Bayesian Credibility Intervals Research Articles

<p>Bayesian Decision Analysis For Benchmarking Daily And Monthly Time Series</p>

In Business Time Series analysis, daily disaggregation of monthly time series is often needed when adjusting financial series (stock options, swaps, mortgages or other loans). The classical stochastic adjustment methods only allow quarterly or monthly benchmarks to be estimated and can only be applied when high frequency is a regular multiple of low frequency. Thus, they fail to offer solutions for such problems, thereby evidencing the need to develop tools and methods for high-frequency series (daily or weekly ones). This paper obtains the first known method for using daily indicators, taking into account the different number of days for each month. The proposed Bayesian (normal-gamma) method can employ several indicators for the likelihood model, also obtaining an explicit (non iterative) solution for the optimal estimate of high frequency series. It is also important to observe that the model includes a correction mechanism for volatile indicators, as is often found in benchmarking problems for small areas. The methodology, in the line of normal-gamma specifications, allows Bayesian Credibility intervals for the estimated daily series.

Multilevel mediation analysis in R: A comparison of bootstrap and Bayesian approaches.

Mediation analysis in repeated measures studies can shed light on the mechanisms through which experimental manipulations change the outcome variable. However, the literature on interval estimation for the indirect effect in the 1-1-1 single mediator model is sparse. Most simulation studies to date evaluating mediation analysis in multilevel data considered scenarios that do not match the expected numbers of level 1 and level 2 units typically encountered in experimental studies, and no study to date has compared resampling and Bayesian methods for constructing intervals for the indirect effect in this context. We conducted a simulation study to compare statistical properties of interval estimates of the indirect effect obtained using four bootstrap and two Bayesian methods in the 1-1-1 mediation model with and without random effects. Bayesian credibility intervals had coverage closest to the nominal value and no instances of excessive Type I error rates, but lower power than resampling methods. Findings indicated that the pattern of performance for resampling methods often depended on the presence of random effects. We provide suggestions for selecting an interval estimator for the indirect effect depending on the most important statistical property for a given study, as well as code in R for implementing all methods evaluated in the simulation study. Findings and code from this project will hopefully support the use of mediation analysis in experimental research with repeated measures.

Modeling the Amount of Carbon Dioxide Emissions Application: New Modified Alpha Power Weibull-X Family of Distributions

The use of statistical distributions to model life phenomena has received considerable attention in the literature. Recent studies have shown the potential of statistical distributions in modeling data in applied sciences, especially in environmental sciences. Among them, the Weibull distribution is one of the most well-known models that can be used very effectively for modeling data in the fields of pollution and gas emissions, to name a few. In this paper, we introduce a family of distributions, which we call the modified Alpha-Power Weibull-X family of distributions. Based on the proposed family, we introduce a new model with five parameters, the modified Alpha-Power Weibull–Weibull distribution. Some mathematical properties were determined. Bayesian and maximum likelihood estimates for the model parameters were derived. The MLEs, bootstrap and Bayesian HPD credibility intervals for the unknown parameters were performed. A Monte Carlo simulation study was performed to evaluate the performance of the estimates. A simulation study was performed based on the parameters of the proposed model. An application to the carbon dioxide emissions dataset was performed to predict unique symmetric and asymmetric patterns and illustrate the applicability and potential of the model. For this data set, the proposed model is compared with the modified alpha power Weibull exponential distribution and the two-parameter Weibull distribution. To show which of the competing distributions is the best, we draw on certain analytical tools such as the Kolmogorov–Smirnov test. Based on these analytical measures, we found that the new model outperforms the competing models.

