resource distribution. Bayesian inference has both practical and philosophical advantages over classical statistical techniques, and advances in Markov chain Monte Carlo (MCMC) are expanding the range of research questions to which fully Bayesian inference may be applied. This code snippet introduces code for fitting spatial conditional autoregressive (CAR) models with the Stan modeling language. Stan is an expressive programming language that uses a dynamic Hamiltonian Monte Carlo (HMC) algorithm to draw samples from user-specified probability models. This paper discusses various CAR model specifications and introduces computationally efficient implementations for Stan users. The paper demonstrates use of the code by modeling United States county mortality data, including censored observations.

scholarly journals Bayesian Inference of Species Trees using Diffusion Models

2020 ◽  
Vol 70 (1) ◽  
pp. 145-161 ◽  
Author(s):  
Marnus Stoltz ◽  
Boris Baeumer ◽  
Remco Bouckaert ◽  
Colin Fox ◽  
Gordon Hiscott ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Numerical Algorithms ◽  
Diffusion Models ◽  
Model Parameters ◽  
Data Sets ◽  
Species Trees ◽  
Computationally Efficient ◽  
Data Set ◽  
Snp Data ◽  
Binary Markers

Abstract We describe a new and computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. Likelihood calculations are carried out using diffusion models of allele frequency dynamics combined with novel numerical algorithms. The diffusion approach allows for analysis of data sets containing hundreds or thousands of individuals. The method, which we call Snapper, has been implemented as part of the BEAST2 package. We conducted simulation experiments to assess numerical error, computational requirements, and accuracy recovering known model parameters. A reanalysis of soybean SNP data demonstrates that the models implemented in Snapp and Snapper can be difficult to distinguish in practice, a characteristic which we tested with further simulations. We demonstrate the scale of analysis possible using a SNP data set sampled from 399 fresh water turtles in 41 populations. [Bayesian inference; diffusion models; multi-species coalescent; SNP data; species trees; spectral methods.]

Exploring a multilevel approach with spatial effects to model housing price in San José, Costa Rica

2021 ◽  
pp. 239980832110411
Author(s):  
Eduardo Pérez-Molina
Keyword(s):  
Costa Rica ◽  
Multilevel Models ◽  
Housing Prices ◽  
Housing Price ◽  
Autoregressive Models ◽  
Metropolitan Region ◽  
Spatial Effects ◽  
San Jose ◽  
Conditional Autoregressive ◽  
Conditional Autoregressive Models

A multilevel model of the housing market for San José Metropolitan Region (Costa Rica) was developed, including spatial effects. The model is used to explore two main questions: the extent to which contextual (of the surroundings) and compositional (of the property itself) effects explain variation of housing prices and how does the relation between price and key covariates change with the introduction of multilevel effects. Hierarchical relations (lower level units nested into higher level) were modeled by specifying multilevel models with random intercepts and a conditional autoregressive term to include spatial effects from neighboring units at the higher level (districts). The random intercepts and conditional autoregressive models presented the best fit to the data. Variation at the higher level accounted for 16% of variance in the random intercepts model and 28% in the conditional autoregressive model. The sign and magnitude of regression coefficients proved remarkably stable across model specifications. Travel time to the city center, which presented a non-linear relation to price, was found to be the most important determinant. Multilevel and conditional autoregressive models constituted important improvements in modeling housing price, despite most of the variation still occurring at the lower level, by improving the overall model fit. They were capable of representing the regional structure and of reducing sampling bias in the data. However, the conditional autoregressive specification only represented a limited advance over the random intercepts formulation.

Effcient Sequential Monte-Carlo Samplers for Bayesian Inference

2017 ◽  
Author(s):  
Thi Le Thu Nguyen ◽  
Francois Septier Septier ◽  
Gareth William Peters
Keyword(s):  
Monte Carlo ◽  
Bayesian Inference ◽  
Sequential Monte Carlo

scholarly journals Bayesian inference across multiple models suggests a strong increase in lethality of COVID-19 in late 2020 in the UK

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0258968
Author(s):  
Patrick Pietzonka ◽  
Erik Brorson ◽  
William Bankes ◽  
Michael E. Cates ◽  
Robert L. Jack ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Time Window ◽  
Fold Increase ◽  
Strong Increase ◽  
Mortality Data ◽  
New Variant ◽  
Model Evidence ◽  
Age Structured ◽  
The Uk ◽  
Inference Methods

We apply Bayesian inference methods to a suite of distinct compartmental models of generalised SEIR type, in which diagnosis and quarantine are included via extra compartments. We investigate the evidence for a change in lethality of COVID-19 in late autumn 2020 in the UK, using age-structured, weekly national aggregate data for cases and mortalities. Models that allow a (step-like or graded) change in infection fatality rate (IFR) have consistently higher model evidence than those without. Moreover, they all infer a close to two-fold increase in IFR. This value lies well above most previously available estimates. However, the same models consistently infer that, most probably, the increase in IFR preceded the time window during which variant B.1.1.7 (alpha) became the dominant strain in the UK. Therefore, according to our models, the caseload and mortality data do not offer unequivocal evidence for higher lethality of a new variant. We compare these results for the UK with similar models for Germany and France, which also show increases in inferred IFR during the same period, despite the even later arrival of new variants in those countries. We argue that while the new variant(s) may be one contributing cause of a large increase in IFR in the UK in autumn 2020, other factors, such as seasonality, or pressure on health services, are likely to also have contributed.

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