RESUMEN

Marginal maximum likelihood, a common estimation method for item response theory models, is not inherently a Bayesian procedure. However, due to estimation difficulties, Bayesian priors are often applied to the likelihood when estimating 3PL models, especially with small samples. Little focus has been placed on choosing the priors for marginal maximum estimation. In this study, using sample sizes of 1,000 or smaller, not using priors often led to extreme, implausible parameter estimates. Applying prior distributions to the c-parameters alleviated the estimation problems with samples of 500 or more; for the samples of 100, priors on both the a-parameters and c-parameters were needed. Estimates were biased when the mode of the prior did not match the true parameter value, but the degree of the bias did not depend on the strength of the prior unless it was extremely informative. The root mean squared error (RMSE) of the a-parameters and b-parameters did not depend greatly on either the mode or the strength of the prior unless it was extremely informative. The RMSE of the c-parameters, like the bias, depended on the mode of the prior for c.

RESUMEN

Mixture distributions are naturally extra attractive to model the heterogeneous environment of processes in reliability analysis than simple probability models. This focus of the study is to develop and Bayesian inference on the 3-component mixture of power distributions. Under symmetric and asymmetric loss functions, the Bayes estimators and posterior risk using priors are derived. The presentation of Bayes estimators for various sample sizes and test termination time (a fact of time after that test is terminated) is examined in this article. To assess the performance of Bayes estimators in terms of posterior risks, a Monte Carlo simulation along with real data study is presented.

RESUMEN

In Bayesian random-effects meta-analysis, the use of weakly informative prior distributions is of particular benefit in cases where only a few studies are included, a situation often encountered in health technology assessment (HTA). Suggestions for empirical prior distributions are available in the literature but it is unknown whether these are adequate in the context of HTA. Therefore, a database of all relevant meta-analyses conducted by the Institute for Quality and Efficiency in Health Care (IQWiG, Germany) was constructed to derive empirical prior distributions for the heterogeneity parameter suitable for HTA. Previously, an extension to the normal-normal hierarchical model had been suggested for this purpose. For different effect measures, this extended model was applied on the database to conservatively derive a prior distribution for the heterogeneity parameter. Comparison of a Bayesian approach using the derived priors with IQWiG's current standard approach for evidence synthesis shows favorable properties. Therefore, these prior distributions are recommended for future meta-analyses in HTA settings and could be embedded into the IQWiG evidence synthesis approach in the case of very few studies.

Asunto(s)

RESUMEN

Objective: Much of psychological research has suffered from small sample sizes and low statistical power, resulting in unstable parameter estimates. The Bayesian approach offers a promising solution by incorporating prior knowledge into statistical models, which may lead to improved stability compared to a frequentist approach. Methods: Simulated data from four populations with known bivariate correlations (ρ = 0.1, 0.2, 0.3, 0.4) was used to estimate the sample correlation as samples were sequentially added from the population, from n = 10 to n = 500. The impact of three different, subjectively defined prior distributions (weakly, moderately, and highly informative) was investigated and compared to a frequentist model. Results: The results show that bivariate correlation estimates are unstable, and that the risk of obtaining an estimate that is exaggerated or in the wrong direction is relatively high, for sample sizes for below 100, and considerably so for sample sizes below 50. However, this instability can be constrained by informative Bayesian priors. Conclusion: Informative Bayesian priors have the potential to significantly reduce sample size requirements and help ensure that obtained estimates are in line with realistic expectations. The combined stabilizing and regularizing effect of a weakly informative prior is particularly useful when conducting research with small samples. The impact of more informative Bayesian priors depends on one's threshold for probability and whether one's goal is to obtain an estimate merely in the correct direction, or to obtain a high precision estimate whose associated interval falls within a narrow range. Implications for sample size requirements and directions for future research are discussed.

RESUMEN

This article proposes a new class of nonhomogeneous Poisson spatiotemporal model. In this approach, we use a state-space model-based prior distribution to handle the scale and shape parameters of the Weibull intensity function. The proposed prior distribution enables the inclusion of changes in the behavior of the intensity function over time. In defining the spatial correlation function of the model, we include anisotropy via spatial deformation. We estimate the model parameters from a Bayesian perspective, employ the Markov chain Monte Carlo approach, and validate this estimation procedure through a simulation exercise. Finally, the extreme rainfall in the southern semiarid region in northeastern Brazil is analyzed using the R10mm index. The proposed model showed better fit and prediction ability than did other nonhomogeneous Poisson spatiotemporal models available in the literature. This improvement in performance is mainly due to the flexibility of the intensity function that is achieved by allowing the incorporation, in time, of the climatic characteristics of this region.

