arXiv subjects

Luiz M. Carvalho

Publications and source records attributed to Luiz M. Carvalho.

6 recordsLinked to original sources

arXiv2025

hdbayes: An R Package for Bayesian Analysis of Generalized Linear Models Using Historical Data

There has been increased interest in the use of historical data to formulate informative priors in regression models. While many such priors for incorporating historical data have been proposed, adoption is limited due to access to software. Where software does exist, the implementations between different methods could be vastly different, making comparisons between methods difficult. In this paper, we introduce the R package hdbayes, an implementation of the power prior, normalized power prior, Bayesian hierarchical model, robust meta-analytic prior, commensurate prior, and latent exchangeability prior for generalized linear models. The bulk of the package is written in the Stan programming language, with user-friendly R wrapper functions to call samplers.

stat.ME↗

arXiv2025

ANPP: the Adapted Normalized Power Prior for Borrowing Information from Multiple Historical Datasets in Clinical Trials

The power prior is a popular class of informative priors for incorporating information from historical data. It involves raising the likelihood for the historical data to a power, which acts as a discounting parameter. When the discounting parameter is modeled as random, the normalized power prior (NPP) is recommended. When there are multiple historical datasets, there has been limited research on how to choose priors for the multiple discounting parameters of the NPP to induce desirable information borrowing behavior. In this work, we address this question by investigating the analytical relationship between the NPP and the Bayesian hierarchical model (BHM), which is a widely used method for synthesizing information from different sources. We develop the adapted normalized power prior (ANPP), which establishes dependence between the dataset-specific discounting parameters of the NPP, leading to inferences that are identical to the BHM. We establish a direct relationship between the prior for the dataset-specific discounting parameters of the ANPP and the prior for the variance parameter of the BHM. Establishing this relationship not only justifies the NPP from the perspective of hierarchical modeling, but also achieves easy prior elicitation for the NPP for the purpose of dynamic borrowing. We examine the borrowing properties of the ANPP through simulations, and apply it to a case study for a pediatric lupus trial.

stat.ME↗

arXiv2024

On the lumpability of tree-valued Markov chains

Phylogenetic trees constitute an interesting class of objects for stochastic processes due to the non-standard nature of the space they inhabit. In particular, many statistical applications require the construction of Markov processes on the space of trees, whose cardinality grows superexponentially with the number of leaves considered. We investigate whether certain lower-dimensional projections of tree space preserve the Markov property in tree-valued Markov processes. We study exact lumpability of tree shapes and $\varepsilon$-lumpability of clades, exploiting the combinatorial structure of the SPR graph to obtain bounds on the lumping error under the random walk and Metropolis-Hastings processes. Finally, we show how to use these results in empirical investigation, leveraging exact and $\varepsilon$-lumpability to improve Monte Carlo estimation of tree-related quantities.

math.PR↗

arXiv2024

Large-scale Epidemiological modeling: Scanning for Mosquito-Borne Diseases Spatio-temporal Patterns in Brazil

The influence of climate on mosquito-borne diseases like dengue and chikungunya is well-established, but comprehensively tracking long-term spatial and temporal trends across large areas has been hindered by fragmented data and limited analysis tools. This study presents an unprecedented analysis, in terms of breadth, estimating the SIR transmission parameters from incidence data in all 5,570 municipalities in Brazil over 14 years (2010-2023) for both dengue and chikungunya. We describe the Episcanner computational pipeline, developed to estimate these parameters, producing a reusable dataset describing all dengue and chikungunya epidemics that have taken place in this period, in Brazil. The analysis reveals new insights into the climate-epidemic nexus: We identify distinct geographical and temporal patterns of arbovirus disease incidence across Brazil, highlighting how climatic factors like temperature and precipitation influence the timing and intensity of dengue and chikungunya epidemics. The innovative Episcanner tool empowers researchers and public health officials to explore these patterns in detail, facilitating targeted interventions and risk assessments. This research offers a new perspective on the long-term dynamics of climate-driven mosquito-borne diseases and their geographical specificities linked to the effects of global temperature fluctuations such as those captured by the ENSO index.

q-bio.PE↗

arXiv2024

Optimal Priors for the Discounting Parameter of the Normalized Power Prior

The power prior is a popular class of informative priors for incorporating information from historical data. It involves raising the likelihood for the historical data to a power, which acts as discounting parameter. When the discounting parameter is modelled as random, the normalized power prior is recommended. In this work, we prove that the marginal posterior for the discounting parameter for generalized linear models converges to a point mass at zero if there is any discrepancy between the historical and current data, and that it does not converge to a point mass at one when they are fully compatible. In addition, we explore the construction of optimal priors for the discounting parameter in a normalized power prior. In particular, we are interested in achieving the dual objectives of encouraging borrowing when the historical and current data are compatible and limiting borrowing when they are in conflict. We propose intuitive procedures for eliciting the shape parameters of a beta prior for the discounting parameter based on two minimization criteria, the Kullback-Leibler divergence and the mean squared error. Based on the proposed criteria, the optimal priors derived are often quite different from commonly used priors such as the uniform prior.

stat.ME↗

arXiv2023

A Comparison of Image and Scalar-Based Approaches in Preconditioner Selection

Within high-performance computing (HPC), solving large sparse linear systems efficiently remains paramount, with iterative methods being the predominant choice. However, the performance of these methods is tightly coupled to the aptness of the chosen preconditioner. The multifaceted nature of sparse matrices makes the universal prescription of preconditioners elusive. Notably, the key attribute of sparsity is not precisely captured by scalar metrics such as bandwidth or matrix dimensions. Advancing prior methodologies, this research introduces matrix sparsity depiction via RGB images. Utilizing a convolutional neural network (CNN), the task of preconditioner selection turns into a multi-class classification problem. Extensive tests on 126 SuiteSparse matrices emphasize the enhanced prowess of the CNN model, noting a 32% boost in accuracy and a 25% reduction in computational slowdown.

math.NA↗