Bayesian analysis of designed reliability improvement experiments with application to adaptive termination

AbstractIn reliability improvement experiments, engineers are very interested in which factors affect the reliability of products. Furthermore, they hope to terminate experiment early without affecting the identified results. In this article, we assume the shape and scale parameters of Weibull distributions vary with experimental factors, and construct a Bayesian framework to identify important factors. We model the relationships between the parameters of Weibull distributions and experimental factors, and determine important factors based on Bayesian credibility intervals. Because the proposed method can analyze lifetime data with heavy censoring, we adaptive terminate experiment through estimating and comparing model coefficients under different experiment times. The results show that experiment time is shortened while the important factors are not changed.

Estimation of the accuracy of an ELISA test applied to bulk tank milk for predicting herd-level status for Salmonella Dublin in dairy herds using Bayesian Latent Class Models

Enzyme-Linked Immunosorbent Assay (ELISA) test is commonly used for detection of antibodies to Salmonella Dublin in individual bovine milk samples. However, little is known about its accuracy when used on bulk tank milk for determining herd-level S. Dublin status and when evaluated without assuming a perfect reference test.The objectives of this study were: i) to estimate the herd prevalence of S. Dublin among dairy cattle herds in Québec, Canada; ii) to estimate the herd sensitivity and specificity of a commercially available ELISA test when used on bulk milk; iii) to examine how the diagnostic test accuracy varies with different bulk milk ELISA cut-offs; and (iv) to assess the added value of combining ELISA screening of bulk milk and individual serum of 10 animals for determining S. Dublin herd status.A cohort of 302 dairy herds selected in three regions (population 1) and 58 herds that have already tested positive to S. Dublin (population 2) were recruited. A total of 715 bulk milk samples and 7150 individual blood samples from cattle over 3 months old (10 animals per herd) sampled on two occasions were collected. Testing was conducted using PrioCHECK™ Salmonella Ab bovine Dublin ELISA test for milk (Bmilk ELISA: test under investigation) and for serum of 10 individual animals (Serum10 ELISA: imperfect reference test) to determine the herd-level S. Dublin status. A latent class model for two populations, two tests, allowing for conditional dependence between tests was fit within a Bayesian framework. At cut-off PP % ≥ 15 for a Bmilk ELISA, which is used by provincial authorities, the herd prevalence of S. Dublin estimated using informative prior was 6.8 % (4.3–9.9) in population 1. The herd sensitivity and specificity estimates (95 % Bayesian Credibility Intervals) for Bmilk ELISA were 40.6 % (15.6–88.8) and 91.9 % (88.3–95.8), respectively. Positive and negative predictive values of Bmilk ELISA applied in population 1 were 26.4 % (8.5–60.2) and 95.8 % (92.1–99.2), respectively. Increasing Bmilk ELISA cut-offs had little influence on predictive values. The combination of both ELISA tests did not improve the diagnostic accuracy of S. Dublin. Our study shows that a test-positive herd based on a single bulk milk sample would require complementary tests for status confirmation. However, a test-negative herd could be classified as true negative with a high certainty.

Comparisons of frequentist and Bayesian inferences for interval estimation on process yield

Process yield has been a standard metric for measuring the capability and performance of manufacturing processes. Process capability index Spk, a concise unit-less gauge with yield-sensitive functionality, communicates succinctly the genuine process yield for normally distributed processes. However, in frequentist statistics, the exact sampling distribution of Spk’s natural estimator is intractable. Various frequentist approaches have attempted to address its wide-scale accuracy in statistical inference. Among them, the approach of generalized confidence interval (GCI) has been demonstrated superiority. In this paper, we incorporate Markov chain Monte Carlo (MCMC) algorithms to introduce a Bayesian-type approach. Extensive simulations in comparison of accuracy and precision performances between the Spk’s frequentist and Bayesian inferences are conducted. Concerning coverage rates and average interval widths of the inferential criteria, Spk’s Bayesian MCMC credibility intervals perform better than frequentist GCIs in most cases, particularly, the cases with only a few samples of information acquired from the manufacturing process.

Optimizing conservation in species-specific agricultural landscapes.