Asunto(s)

RESUMEN

In Bayesian meta-analysis, the specification of prior probabilities for the between-study heterogeneity is commonly required, and is of particular benefit in situations where only few studies are included. Among the considerations in the set-up of such prior distributions, the consultation of available empirical data on a set of relevant past analyses sometimes plays a role. How exactly to summarize historical data sensibly is not immediately obvious; in particular, the investigation of an empirical collection of heterogeneity estimates will not target the actual problem and will usually only be of limited use. The commonly used normal-normal hierarchical model for random-effects meta-analysis is extended to infer a heterogeneity prior. Using an example data set, we demonstrate how to fit a distribution to empirically observed heterogeneity data from a set of meta-analyses. Considerations also include the choice of a parametric distribution family. Here, we focus on simple and readily applicable approaches to then translate these into (prior) probability distributions.

Asunto(s)

RESUMEN

Bayesian bandwidth selections in multivariate associated kernel estimation of probability density functions are known to improve classical methods such as cross-validation techniques in terms of execution time and smoothing quality. The paper focuses on a basic multivariate gamma kernel which is appropriated to estimate densities with support [ 0 , ∞ ) d . For this purpose, we consider a Bayesian adaptive estimation of the bandwidths vector under the usual quadratic loss function. The exact expression of the posterior distribution and the vector of bandwidths are obtained. Simulations studies highlight the excellent performance of the proposed approach, comparing to the global cross-validation bandwidth selection, and under integrated squared errors. Two bivariate and trivariate applications to the Old Faithful geyser data and new ones on drinking water pumps in the Sahel, respectively, are made.

RESUMEN

BACKGROUND: Design and analysis of clinical trials for rare and ultra-rare disease pose unique challenges to the practitioners. Meeting conventional power requirements is infeasible for diseases where sample sizes are inherently very small. Moreover, rare disease populations are generally heterogeneous and widely dispersed, which complicates study enrollment and design. Leveraging all available information in rare and ultra-rare disease trials can improve both drug development and informed decision-making processes. MAIN TEXT: Bayesian statistics provides a formal framework for combining all relevant information at all stages of the clinical trial, including trial design, execution, and analysis. This manuscript provides an overview of different Bayesian methods applicable to clinical trials in rare disease. We present real or hypothetical case studies that address the key needs of rare disease drug development highlighting several specific Bayesian examples of clinical trials. Advantages and hurdles of these approaches are discussed in detail. In addition, we emphasize the practical and regulatory aspects in the context of real-life applications. CONCLUSION: The use of innovative trial designs such as master protocols and complex adaptive designs in conjunction with a Bayesian approach may help to reduce sample size, select the correct treatment and population, and accurately and reliably assess the treatment effect in the rare disease setting.

Asunto(s)

RESUMEN

Bayesian inference requires the specification of prior distributions that quantify the pre-data uncertainty about parameter values. One way to specify prior distributions is through prior elicitation, an interview method guiding field experts through the process of expressing their knowledge in the form of a probability distribution. However, prior distributions elicited from experts can be subject to idiosyncrasies of experts and elicitation procedures, raising the spectre of subjectivity and prejudice. Here, we investigate the effect of interpersonal variation in elicited prior distributions on the Bayes factor hypothesis test. We elicited prior distributions from six academic experts with a background in different fields of psychology and applied the elicited prior distributions as well as commonly used default priors in a re-analysis of 1710 studies in psychology. The degree to which the Bayes factors vary as a function of the different prior distributions is quantified by three measures of concordance of evidence: We assess whether the prior distributions change the Bayes factor direction, whether they cause a switch in the category of evidence strength, and how much influence they have on the value of the Bayes factor. Our results show that although the Bayes factor is sensitive to changes in the prior distribution, these changes do not necessarily affect the qualitative conclusions of a hypothesis test. We hope that these results help researchers gauge the influence of interpersonal variation in elicited prior distributions in future psychological studies. Additionally, our sensitivity analyses can be used as a template for Bayesian robustness analyses that involve prior elicitation from multiple experts.

