Bayesian Version Research Articles

The Bayesian Phylogenetic Bootstrap and its Application to Short Trees and Branches.

Felsenstein's bootstrap is the most commonly used method to measure branch support in phylogenetics. Current sequencing technologies can result in massive sampling of taxa (e.g. SARS-CoV-2). In this case, the sequences are very similar, the trees are short, and the branches correspond to a small number of mutations (possibly 0). Nevertheless, these trees contain a strong signal, with unresolved parts but a low rate of false branches. With such data, Felsenstein's bootstrap is not satisfactory. Due to the frequentist nature of bootstrap sampling, the expected support of a branch corresponding to a single mutation is ∼63%, even though it is highly likely to be correct. Here, we propose a Bayesian version of the phylogenetic bootstrap in which sites are assigned uninformative prior probabilities. The branch support can then be interpreted as a posterior probability. We do not view the alignment as a small subsample of a large sample of sites, but rather as containing all available information (e.g. as with complete viral genomes, which are becoming routine). We give formulas for expected supports under the assumption of perfect phylogeny, in both the frequentist and Bayesian frameworks, where a branch corresponding to a single mutation now has an expected support of ∼90%. Simulations show that these theoretical results are robust to realistic data. Analyses on low-homoplasy viral and nonviral datasets show that Bayesian bootstrap support is easier to interpret, with high supports for branches very likely to be correct. As homoplasy increases, the two supports become closer and strongly correlated.

ZIBGLMM: Zero-Inflated Bivariate Generalized Linear Mixed Model for Meta-Analysis with Double-Zero-Event Studies.

Double-zero-event studies (DZS) pose a challenge for accurately estimating the overall treatment effect in meta-analysis. Current approaches, such as continuity correction or omission of DZS, are commonly employed, yet these ad hoc methods can yield biased conclusions. Although the standard bivariate generalized linear mixed model can accommodate DZS, it fails to address the potential systemic differences between DZS and other studies. In this paper, we propose a zero-inflated bivariate generalized linear mixed model (ZIBGLMM) to tackle this issue. This two-component finite mixture model includes zero-inflation for a subpopulation with negligible or extremely low risk. We develop both frequentist and Bayesian versions of ZIBGLMM and examine its performance in estimating risk ratios (RRs) against the bivariate generalized linear mixed model and conventional two-stage meta-analysis that excludes DZS. Through extensive simulation studies and real-world meta-analysis case studies, we demonstrate that ZIBGLMM outperforms the bivariate generalized linear mixed model and conventional two-stage meta-analysis that excludes DZS in estimating the true effect size with substantially less bias and comparable coverage probability.

Parameter optimisation using Bayesian inference for spallation models

The accuracy and precision of high-energy spallation models are key issues for the design and development of new applications and experiments. We present a method to estimate model parameters and associated uncertainties by leveraging the Bayesian version of the Generalised Least Squares method, which enables us to incorporate prior knowledge on the parameter values. This approach is designed to adjust parameters based on experimental data, accounting for experimental uncertainty information, and providing uncertainties for all adjusted parameters. This approach is designed in order both to improve the accuracy of models through the modification of free parameters of these models, which results in a better reproduction of experimental data, and to estimate the uncertainties of these parameters and, by extension, their impacts on the model output. We aim at demonstrating the Generalised Least Square method can be applied in the case of Monte Carlo models. We present a proof-of-concept for Monte Carlo models in the specific case of nuclear physics with the model combination INCL/ABLA. We discuss the challenges in the application of this method to high-energy spallation models, notably the large runtime and the stochasticity of the models. Our results indicate this framework can also be applied to analogous situations where parameters of a computationally expensive Monte Carlo code should be inferred/improved.

Delving into the Complexity of Analogical Reasoning: A Detailed Exploration with the Generalized Multicomponent Latent Trait Model for Diagnosis.