Recovery of grassland birds in agricultural landscapes is a global imperative. Agricultural landscapes are complex, and the value of resource patches may vary substantially among species. The spatial extent at which landscape features affect populations (i.e., scale of effect) may also differ among species. There is a need for regional-scale conservation planning that considers landscape-scale and species-specific responses of grassland birds to environmental change. We developed a spatially explicit approach to optimizing grassland conservation in the context of species-specific landscapes and prioritization of species recovery and applied it to a conservation program in Kentucky (USA). We used a hierarchical distance-sampling model with an embedded scale of effect predictor to estimate the relationship between landscape structure and abundance of eastern meadowlarks (Sturnella magna), field sparrows (Spizella pusilla), and northern bobwhites (Colinus virginianus). We used a novel spatially explicit optimization procedure rooted in multi-attribute utility theory to design alternative conservation strategies (e.g., prioritize only northern bobwhite recovery or assign equal weight to each species' recovery). Eastern meadowlarks and field sparrows were more likely to respond to landscape-scale resource patch adjacencies than landscape-scale patch densities. Northern bobwhite responded to both landscape-scale resource patch adjacencies and densities and responded strongly to increased grassland density. Effects of landscape features on local abundance decreased as distance increased and had negligible influence at 0.8 km for eastern meadowlarks (0.7-1.2 km 95% Bayesian credibility intervals [BCI]), 2.5 km for field sparrows (1.5-5.8 km 95% BCI), and 8.4 km for bobwhite (6.4-26 km 95% BCI). Northern bobwhites were predicted to benefit greatly from future grassland conservation regardless of conservation priorities, but eastern meadowlark and field sparrow were not. Our results suggest similar species can respond differently to broad-scale conservation practices because of species-specific, distance-dependent relationships with landscape structure. Our framework is quantitative, conceptually simple, customizable, and predictive and can be used to optimize conservation in heterogeneous ecosystems while considering landscape-scale processes and explicit prioritization of species recovery.

Estimating Relative Risk When Observing Zero Events-Frequentist Inference and Bayesian Credibility Intervals.

Relative risk (RR) is a preferred measure for investigating associations in clinical and epidemiological studies with dichotomous outcomes. However, if the outcome of interest is rare, it frequently occurs that no events are observed in one of the comparison groups. In this case, many of the standard methods used to obtain confidence intervals (CIs) for the RRs are not feasible, even in studies with strong statistical evidence of an association. Different strategies for solving this challenge have been suggested in the literature. This paper, which uses both mathematical arguments and statistical simulations, aims to present, compare, and discuss the different statistical approaches to obtain CIs for RRs in the case of no events in one of the comparison groups. Moreover, we compare these frequentist methods with Bayesian approaches to determine credibility intervals (CrIs) for the RRs. Our results indicate that most of the suggested approaches can be used to obtain CIs (or CrIs) for RRs in the case of no events, although one-sided intervals obtained by methods based on deliberate, probabilistic considerations should be preferred over ad hoc methods. In addition, we demonstrate that Bayesian approaches can be used to obtain CrIs in these situations. Thus, it is possible to obtain statistical inference for the RR, even in studies with no events in one of the comparison groups, and CIs for the RRs should always be provided. However, it is important to note that the obtained intervals are sensitive to the method chosen in the case of small sample sizes.

Accuracy of direct and indirect methods for assessing bovine colostrum quality using a latent class model fit within a Bayesian framework