Asunto(s)

RESUMEN

Postpartum diseases (PD) in dairy cows cause serious concerns about economic losses worldwide. This study intended to investigate the relationship between PD susceptibility and counts of monocyte subgroup cells (MCC), in the blood samples taken from 27 German Holstein cows 42 and 14 days before the expected calving by adopting the Bayesian approach. The paper also aimed to discuss the prior selection problem in the Bayesian approach and to reveal the parameter estimation difference based on the available data. The parameters were estimated according to the models established at two different time points with eight different prior distributions. As a result of the study, all the models revealed strong evidence that cows with PD, compared to healthy cows, had a higher increase in MCC counts on Day 14. There was no difference between the models according to their WAIC and LOO values. In terms of the parameter estimates, the models produced identical results; however, the models with noninformative priors presented strong evidence for the absence of effects by Bayes factor but, provided evidence for the existence of the effect according to the credible interval. The models with weakly informative and shrinkage priors provided strong evidence for the presence of the effect. The findings suggest that MCC can be considered to serve as a prospective indicator for early detection of PD.

Asunto(s)

RESUMEN

Federated learning (FL) enables collaboratively training a joint model for multiple medical centers, while keeping the data decentralized due to privacy concerns. However, federated optimizations often suffer from the heterogeneity of the data distribution across medical centers. In this work, we propose Federated Learning with Shared Label Distribution (FedSLD) for classification tasks, a method that adjusts the contribution of each data sample to the local objective during optimization via knowledge of clients' label distribution, mitigating the instability brought by data heterogeneity. We conduct extensive experiments on four publicly available image datasets with different types of non-IID data distributions. Our results show that FedSLD achieves better convergence performance than the compared leading FL optimization algorithms, increasing the test accuracy by up to 5.50 percentage points.

RESUMEN

We outline a Bayesian model-averaged (BMA) meta-analysis for standardized mean differences in order to quantify evidence for both treatment effectiveness δ and across-study heterogeneity τ . We construct four competing models by orthogonally combining two present-absent assumptions, one for the treatment effect and one for across-study heterogeneity. To inform the choice of prior distributions for the model parameters, we used 50% of the Cochrane Database of Systematic Reviews to specify rival prior distributions for δ and τ . The relative predictive performance of the competing models and rival prior distributions was assessed using the remaining 50% of the Cochrane Database. On average, ℋ1r -the model that assumes the presence of a treatment effect as well as across-study heterogeneity-outpredicted the other models, but not by a large margin. Within ℋ1r , predictive adequacy was relatively constant across the rival prior distributions. We propose specific empirical prior distributions, both for the field in general and for each of 46 specific medical subdisciplines. An example from oral health demonstrates how the proposed prior distributions can be used to conduct a BMA meta-analysis in the open-source software R and JASP. The preregistered analysis plan is available at https://osf.io/zs3df/.

Asunto(s)

RESUMEN

Maximum a posteriori estimation (MAP) with Dirichlet prior has been shown to be effective in improving the parameter learning of Bayesian networks when the available data are insufficient. Given no extra domain knowledge, uniform prior is often considered for regularization. However, when the underlying parameter distribution is non-uniform or skewed, uniform prior does not work well, and a more informative prior is required. In reality, unless the domain experts are extremely unfamiliar with the network, they would be able to provide some reliable knowledge on the studied network. With that knowledge, we can automatically refine informative priors and select reasonable equivalent sample size (ESS). In this paper, considering the parameter constraints that are transformed from the domain knowledge, we propose a Constrained adjusted Maximum a Posteriori (CaMAP) estimation method, which is featured by two novel techniques. First, to draw an informative prior distribution (or prior shape), we present a novel sampling method that can construct the prior distribution from the constraints. Then, to find the optimal ESS (or prior strength), we derive constraints on the ESS from the parameter constraints and select the optimal ESS by cross-validation. Numerical experiments show that the proposed method is superior to other learning algorithms.