Research on analogical reasoning has facilitated the understanding of response processes such as pattern identification and creative problem solving, emerging as an intelligence predictor. While analogical tests traditionally combine various composition rules for item generation, current statistical models like the Logistic Latent Trait Model (LLTM) and Embretson's Multicomponent Latent Trait Model for Diagnosis (MLTM-D) face limitations in handling the inherent complexity of these processes, resulting in suboptimal model fit and interpretation. The primary aim of this research was to extend Embretson's MLTM-D to encompass complex multidimensional models that allow the estimation of item parameters. Concretely, we developed a three-parameter (3PL) version of the MLTM-D that provides more informative interpretations of participant response processes. We developed the Generalized Multicomponent Latent Trait Model for Diagnosis (GMLTM-D), which is a statistical model that extends Embretson's multicomponent model to explore complex analogical theories. The GMLTM-D was compared with LLTM and MLTM-D using data from a previous study of a figural analogical reasoning test composed of 27 items based on five composition rules: figure rotation, trapezoidal rotation, reflection, segment subtraction, and point movement. Additionally, we provide an R package (GMLTM) for conducting Bayesian estimation of the models mentioned. The GMLTM-D more accurately replicated the observed data compared to the Bayesian versions of LLTM and MLTM-D, demonstrating a better model fit and superior predictive accuracy. Therefore, the GMLTM-D is a reliable model for analyzing analogical reasoning data and calibrating intelligence tests. The GMLTM-D embraces the complexity of real data and enhances the understanding of examinees' response processes.

Bayesian Forecasting of Mortality Rates for Small Areas Using Spatiotemporal Models

Estimation and prediction of subnational mortality rates for small areas are essential planning tools for studying health inequalities. Standard methods do not perform well when data are noisy, a typical behavior of subnational datasets. Thus, reliable estimates are difficult to obtain. I present a Bayesian hierarchical model framework for prediction of mortality rates at a small or subnational level. By combining ideas from demography and epidemiology, the classical mortality modeling framework is extended to include an additional spatial component capturing regional heterogeneity. Information is pooled across neighboring regions and smoothed over time and age. To make predictions more robust and address the issue of model selection, a Bayesian version of stacking is considered using leave-future-out validation. I apply this method to forecast mortality rates for 96 regions in Bavaria, Germany, disaggregated by age and sex. Uncertainty surrounding the forecasts is provided in terms of prediction intervals. Using posterior predictive checks, I show that the models capture the essential features and are suitable to forecast the data at hand. On held-out data, my predictions outperform those of standard models lacking a regional component.

A stratified Bayesian decision-making model for occupational risk assessment of production facilities

In the production industry, harmony and good management of the workplace environment, production machinery/vehicles, and workers are necessary to carry out production by occupational health and safety (OHS) principles. Therefore, occupational risk assessment (ORA) is crucial for manufacturing-based industries. When deciding on the prioritization of risks in ORA, adding to the analysis “how the parameters defining the risk changes in possible different states in the future” positively affects the soundness of decision-making. Therefore, this study aims to develop a unique ORA model handling future changes in the importance levels of risk parameters in the risk assessment process. To this aim, the concept of stratification and the best-worst method (BWM) are used together to determine the importance weights of the risk parameters in the ORA. In addition, the Bayesian version of BWM considers more than one expert's evaluations without losing information. In a nutshell, an approach called stratified Bayesian BWM (SBBWM) that can be used for further studies has been introduced to the literature. The technique determines the priority scores of each hazard by technique for order preference by similarity to the ideal solution sorting (TOPSIS-Sort) method. Thus, while determining each hazard's priority score and order, the class of this risk has also been determined. The proposed approach evaluated thirty-six risks encountered in manufacturing, storage, handling, and laboratory processes of a flour production facility. Control measures to be taken for each risk were also determined. Methodologically, various scenario analyses and sensitivity studies were conducted to reveal how the results changed in different conditions. The proposed approach provides a more comprehensive procedure for production facilities than traditional methods and avoids the deficiencies of traditional methods.

Marginal Percentile Intervals in Bayesian Inference are Overconfident

In Bayesian statistics, Highest Posterior Density Regions (HPDR) measure the uncertainty of parameter estimates at a given credibility level. HPDRs are the Bayesian version of Highest Density Intervals (HDI) based on the posterior probability. The calculation of Percentile Intervals (PI) is a common method for approximating HDIs in many popular Python toolboxes. The PI calculation differs from the HPDR calculation as it ignores the posterior probability by simply cutting the lower and upper values of the marginalized posterior distribution symmetrically. Here, we use the phenomenological retarded transient functions to infer the posterior distribution of a clinical dataset. The one-dimensional HPDR projections were compared to the PIs for all inferred parameters. The direct comparison revealed that the one-dimensional HPDR projections of all inferred parameter posteriors exceeded the percentile-based intervals, demonstrating that the PIs were overconfident. Overall, we argue that only HPDRs can be interpreted in terms of probability.