Feeding high-quality colostrum is essential for calf health and future productivity. Therefore, accurate assessment of colostrum quality is a key component of dairy farm management plans. Direct and indirect methods are available for assessment of colostrum quality; however, the indirect methods are rapid, inexpensive, and can be performed under field settings. A hierarchical latent class model fit within a Bayesian framework was used to estimate the sensitivity (Se) and specificity (Sp) of the radial immunodiffusion (RID) assay, transmission infrared (TIR) spectroscopy, and digital Brix refractometer for the assessment of low-quality bovine colostrum in Atlantic Canada dairy herds. The secondary objective of the study was to describe the distribution of herd prevalence of low-quality colostrum. Colostrum quality of 591 samples from 42 commercial Holstein dairy herds in 4 Atlantic Canada provinces was assessed using RID, TIR spectroscopy, and digital Brix refractometer. The accuracy of all tests at different Brix value thresholds was estimated using Bayesian latent class models to obtain posterior estimates [medians and 95% Bayesian credibility intervals (95% BCI)] for each parameter. Using a threshold of <23% for digital Brix refractometer and <50 g/L for RID and TIR spectroscopy, median (95% BCI) Se estimates were 73.2 (68.4-77.7), 86.2 (80.6-91.0), and 91.9% (89.0-94.2), respectively. Median (95% BCI) Sp estimates were 85.2% (81.0-88.9) for digital Brix refractometer, 99.4% (97.0-100) for RID, and 90.7% (87.8-93.2) for TIR spectroscopy. Median (95% BCI) within-herd low-quality colostrum prevalence was estimated at 32.5% (27.9-37.4). In conclusion, using digital Brix refractometer at a Brix threshold of <23% could reduce feeding of low-quality colostrum to calves and improve colostrum and calf management practices in Atlantic Canada dairy herds. The TIR spectroscopy showed high Se in detection of low-quality colostrum. However, the RID assay, which is used as the reference test in several studies, showed limited Se for detection of low-quality colostrum.

Bayesian inference in based-kernel regression: comparison of count data of condition factor of fish in pond systems

ABSTRACT The discrete kernel-based regression approach generally provides pointwise estimates of count data that do not account for uncertainty about both parameters and resulting estimates. This work aims to provide probabilistic kernel estimates of count regression function by using Bayesian approach and then allows for a readily quantification of uncertainty. Bayesian approach enables to incorporate prior knowledge of parameters used in discrete kernel-based regression. An application was proposed on count data of condition factor of fish (K) provided from an experimental project that analyzed various pond management strategies. The probabilistic distribution of estimates were contrasted by discrete kernels, as a support to theoretical results on the performance of kernels. More practically, Bayesian credibility intervals of K-estimates were evaluated to compare pond management strategies. Thus, similarities were found between performances of semi-intensive and coupled fishponds, with formulated feed, in comparison with extensive fishponds, without formulated feed. In particular, the fish development was less predictable in extensive fishpond, dependent on natural resources, than in the two other fishponds, supplied in formulated feed.

Cardiovascular Risk Distribution in Argentina in 2018

Background: Cardiovascular diseases are the main cause of disability and death globally. Total cardiovascular risk (CR) is the probabilityof having a cardiovascular event in a defined period and is determined by the combined effect of risk factors.Objectives: The aim of this study was to estimate CR and describe its distribution in Argentina in 2018.Methods: Cardiovascular risk was analyzed in 11,450 individuals over 30 years of age from the 4th National Risk Factor Survey(NRFS). The Framingham risk equations used to estimate and calibrate global CR classified the individuals into the following threegroups: optimum CR ( 20%). Bayesian prevalence and credibility intervals (BCI)were estimated under the non-informative beta prior distribution.Results: Nationally, 60.6% of the individuals presented moderate/high CR. Moderate CR by region was distributed homogeneously.When analyzing extreme CRs, the metropolitan (47.6%) and Pampean (28.6%) regions presented the greatest incidence of high CR.The highest prevalence of optimum CR was found in the Patagonian region, followed by the Northwest, Northeast and Cuyo, allabove 40%. The analysis by province showed that the greatest incidence of high CR was found in Buenos Aires (49.9%) and CABA(45.7%). At all levels, the prevalence of moderate/high CR is much higher in men, with the exception of the metropolitan region.Conclusions: Geographical differences position the metropolitan region as the one with maximum CR due to the great incidence ofhigh and moderate CR. Prevalence of high CR in men is almost 4 times greater than that registered in women.