RESUMEN

PURPOSE: Compressed sensing (CS) reduces the measurement time of magnetic resonance (MR) imaging, where the use of regularizers or image priors are key techniques to boost reconstruction precision. The optimal prior generally depends on the subject and the hand-building of priors is hard. A methodology of combining priors to create a better one would be useful for various forms of image processing that use image priors. METHODS: We propose a theory, called prior ensemble learning (PEL), which combines many weak priors (not limited to images) efficiently and approximates the posterior mean (PM) estimate, which is Bayes optimal for minimizing the mean squared error (MSE). The way of combining priors is changed from that of an exponential family to a mixture family. We applied PEL to an undersampled (10%) multicoil MR image reconstruction task. RESULTS: We demonstrated that PEL could combine 136 image priors (norm-based priors such as total variation (TV) and wavelets with various regularization coefficient (RC) values) from only two training samples and that it was superior to the CS-SENSE-based method in terms of the MSE of the reconstructed image. The resulting combining weights were sparse (18% of the weak priors remained), as expected. CONCLUSION: By the theory, the PM estimator was decomposed into the sparse weighted sum of each weak prior's PM estimator, and the exponential computational complexity for RCs was reduced to polynomial order w.r.t. the number of weak priors. PEL is feasible and effective for a practical MR image reconstruction task.

Asunto(s)

RESUMEN

Inter-rater agreement measures are used to estimate the degree of agreement between two or more assessors. When the agreement table is ordinal, different weight functions that incorporate row and column scores are used along with the agreement measures. The selection of row and column scores is effectual on the estimated degree of agreement. The weighted measures are prone to the anomalies frequently seen in agreement tables such as unbalanced table structures or grey zones due to the assessment behaviour of the raters. In this study, Bayesian approaches for the estimation of inter-rater agreement measures are proposed. The Bayesian approaches make it possible to include prior information on the assessment behaviour of the raters in the analysis and impose order restrictions on the row and column scores. In this way, we improve the accuracy of the agreement measures and mitigate the impact of the anomalies in the estimation of the strength of agreement between the raters. The elicitation of prior distributions is described theoretically and practically for the Bayesian estimation of five agreement measures with three different weights using an agreement table having two grey zones. A Monte Carlo simulation study is conducted to assess the classification accuracy of the Bayesian and classical approaches for the considered agreement measures for a given level of agreement. Recommendations for the selection of the highest performing agreement measure and weight combination are made in the breakdown of the table structure and sample size.

Asunto(s)

RESUMEN

Planetary Protection is applicable for missions to biologically sensitive targets of interest in the solar system. For robotic missions landing on the Martian surface, Earth-based biological contamination must be reduced, controlled, and monitored to adhere to forward planetary protection requirements. To address the overall biological load limit and microbial density requirements per spacecraft each component is tracked based on its manufacturing pedigree and/or directly assessed using a direct sampling technique with either a swab or wipe. The tracking and reporting of requirements compliance has varied from mission to mission and reporting of numbers has consistently leaned towards the conservative worst-case scenario. With an increase in the number of missions and mission complexities, the need to establish a technically sound, statistical, and biological solution that provides a single point solution which addresses the distribution of spacecraft contamination becomes critical. Select components of the InSight mission, launched in 2018, have been used as a test case to evaluate the efficacy of applying Bayesian statistics to planetary protection data sets. Eight representative components covering the various bounding cases of high and low surface area, biological count, and sampling devices were analyzed as well as an assembly level case to evaluate the rollup of directly sampled and manufacturing pedigree components. A Bayesian approach was developed leveraging different priors from the zero-inflated data sets and compared to the heritage and existing NASA bioburden assessment approaches. In addition, several non-informative priors were evaluated for use in performing bioburden calculations. The results have demonstrated a viable framework to enable a Bayesian statistical approach to be further developed and utilized for planetary protection requirements assessment.

Asunto(s)

RESUMEN

With small to modest sample sizes and complex models, maximum likelihood (ML) estimation of confirmatory factor analysis (CFA) models can show serious estimation problems such as non-convergence or parameter estimates outside the admissible parameter space. In this article, we distinguish different Bayesian estimators that can be used to stabilize the parameter estimates of a CFA: the mode of the joint posterior distribution that is obtained from penalized maximum likelihood (PML) estimation, and the mean (EAP), median (Med), or mode (MAP) of the marginal posterior distribution that are calculated by using Markov Chain Monte Carlo (MCMC) methods. In two simulation studies, we evaluated the performance of the Bayesian estimators from a frequentist point of view. The results show that the EAP produced more accurate estimates of the latent correlation in many conditions and outperformed the other Bayesian estimators in terms of root mean squared error (RMSE). We also argue that it is often advantageous to choose a parameterization in which the main parameters of interest are bounded, and we suggest the four-parameter beta distribution as a prior distribution for loadings and correlations. Using simulated data, we show that selecting weakly informative four-parameter beta priors can further stabilize parameter estimates, even in cases when the priors were mildly misspecified. Finally, we derive recommendations and propose directions for further research.