Combining voter preferences with party position estimates from different sources for studying voting behavior and representation

Researchers interested in policy voting and substantive representation face the challenge to combine party positions with voter preference data on a common scale. One solution is to rely on voters’ perceptions of parties’ policy positions, as reported in surveys. However, this kind of data is often only available for the common left–right dimension, but not for more concrete policy scales, and it suffers from bias. We first discuss how to free perceptual data from bias by relying on a Bayesian version of the Aldrich–McKelvey rescaling technique. Then we discuss two prominent alternative sources of party position estimates: expert survey positions, and positions based on the CMP coding scheme of the manifesto project. While both types of party position estimates are considered to be of good quality, it is unclear how they fit into voter preference scales. This paper presents a simple rescaling technique that improves the matching.

How trace plots help interpret meta-analysis results.

The trace plot is seldom used in meta-analysis, yet it is a very informative plot. In this article, we define and illustrate what the trace plot is, and discuss why it is important. The Bayesian version of the plot combines the posterior density of , the between-study standard deviation, and the shrunken estimates of the study effects as a function of . With a small or moderate number of studies, is not estimated with much precision, and parameter estimates and shrunken study effect estimates can vary widely depending on the correct value of . The trace plot allows visualization of the sensitivity to along with a plot that shows which values of are plausible and which are implausible. A comparable frequentist or empirical Bayes version provides similar results. The concepts are illustrated using examples in meta-analysis and meta-regression; implementation in R is facilitated in a Bayesian or frequentist framework using the bayesmeta and metafor packages, respectively.

Analysis of the Clever Hans effect in COVID-19 detection using Chest X-Ray images and Bayesian Deep Learning

In recent months, the detection of COVID-19 from radiological images has become a topic of significant interest. Several works have proposed different AI models to demonstrate the feasibility of the application. However, the literature has also reported unwanted behaviours, spurious correlations, and biases of the developed systems that significantly limit their translation to the clinic. This paper deals with a set of interpretability techniques to analyse spurious correlations during the inference, the consistency of the decisions, and the uncertainty of the models, and evaluate the model’s performance in a broader and thoughtful way, especially regarding biasing effects, aiming to provide new methodological cues that can increase the systems’ robustness. Two different off-the-shelf convolutional neural networks (DenseNet-121 and EfficientNet-B6) were tested along with their Bayesian counterparts. Different saliency maps are used to evaluate the effects of artifacts and confounding factors, and, taking advantage of uncertainty estimations, a new version of the importance of context measure was proposed, to provide more evidence of the spurious correlation affecting models’ performance. In view of the results, DenseNet is preferred in both its standard and Bayesian versions, reaching BAcc over 97% training with a large data set (more than 70,000 images). However, results demonstrate that models are significantly affected by the biasing effects, which is minimised by pre-processing with a semantic segmentation of the lungs to guide the learning process towards areas with causal relationships with the problem under study. The conclusions could be extrapolated to the general context of pneumonia detection from chest RX.

Dynamic rainfall-induced landslide susceptibility: A step towards a unified forecasting system

The initial inception of the landslide susceptibility concept defined it as a static property of the landscape, explaining the proneness of certain locations to generate slope failures. Since the spread of data-driven probabilistic solutions though, the original susceptibility definition has been challenged to incorporate dynamic elements that would lead the occurrence probability to change both in space and in time. This is the starting point of this work, which combines the traditional strengths of the susceptibility framework together with the strengths typical of landslide early warning systems. Specifically, we model landslide occurrences in the norther sector of Vietnam, using a multi-temporal landslide inventory recently released by NASA. A set of static (terrain) and dynamic (cumulated rainfall) covariates are selected to explain the landslide presence/absence distribution via a Bayesian version of a binomial Generalized Additive Models (GAM). Thanks to the large spatiotemporal domain under consideration, we include a large suite of cross-validation routines, testing the landslide prediction through random sampling, as well as through stratified spatial and temporal sampling. We even extend the model test towards regions far away from the study site, to be used as external validation datasets. The overall performance appears to be quite high, with Area Under the Curve (AUC) values in the range of excellent model results, and very few localized exceptions.This model structure may serve as the basis for a new generation of early warning systems. However, the use of The Climate Hazards group Infrared Precipitation with Stations (CHIRPS) for the rainfall component limits the model ability in terms of future prediction. Therefore, we envision subsequent development to take this direction and move towards a unified dynamic landslide forecast. Ultimately, as a proof-of-concept, we have also implemented a potential early warning system in Google Earth Engine.