Improving urban trash reduction tracking with spatially distributed Bayesian uncertainty estimates

Urban stormwater runoff is among the most significant sources of trash delivery to waterways, degrading aquatic habitats and contributing to oceanic trash gyres across the globe. Municipal water quality permits that require elimination of trash inputs to stormwater systems employ visual trash assessments on city streets to demonstrate litter reduction progress. We present a novel method to increase the utility of these assessments by quantifying their degree of certainty at a granular spatial scale via Bayesian credibility intervals. Using data collected in the City of Salinas, California, we illustrate how the outputs can be used to determine effective trash controls and prioritize areas for management actions. Spatial dependence was incorporated to the uncertainty estimates within individual stormwater drainages and results were interpolated to adjacent parcels. After 3–6 observation periods over 20 months, we found approximately 30% of the city area showed minimal litter accumulation at an 80% certainty level. The outputs provide a practical alternative for cities to determine compliance with stormwater trash regulations, update understanding of trash accumulation patterns, and iteratively adjust sampling designs in response to new observations. The methods described have been implemented as a web-based geospatial decision support tool to help stormwater managers target implementation actions and report progress to regulators.

Retrieving Temperatures and Abundances of Exoplanet Atmospheres with High-resolution Cross-correlation Spectroscopy

Abstract High-resolution spectroscopy (R ≥ 25,000) has recently emerged as one of the leading methods for detecting atomic and molecular species in the atmospheres of exoplanets. However, it has so far been lacking a robust method for extracting quantitative constraints on the temperature structure and molecular/atomic abundances. In this work, we present a novel Bayesian atmospheric retrieval framework applicable to high-resolution cross-correlation spectroscopy (HRCCS) that relies on the cross-correlation between data and models to extract the planetary spectral signal. We successfully test the framework on simulated data and show that it can correctly determine Bayesian credibility intervals on atmospheric temperatures and abundances, allowing for a quantitative exploration of the inherent degeneracies. Furthermore, our new framework permits us to trivially combine and explore the synergies between HRCCS and low-resolution spectroscopy to maximally leverage the information contained within each. This framework also allows us to quantitatively assess the impact of molecular line opacities at high resolution. We apply the framework to VLT CRIRES K-band spectra of HD 209458 b and HD 189733 b and retrieve abundant carbon monoxide but subsolar abundances for water, which are largely invariant under different model assumptions. This confirms previous analysis of these data sets, but is possibly at odds with detections of H2O at different wavelengths and spectral resolutions. The framework presented here is the first step toward a true synergy between space observatories and ground-based high-resolution observations.

Estimating diagnostic accuracy of fecal culture in liquid media for the detection of Mycobacterium avium subsp. paratuberculosis infections in Québec dairy cows: A latent class model

A latent class model fit within a Bayesian framework was used to estimate the sensitivity and specificity of individual fecal culture (IFC) in liquid medium (Para TB culture liquid medium and BACTEC MGIT 960 system) for the detection of Mycobacterium avium subsp. paratuberculosis (MAP) infections in Québec dairy cows. As a secondary objective, the within-herd paratuberculosis prevalence was estimated. A dataset including 21 commercial Québec dairy herds participating in previous research projects was retrospectively analyzed. In total, 1386 adult cows on which both IFC and serum-ELISA were available were included. The selected latent class model assumed conditional dependence between the tests. Non-informative priors for IFC accuracy and paratuberculosis prevalence were used while informative priors, obtained from the literature, were used for serum-ELISA accuracy. The WinBUGS statistical freeware was used to obtain posterior estimates (medians and 95% Bayesian credibility intervals (95% BCI)) for each parameter. The sensitivity and specificity estimates for IFC were 34.4% (95% BCI: 20.3–66.1) and 99.5% (95% BCI: 98.6–100), respectively. Sensitivity and specificity for serum-ELISA were 27.3% (95% BCI: 18.1–38.3) and 97.4% (95% BCI: 96.6–98.0). Median paratuberculosis within herd prevalence was estimated to be 0.3% (0–3.3). In conclusion, a higher sensitivity of IFC compared to serum-ELISA was observed both in the unconditional and conditional dependent models. Since the sensitivity of both IFC and serum-ELISA was relatively low, conditional dependence between the tests is more likely in the true disease positive animals. We hypothesize that conditional dependence arises because an unmeasured covariate influences the performance of both tests among disease positive animals causing both tests to incorrectly misclassify the animal as negative. One limitation of this study was the very low within herd prevalence of the participant herds.

