Posterior Predictive Checks Research Articles

Bridging Models of Biometric and Psychometric Assessment: A Three-Way Joint Modeling Approach of Item Responses, Response Times, and Gaze Fixation Counts.

Recently, joint models of item response data and response times have been proposed to better assess and understand test takers' learning processes. This article demonstrates how biometric information such as gaze fixation counts obtained from an eye-tracking machine can be integrated into the measurement model. The proposed joint modeling framework accommodates the relations among a test taker's latent ability, working speed and test engagement level via a person-side variance-covariance structure, while simultaneously permitting the modeling of item difficulty, time-intensity, and the engagement intensity through an item-side variance-covariance structure. A Bayesian estimation scheme is used to fit the proposed model to data. Posterior predictive model checking based on three discrepancy measures corresponding to various model components are introduced to assess model-data fit. Findings from a Monte Carlo simulation and results from analyzing experimental data demonstrate the utility of the model.

Bayesian framework for interval-valued data using Jeffreys’ prior and posterior predictive checking methods

Interval-valued data have been widely used in both academic and industry research areas. With the development of computational statistics, the Bayesian methods are growing rapidly. Based on the existing theoretical researches, this paper tries to establish a Bayesian framework for interval-valued data, which contains the determination of Jeffreys’ prior, posterior inferences, and posterior predictive checking methods. First, Jeffreys’ prior for interval-valued data is proposed for the first time. Then, the posterior conditional distribution is derived, and posterior samples are obtained by using Gibbs sampling methods. Based on posterior samples, we obtain the Bayesian point and credible interval estimations for interval-valued data. Finally, we propose a posterior predictive checking method for interval-valued data based on novel test quantities. If the posterior predictive checking method shows that the data do not meet the distribution assumptions, we suggest the use of a data transformation. The effectiveness of our method is demonstrated by simulations and two cardiological data sets.

Detecting Differential Item Functioning Using Posterior Predictive Model Checking: A Comparison of Discrepancy Statistics

AbstractThis study proposes a new Bayesian differential item functioning (DIF) detection method using posterior predictive model checking (PPMC). Item fit measures including infit, outfit, observed score distribution (OSD), and Q1 were considered as discrepancy statistics for the PPMC DIF methods. The performance of the PPMC DIF method was evaluated via a Monte Carlo simulation manipulating sample size, DIF size, DIF type, DIF percentage, and subpopulation trait distribution. Parametric DIF methods, such as Lord's chi‐square and Raju's area approaches, were also included in the simulation design in order to compare the performance of the proposed PPMC DIF methods to those previously existing. Based on Type I error and power analysis, we found that PPMC DIF methods showed better‐controlled Type I error rates than the existing methods and comparable power to detect uniform DIF. The implications and recommendations for applied researchers are discussed.

A Bayesian Framework for Addressing the Uncertainty in Production Forecasts of Tight-Oil Reservoirs Using a Physics-Based Two-Phase Flow Model

Summary Extrapolation of history matched single-phase flow solutions is a common practice to forecast production from tight-oil reservoirs. Nonetheless, this approach (a) omits multiphase flow effects that exist below bubblepoint conditions and (b) has not included the quantification of the uncertainty of the estimated ultimate recovery (EUR). This work combines a new two-phase (oil and gas) flow solution within a Bayesian framework to address the uncertainty in the EUR. We illustrate the application of the procedure to tight-oil wells of west Texas. First, we combine the oil and the gas flow equations into a single dimensionless two-phase flow equation. The solution is a dimensionless flow rate model that can be easily scaled using two parameters: hydrocarbon pore volume and characteristic time. Second, this study generates the probabilistic production forecasts using a Bayesian approach in which the parameters of the model are treated as random variables. We construct parallel Markov chains of the parameters using an adaptative Metropolis-Hastings (M-H) Markov chain Monte Carlo (MCMC) for this purpose. Third, we evaluate the robustness of our inferences using posterior predictive checks (PPCs). Finally, we quantify the uncertainty in the EUR percentiles using the bootstrap method. The results of this research are as follows. First, this work shows that EUR estimates based on single-phase flow solutions will consistently underestimate the ultimate oil recovery factors in solution-gas drives where the reservoir pressure is less than the bubblepoint. The degree of underestimation will depend on the reservoir and flowing conditions as well as the fluid properties. Second, the application of parallel Markov chains using an adaptative M-H MCMC scheme that addresses the correlation between the model’s parameters solves the issues of mixing and autocorrelation of Markov chains and, thus, it speeds up speeding up the convergence of the Markov chains. Third, we generate replicated data from our posterior distributions to assess the robustness of our inferences (PPCs). Finally, we use hindcasting to calibrate and strengthen our inferences. To our knowledge, all these approaches are novel in EUR forecasting. Using a Bayesian framework with a low-dimensional (two-parameter) physics-based model provides a fast and reliable technique to quantify the uncertainty in production forecasts. In addition, the use of parallel chains with an adaptative M-H MCMC accelerates the rate of convergence and increases the robustness of the method.