Some statistical problems involved in forecasting and estimating the spread of SARS-CoV-2 using Hawkes point processes and SEIR models

This article reviews some of the statistical issues involved with modeling SARS-CoV02 (Covid-19) in Los Angeles County, California, using Hawkes point process models and SEIR models. The two types of models are compared, and their pros and cons are discussed. We also discuss particular statistical decisions, such as where to place the upper limits on y-axes, and whether to use a Bayesian or frequentist version of the model, how to estimate seroprevalence, and fitting the density of transmission times in the Hawkes model.

Bayesian joint quantile autoregression

Quantile regression continues to increase in usage, providing a useful alternative to customary mean regression. Primary implementation takes the form of so-called multiple quantile regression, creating a separate regression for each quantile of interest. However, recently, advances have been made in joint quantile regression, supplying a quantile function which avoids crossing of the regression across quantiles. Here, we turn to quantile autoregression (QAR), offering a fully Bayesian version. We extend the initial quantile regression work of Koenker and Xiao (J Am Stat Assoc 101(475):980–990, 2006. https://doi.org/10.1198/016214506000000672) in the spirit of Tokdar and Kadane (Bayesian Anal 7(1):51–72, 2012. https://doi.org/10.1214/12-BA702). We offer a directly interpretable parametric model specification for QAR. Further, we offer a pth-order QAR(p) version, a multivariate QAR(1) version, and a spatial QAR(1) version. We illustrate with simulation as well as a temperature dataset collected in Aragón, Spain.

Parsing memory and nonmemory contributions to age-related declines in mnemonic discrimination performance: a hierarchical Bayesian diffusion decision modeling approach.

The mnemonic discrimination task (MDT) is a widely used cognitive assessment tool. Performance in this task is believed to indicate an age-related deficit in episodic memory stemming from a decreased ability to pattern-separate among similar experiences. However, cognitive processes other than memory ability might impact task performance. In this study, we investigated whether nonmnemonic decision-making processes contribute to the age-related deficit in the MDT. We applied a hierarchical Bayesian version of the Ratcliff diffusion model to the MDT performance of 26 younger and 31 cognitively normal older adults. It allowed us to decompose decision behavior in the MDT into different underlying cognitive processes, represented by specific model parameters. Model parameters were compared between groups, and differences were evaluated using the Bayes factor. Our results suggest that the age-related decline in MDT performance indicates a predominantly mnemonic deficit rather than differences in nonmnemonic decision-making processes. In addition, this mnemonic deficit might also involve a slowing in processes related to encoding and retrieval strategies, which are relevant for successful memory as well. These findings help to better understand what cognitive processes contribute to the age-related decline in MDT performance and may help to improve the diagnostic value of this popular task.

A bayesian version of Galton–Watson for population growth and its use in the management of small population

A bayesian version of Galton–Watson for population growth and its use in the management of small population

Bayesian hierarchical model for dose-finding trial incorporating historical data

ABSTRACT The Multiple Comparison Procedure and Modelling (MCPMod) approach has been shown to be a powerful statistical technique that can significantly improve the design and analysis of dose-finding studies under model uncertainty. Due to its frequentist nature, however, it is difficult to incorporate information into MCPMod from historical trials on the same drug. BMCPMod, a recently introduced Bayesian version of MCPMod, is designed to take into account historical information on the placebo dose group. We introduce a Bayesian hierarchical framework capable of incorporating historical information on an arbitrary number of dose groups, including both placebo and active ones, taking into account the relationship between responses of these dose groups. Our approach can also model both prognostic and predictive between-trial heterogeneity and is particularly useful in situations where the effect sizes of two trials are different. Our goal is to reduce the necessary sample size in the dose-finding trial while maintaining its target power.