Evaluation of antenatal rapid human immunodeficiency virus testing in rural South Africa

Introduction: South African guidelines recommend two rapid tests for diagnosing human immunodeficiency virus (HIV) using the serial HIV testing algorithm, but the accuracy and compliance to this algorithm is unknown in rural clinics. We evaluated the accuracy of HIV rapid testing and the time to receiving test results among pregnant women in rural KwaZulu-Natal (KZN).Method: We observed the accuracy of rapid HIV testing algorithms for 208 consenting antenatal patients accessing voluntary HIV testing services in nine rural primary healthcare (PHC) clinics in KZN. A PHC-based HIV counsellor obtained finger-prick whole blood from each participant to perform rapid testing using the Advanced Quality™ One Step anti-HIV (1&amp;2) and/or ABON™ HIV 1/2/O Tri-Line HIV test. A research nurse obtained venous blood for an enzyme-linked immunosorbent assay (ELISA) HIV test, which is the gold standard diagnostic test. We recorded the time of receipt of HIV test results for each test.Results: Among 208 pregnant women with a mean age of 26 years, 72 women from nine rural PHC clinics were identified as HIV-positive by two rapid tests with an HIV-prevalence of 35% (95% Bayesian credibility intervals [BCI]: 28% – 41%). Of the 208 patients, 135 patients from six clinics were tested with the serial HIV testing algorithm. The estimated sensitivity and specificity for the 135 participants were 100% (95% confidence interval [CI]: 93% – 100%) and 99% (CI: 95% – 100%), respectively. The positive predictive value and negative predictive value were estimated at 98% (CI: 94% – 100%) and 95% (CI: 88% – 99%), respectively. All women received their HIV rapid test results within 20 min of testing. Test stock-out resulted in poor test availability at point-of-care, preventing performance of a second HIV test in three out of nine PHC clinics in rural KZN.Conclusion: Despite the poor compliance with national guidelines for HIV rapid testing services, HIV rapid test results provided to pregnant women in rural PHC clinics in KZN were generally accurate and timely. Test stock-out was shown to be one of the barriers to test availability in rural PHC clinics, resulting in poor compliance with guidelines. We recommend a compulsory confirmation HIV rapid test for all HIV-negative test results obtained from pregnant patients in rural and resource-limited settings.

Author Correction: Phase-resolved X-ray polarimetry of the Crab pulsar with the AstroSat CZT Imager

In the Supplementary Information file originally published for this Letter, in Supplementary Fig. 7 the error bars for the polarization fraction were provided as confidence intervals but instead should have been Bayesian credibility intervals. This has been corrected and does not alter the conclusions of the Letter in any way.

Prospects for stakeholder coordination by protected-area managers in Europe.