RESUMEN

Bayesian methods are an important set of tools for performing meta-analyses. They avoid some potentially unrealistic assumptions that are required by conventional frequentist methods. More importantly, meta-analysts can incorporate prior information from many sources, including experts' opinions and prior meta-analyses. Nevertheless, Bayesian methods are used less frequently than conventional frequentist methods, primarily because of the need for nontrivial statistical coding, while frequentist approaches can be implemented via many user-friendly software packages. This article aims at providing a practical review of implementations for Bayesian meta-analyses with various prior distributions. We present Bayesian methods for meta-analyses with the focus on odds ratio for binary outcomes. We summarize various commonly used prior distribution choices for the between-studies heterogeneity variance, a critical parameter in meta-analyses. They include the inverse-gamma, uniform, and half-normal distributions, as well as evidence-based informative log-normal priors. Five real-world examples are presented to illustrate their performance. We provide all of the statistical code for future use by practitioners. Under certain circumstances, Bayesian methods can produce markedly different results from those by frequentist methods, including a change in decision on statistical significance. When data information is limited, the choice of priors may have a large impact on meta-analytic results, in which case sensitivity analyses are recommended. Moreover, the algorithm for implementing Bayesian analyses may not converge for extremely sparse data; caution is needed in interpreting respective results. As such, convergence should be routinely examined. When select statistical assumptions that are made by conventional frequentist methods are violated, Bayesian methods provide a reliable alternative to perform a meta-analysis.

Asunto(s)

RESUMEN

Previous research has shown the potential value of Bayesian methods in fMRI (functional magnetic resonance imaging) analysis. For instance, the results from Bayes factor-applied second-level fMRI analysis showed a higher hit rate compared with frequentist second-level fMRI analysis, suggesting greater sensitivity. Although the method reported more positives as a result of the higher sensitivity, it was able to maintain a reasonable level of selectivity in term of the false positive rate. Moreover, employment of the multiple comparison correction method to update the default prior distribution significantly improved the performance of Bayesian second-level fMRI analysis. However, previous studies have utilized the default prior distribution and did not consider the nature of each individual study. Thus, in the present study, a method to adjust the Cauchy prior distribution based on a priori information, which can be acquired from the results of relevant previous studies, was proposed and tested. A Cauchy prior distribution was adjusted based on the contrast, noise strength, and proportion of true positives that were estimated from a meta-analysis of relevant previous studies. In the present study, both the simulated images and real contrast images from two previous studies were used to evaluate the performance of the proposed method. The results showed that the employment of the prior adjustment method resulted in improved performance of Bayesian second-level fMRI analysis.

RESUMEN

BACKGROUND: Network meta-analysis (NMA) is a popular tool to compare multiple treatments in medical research. It is frequently implemented via Bayesian methods. The prior choice of between-study heterogeneity is critical in Bayesian NMAs. This study evaluates the impact of different priors for heterogeneity on NMA results. METHODS: We identified all NMAs with binary outcomes published in The BMJ, JAMA, and The Lancet during 2010-2018, and extracted information about their prior choices for heterogeneity. Our primary analyses focused on those with publicly available full data. We re-analyzed the NMAs using 3 commonly-used non-informative priors and empirical informative log-normal priors. We obtained the posterior median odds ratios and 95% credible intervals of all comparisons, assessed the correlation among different priors, and used Bland-Altman plots to evaluate their agreement. The kappa statistic was also used to evaluate the agreement among these priors regarding statistical significance. RESULTS: Among the selected Bayesian NMAs, 52.3% did not specify the prior choice for heterogeneity, and 84.1% did not provide rationales. We re-analyzed 19 NMAs with full data available, involving 894 studies, 173 treatments, and 395,429 patients. The correlation among posterior median (log) odds ratios using different priors were generally very strong for NMAs with over 20 studies. The informative priors produced substantially narrower credible intervals than non-informative priors, especially for NMAs with few studies. Bland-Altman plots and kappa statistics indicated strong overall agreement, but this was not always the case for a specific NMA. CONCLUSIONS: Priors should be routinely reported in Bayesian NMAs. Sensitivity analyses are recommended to examine the impact of priors, especially for NMAs with relatively small sample sizes. Informative priors may produce substantially narrower credible intervals for such NMAs.

Asunto(s)