Optimized Bayesian convolutional neural networks for invasive breast cancer diagnosis system

Deep learning (DL) has depicted unprecedented results in the diagnosis of invasive ductal carcinoma (IDC). However, most DL methods are not able to infer the uncertainty in their predictions, and are often too confident which may cause undesirable consequences. The ability of DL models to express their uncertainty in their predictions is particularly important in diagnosing diseases. Therefore, this paper proposes an uncertainty-aware approach called optimized Bayesian convolutional neural network (OBCNN) for the automated detection of IDC from histopathology images and is capable of estimating and inferring the uncertainty in its predictions. The proposed OBCNN employs an approximate Bayesian version of a pre-trained convolutional neural network (CNN) model named ResNet101V2 that is fine-tuned to the histopathology images of IDC. The Bayesian approximation is performed by adding Monte Carlo dropout (MC-dropout) to ResNet101V2 architecture. Due to the effect of MC-dropout on the obtained posterior predictive distribution (PPD), the value of MC-dropout should be chosen carefully because if the MC-dropout value is too large, the predictive distribution (PD) will be very diverse. Whereas if the MC-dropout value is very small, the PD will be very similar. Therefore, an optimization algorithm known as the slime mould algorithm is utilized to set the optimal value of the MC-dropout. During inference, the proposed OBCNN runs for T forward passes to configure the PPD. The mean, standard deviation (SD) and entropy are then calculated over the obtained PD to estimate the predictive uncertainty (PU) of the OBCNN. The proposed OBCNN achieved an accuracy of 93.83%, a precision of 96.14%, a G-mean of 93.04%, False Negative Rate of 4.72%, and False Positive Rate of 9.96 %. The proposed OBCNN has also been compared with recent related work, the comparison’s results demonstrated that OBCNN performed better in the diagnosis of IDC.

Fractional Polynomial Models as Special Cases of Bayesian Generalized Nonlinear Models

We propose a framework for fitting multivariable fractional polynomial models as special cases of Bayesian generalized nonlinear models, applying an adapted version of the genetically modified mode jumping Markov chain Monte Carlo algorithm. The universality of the Bayesian generalized nonlinear models allows us to employ a Bayesian version of fractional polynomials in any supervised learning task, including regression, classification, and time-to-event data analysis. We show through a simulation study that our novel approach performs similarly to the classical frequentist multivariable fractional polynomials approach in terms of variable selection, identification of the true functional forms, and prediction ability, while naturally providing, in contrast to its frequentist version, a coherent inference framework. Real-data examples provide further evidence in favor of our approach and show its flexibility.

Hierarchical Bayesian Aldrich–McKelvey Scaling

AbstractEstimating the ideological positions of political actors is an important step toward answering a number of substantive questions in political science. Survey scales provide useful data for such estimation, but also present a challenge, as respondents tend to interpret the scales differently. The Aldrich–McKelvey model addresses this challenge, but the existing implementations of the model still have notable shortcomings. Focusing on the Bayesian version of the model (BAM), the analyses in this article demonstrate that the model is prone to overfitting and yields poor results for a considerable share of respondents. The article addresses these shortcomings by developing a hierarchical Bayesian version of the model (HBAM). The new version treats self-placements as data to be included in the likelihood function while also modifying the likelihood to allow for scale flipping. The resulting model outperforms the existing Bayesian version both on real data and in a Monte Carlo study. An R package implementing the models in Stan is provided to facilitate future use.

Impact of quasi-periodic and steep-spectrum timing noise on the measurement of pulsar timing parameters

Abstract Timing noise in pulsars is often modelled with a Fourier-basis Gaussian process that follows a power law with periodic boundary conditions on the observation time, Tspan. However the actual noise processes can extend well below 1/Tspan, and many pulsars are known to exhibit quasi-periodic timing noise. In this paper we investigate several adaptions that try to account for these differences between the observed behaviour and the simple power-law model. Firstly, we propose to include an additional term that models the quasi-periodic spin-down variations known to be present in many pulsars. Secondly, we show that a Fourier basis of 1/2Tspan can be more suited for estimating long term timing parameters such as the spin frequency second derivative (F2), and is required when the exponent of the power spectrum is greater than ∼4. We also implement a Bayesian version of the generalised least squares ‘Cholesky’ method which has different limitations at low frequency, but find that there is little advantage over Fourier-basis methods. We apply our quasi-periodic spin down model to a sample of pulsars with known spin-down variations and show that this improves parameter estimation of F2 and proper motion for the most pathological cases, but in general the results are consistent with a power-law model. The models are all made available through the run_enterprise software package.