Shaky Student Growth? A Comparison of Robust Bayesian Learning Progress Estimation Methods.

Monitoring the progress of student learning is an important part of teachers’ data-based decision making. One such tool that can equip teachers with information about students’ learning progress throughout the school year and thus facilitate monitoring and instructional decision making is learning progress assessments. In practical contexts and research, estimating learning progress has relied on approaches that seek to estimate progress either for each student separately or within overarching model frameworks, such as latent growth modeling. Two recently emerging lines of research for separately estimating student growth have examined robust estimation (to account for outliers) and Bayesian approaches (as opposed to commonly used frequentist methods). The aim of this work was to combine these approaches (i.e., robust Bayesian estimation) and extend these lines of research to the framework of linear latent growth models. In a sample of N = 4970 second-grade students who worked on the quop-L2 test battery (to assess reading comprehension) at eight measurement points, we compared three Bayesian linear latent growth models: (a) a Gaussian model, (b) a model based on Student’s t-distribution (i.e., a robust model), and (c) an asymmetric Laplace model (i.e., Bayesian quantile regression and an alternative robust model). Based on leave-one-out cross-validation and posterior predictive model checking, we found that both robust models outperformed the Gaussian model, and both robust models performed comparably well. While the Student’s t model performed statistically slightly better (yet not substantially so), the asymmetric Laplace model yielded somewhat more realistic posterior predictive samples and a higher degree of measurement precision (i.e., for those estimates that were either associated with the lowest or highest degree of measurement precision). The findings are discussed for the context of learning progress assessment.

A Model Comparison Approach to Posterior Predictive Model Checks in Bayesian Confirmatory Factor Analysis

ABSTRACT Posterior Predictive Model Checking (PPMC) is frequently used for model fit evaluation in Bayesian Confirmatory Factor Analysis (BCFA). In standard PPMC procedures, model misfit is quantified by comparing the location of an ML-based point estimate to the predictive distribution of a statistic. When the point estimate is far from the center posterior predictive distribution, model fit is poor. Not included in this approach, however, is the variability of the Maximum Likelihood (ML)-based point estimates. We propose a new method of PPMC based on comparing posterior predictive distributions of a hypothesized and saturated BCFA model. The method uses the predictive distribution of the saturated model as a reference and the Kolmogorov-Smirnov (KS) statistic to quantify the local misfit of hypothesized models. The results of the simulation study suggest that the saturated model PPMC approach was an accurate method of determining local model misfit and could be used for model comparison. A real data example is also provided in this study.

The Mass of the Milky Way from the H3 Survey

Abstract The mass of the Milky Way is a critical quantity that, despite decades of research, remains uncertain within a factor of two. Until recently, most studies have used dynamical tracers in the inner regions of the halo, relying on extrapolations to estimate the mass of the Milky Way. In this paper, we extend the hierarchical Bayesian model applied in Eadie & Juri to study the mass distribution of the Milky Way halo; the new model allows for the use of all available 6D phase-space measurements. We use kinematic data of halo stars out to 142 kpc, obtained from the H3 survey and Gaia EDR3, to infer the mass of the Galaxy. Inference is carried out with the No-U-Turn sampler, a fast and scalable extension of Hamiltonian Monte Carlo. We report a median mass enclosed within 100 kpc of M ( < 100 kpc ) = 0.69 − 0.04 + 0.05 × 10 12 M ⊙ (68% Bayesian credible interval), or a virial mass of M 200 = M ( < 216.2 − 7.5 + 7.5 kpc ) = 1.08 − 0.11 + 0.12 × 10 12 M ⊙ , in good agreement with other recent estimates. We analyze our results using posterior predictive checks and find limitations in the model’s ability to describe the data. In particular, we find sensitivity with respect to substructure in the halo, which limits the precision of our mass estimates to ∼15%.

When and why direct transmission models can be used for environmentally persistent pathogens.

