The cover image is based on the Research Article Bayesian backcalculation of pavement properties using parallel transitional Markov chain Monte Carlo by Keaton Coletti et al., ...https://doi.org/10.1111/mice.13123.
One criterion for validation of trachoma elimination is the management of Trachomatous Trichiasis (TT) after Trachoma inflammation—follicular (TF) is eliminated in children ages 1–9 years at district ...level. No data exist on how long countries must have dedicated TT programs, as the timeline for progression to TT from trachomatous scarring is unknown. We used eight years of longitudinal data in women in Kongwa Tanzania to model progression from no scarring (S0) through grades of scarring severity (S1–S4) to TT. Markov models were used, with age, community prevalence of TF (CPTF), and household characteristics as co-variates. Adjusted for covariates, the incidence of S1 was estimated at 4∙7% per year, and the risk increased by 26% if the CPTF was between 5–10% and by 48% if greater than 10%. The transition from S4 to TT was estimated at 2∙6% per year. Districts, even after elimination of TF, may have some communities with TF ≥ 5% and increased risk of incident scarring. Once scarring progresses to S2, further progression is not dependent on CPTF. These data suggest that, depending on the district level of scarring and degree of heterogeneity in CPTF at the time of elimination, incident TT will still be an issue for decades.
Bayesian inference of phylogeny using Markov chain Monte Carlo (MCMC) plays a central role in understanding evolutionary history from molecular sequence data. Visualizing and analyzing the ...MCMC-generated samples from the posterior distribution is a key step in any non-trivial Bayesian inference. We present the software package Tracer (version 1.7) for visualizing and analyzing the MCMC trace files generated through Bayesian phylogenetic inference. Tracer provides kernel density estimation, multivariate visualization, demographic trajectory reconstruction, conditional posterior distribution summary, and more. Tracer is open-source and available at http://beast.community/tracer.
There is a lack of methodological results to design efficient Markov chain Monte Carlo (
MCMC
) algorithms for statistical models with discrete-valued high-dimensional parameters. Motivated by this ...consideration, we propose a simple framework for the design of informed
MCMC
proposals (i.e., Metropolis-Hastings proposal distributions that appropriately incorporate local information about the target) which is naturally applicable to discrete spaces. Using Peskun-type comparisons of Markov kernels, we explicitly characterize the class of asymptotically optimal proposal distributions under this framework, which we refer to as locally balanced proposals. The resulting algorithms are straightforward to implement in discrete spaces and provide orders of magnitude improvements in efficiency compared to alternative
MCMC
schemes, including discrete versions of Hamiltonian Monte Carlo. Simulations are performed with both simulated and real datasets, including a detailed application to Bayesian record linkage. A direct connection with gradient-based
MCMC
suggests that locally balanced proposals can be seen as a natural way to extend the latter to discrete spaces.
Supplementary materials
for this article are available online.
•The most popular sampling techniques for model updating are presented.•Methods, numerical implementations and tuning strategies are provided.•Examples with increase complexity are used to present ...and evaluate the samplers.•The DLR-AIRMOD model updating problem is used as a benchmark for the different solvers.•Algorithms, codes and tutorials are provided as additional material.
This tutorial paper reviews the use of advanced Monte Carlo sampling methods in the context of Bayesian model updating for engineering applications. Markov Chain Monte Carlo, Transitional Markov Chain Monte Carlo, and Sequential Monte Carlo methods are introduced, applied to different case studies and finally their performance is compared. For each of these methods, numerical implementations and their settings are provided.
Three case studies with increased complexity and challenges are presented showing the advantages and limitations of each of the sampling techniques under review. The first case study presents the parameter identification for a spring-mass system under a static load. The second case study presents a 2-dimensional bi-modal posterior distribution and the aim is to observe the performance of each of these sampling techniques in sampling from such distribution. Finally, the last case study presents the stochastic identification of the model parameters of a complex and non-linear numerical model based on experimental data.
The case studies presented in this paper consider the recorded data set as a single piece of information which is used to make inferences and estimations on time-invariant model parameters.
One of the most appealing approaches to ease the Hubble tension is the inclusion of an early dark energy (EDE) component that adds energy to the Universe in a narrow redshift window around the time ...of recombination and dilutes faster than radiation afterwards. In this paper, we analyze EDE in the framework of α-attractor models. As is well known, the success in alleviating the Hubble tension crucially depends on the shape of the energy injection. We show how different types of energy injections can be obtained, thanks to the freedom in choosing the functional form of the potential inspired by α-attractor models. To confirm our intuition, we perform a Markov-chain Monte Carlo analysis for three representative cases and find indeed that H0 is significantly larger than in Λ CDM, like in other EDE models. Unlike axion-driven EDE models with a super-Planckian decay constant, the curvature of the potential in the EDE models required by the data is natural in the context of recent theoretical developments in α-attractors.
Abstract
We consider fluxes and forces in Markov chains. In physics, the concept of so-called iso-surfaces has recently been introduced. In generic cases, there are infinitely many associated ...iso-dissipation forces. We first show that this is due to different notions of duality, each giving rise to dual force. We then study Hamiltonians associated to variational formulations of Markov processes, and develop different decompositions for them.
Visualization in Bayesian workflow Gabry, Jonah; Simpson, Daniel; Vehtari, Aki ...
Journal of the Royal Statistical Society. Series A, Statistics in society,
February 2019, Letnik:
182, Številka:
2
Journal Article
Recenzirano
Odprti dostop
Bayesian data analysis is about more than just computing a posterior distribution, and Bayesian visualization is about more than trace plots of Markov chains. Practical Bayesian data analysis, like ...all data analysis, is an iterative process of model building, inference, model checking and evaluation, and model expansion. Visualization is helpful in each of these stages of the Bayesian workflow and it is indispensable when drawing inferences from the types of modern, high dimensional models that are used by applied researchers.
Markov Chain Monte–Carlo (MCMC) is an increasingly popular method for obtaining information about distributions, especially for estimating posterior distributions in Bayesian inference. This article ...provides a very basic introduction to MCMC sampling. It describes what MCMC is, and what it can be used for, with simple illustrative examples. Highlighted are some of the benefits and limitations of MCMC sampling, as well as different approaches to circumventing the limitations most likely to trouble cognitive scientists.
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