Growing resource demands by humans, invasive species, natural hazards, and a changing climate have created broad-scale impacts and the need for broader-extent conservation activities that span ownerships and even political borders. Implementing regional-scale conservation brings great challenges, and learning how to overcome these challenges is essential for maintaining biodiversity (i.e., richness and evenness of biological communities) and ecosystem functions and services across scales and borders in the face of system change. We administered an online survey to examine factors potentially driving perspectives of protected-area (PA) managers regarding coordination with neighboring PAs and other stakeholders (i.e., stakeholder coordination) for conserving biodiversity and ecosystem services during the next decade within diverse regions across Europe. Although >70% (n = 58) of responding PA managers indicated that climate change and invasive species are relevant for their PAs, they gave <50% probability that these threats could be mitigated through stakeholder coordination. They thought there was a >60% probability (n = 85) that stakeholder coordination would take place with the aim to improve conservation outcomes. Consistent with the foundation on which many European PAs were established, managers viewed maintaining or enhancing biodiversity as the most important (>70%; n = 61) expected benefit. Other benefits included maintaining or enhancing human resources and environmental education (range of Bayesian credibility intervals [CIs] 57-93%). They thought the main barriers to stakeholder coordination were the lack of human and economic resources (CI 59-67% chance of hindering; n = 64) followed by communication and interstakeholder differences in political structures and laws (CI 51-64% probability of hindering). European policies and strategies that address these hindering factors could be particularly effective means of enabling implementation of green infrastructure networks in which PAs are the nodes.

Power in Bayesian Mediation Analysis for Small Sample Research

Bayesian methods have the potential for increasing power in mediation analysis (Koopman, Howe, Hollenbeck, & Sin, 2015; Yuan & MacKinnon, 2009). This article compares the power of Bayesian credibility intervals for the mediated effect to the power of normal theory, distribution of the product, percentile, and bias-corrected bootstrap confidence intervals at N ≤ 200. Bayesian methods with diffuse priors have power comparable to the distribution of the product and bootstrap methods, and Bayesian methods with informative priors had the most power. Varying degrees of precision of prior distributions were also examined. Increased precision led to greater power only when N ≥ 100 and the effects were small, N < 60 and the effects were large, and N < 200 and the effects were medium. An empirical example from psychology illustrated a Bayesian analysis of the single mediator model from prior selection to interpreting results.

A Bayesian approach for the reliability of scientific co-authorship networks with emphasis on nodes

The co-authorship among members of a research group commonly can be represented by a (co-authorship) graph in which nodes represent the researchers that make up of this group and edges represent the connections between two agents (i.e., the co-authorship between these agents). Current study measures the reliability of networks by taking into consideration unreliable nodes (researchers) and perfectly reliable edges (co-authorship between two researchers). A Bayesian approach for the reliability of a network represented by the co-authorship among members of a real research group is proposed, obtaining Bayesian estimates and credibility intervals for the individual components (nodes or researchers) and the network. Weakly informative and non-informative prior distributions are assumed for those components and the posterior summaries are obtained by Monte Carlo-Markov Chain methods. The results show the relevance of an inferential approach for the reliability of scientific co-authorship network. The results also demonstrate that the contribution of each researcher is highly relevant for the maintenance of a research group. In addition, the Bayesian methodology was a feasible and easy computational implementation.

Meta-analysis of few small studies in orphan diseases.

Meta‐analyses in orphan diseases and small populations generally face particular problems, including small numbers of studies, small study sizes and heterogeneity of results. However, the heterogeneity is difficult to estimate if only very few studies are included. Motivated by a systematic review in immunosuppression following liver transplantation in children, we investigate the properties of a range of commonly used frequentist and Bayesian procedures in simulation studies. Furthermore, the consequences for interval estimation of the common treatment effect in random‐effects meta‐analysis are assessed. The Bayesian credibility intervals using weakly informative priors for the between‐trial heterogeneity exhibited coverage probabilities in excess of the nominal level for a range of scenarios considered. However, they tended to be shorter than those obtained by the Knapp–Hartung method, which were also conservative. In contrast, methods based on normal quantiles exhibited coverages well below the nominal levels in many scenarios. With very few studies, the performance of the Bayesian credibility intervals is of course sensitive to the specification of the prior for the between‐trial heterogeneity. In conclusion, the use of weakly informative priors as exemplified by half‐normal priors (with a scale of 0.5 or 1.0) for log odds ratios is recommended for applications in rare diseases. © 2016 The Authors. Research Synthesis Methods published by John Wiley & Sons Ltd.