Variants of the susceptible-infected-removed (SIR) model of Kermack & McKendrick (1927) enjoy wide application in epidemiology, offering simple yet powerful inferential and predictive tools in the study of diverse infectious diseases across human, animal and plant populations. Direct transmission models (DTM) are a subset of these that treat the processes of disease transmission as comprising a series of discrete instantaneous events. Infections transmitted indirectly by persistent environmental pathogens, however, are examples where a DTM description might fail and are perhaps better described by models that comprise explicit environmental transmission routes, so-called environmental transmission models (ETM). In this paper we discuss the stochastic susceptible-exposed-infected-removed (SEIR) DTM and susceptible-exposed-infected-removed-pathogen (SEIR-P) ETM and we show that the former is the timescale separation limit of the latter, with ETM host-disease dynamics increasingly resembling those of a DTM when the pathogen’s characteristic timescale is shortened, relative to that of the host population. Using graphical posterior predictive checks (GPPC), we investigate the validity of the SEIR model when fitted to simulated SEIR-P host infection and removal times. Such analyses demonstrate how, in many cases, the SEIR model is robust to departure from direct transmission. Finally, we present a case study of white spot disease (WSD) in penaeid shrimp with rates of environmental transmission and pathogen decay (SEIR-P model parameters) estimated using published results of experiments. Using SEIR and SEIR-P simulations of a hypothetical WSD outbreak management scenario, we demonstrate how relative shortening of the pathogen timescale comes about in practice. With atttempts to remove diseased shrimp from the population every 24h, we see SEIR and SEIR-P model outputs closely conincide. However, when removals are 6-hourly, the two models’ mean outputs diverge, with distinct predictions of outbreak size and duration.

A composite likelihood approach for inference under photometric redshift uncertainty

ABSTRACTObtaining accurately calibrated redshift distributions of photometric samples is one of the great challenges in photometric surveys like LSST, Euclid, HSC, KiDS, and DES. We present an inference methodology that combines the redshift information from the galaxy photometry with constraints from two-point functions, utilizing cross-correlations with spatially overlapping spectroscopic samples, and illustrate the approach on CosmoDC2 simulations. Our likelihood framework is designed to integrate directly into a typical large-scale structure and weak lensing analysis based on two-point functions. We discuss efficient and accurate inference techniques that allow us to scale the method to the large samples of galaxies to be expected in LSST. We consider statistical challenges like the parametrization of redshift systematics, discuss and evaluate techniques to regularize the sample redshift distributions, and investigate techniques that can help to detect and calibrate sources of systematic error using posterior predictive checks. We evaluate and forecast photometric redshift performance using data from the CosmoDC2 simulations, within which we mimic a DESI-like spectroscopic calibration sample for cross-correlations. Using a combination of spatial cross-correlations and photometry, we show that we can provide calibration of the mean of the sample redshift distribution to an accuracy of at least 0.002(1 + z), consistent with the LSST-Y1 science requirements for weak lensing and large-scale structure probes.

Bayesian inference for zero-and/or-one augmented beta rectangular regression models

In this paper, we developed a full set of Bayesian inference tools, for zero-and/or-one augmented beta rectangular regression models to analyze limited-augmented data, under a new parameterization. This parameterization: facilitates the development of both regression models and inferential tools as well as make simplifies the respective computational implementations. The proposed Bayesian tools were parameter estimation, model fit assessment, model comparison (information criteria), residual analysis and case influence diagnostics, developed through MCMC algorithms. In addition, we adapted available methods of posterior predictive checking, using appropriate discrepancy measures. We conducted several simulation studies, considering some situations of practical interest, aiming to evaluate: prior sensitivity choice, parameter recovery of the proposed model and estimation method, the impact of transforming the observed zeros and ones, along with the use of non-augmented models, and the behavior of the proposed model fit assessment and model comparison tools. A psychometric real data set was analyzed to illustrate the performance of the developed tools, illustrating the advantages of the developed analysis framework.

Assessing Dimensionality of the Ideal Point Item Response Theory Model Using Posterior Predictive Model Checking

Although the use of ideal point item response theory (IRT) models for organizational research has increased over the last decade, the assessment of construct dimensionality of ideal point scales has been overlooked in previous research. In this study, we developed and evaluated dimensionality assessment methods for an ideal point IRT model under the Bayesian framework. We applied the posterior predictive model checking (PPMC) approach to the most widely used ideal point IRT model, the generalized graded unfolding model (GGUM). We conducted a Monte Carlo simulation to compare the performance of item pair discrepancy statistics and to evaluate the Type I error and power rates of the methods. The simulation results indicated that the Bayesian dimensionality detection method controlled Type I errors reasonably well across the conditions. In addition, the proposed method showed better performance than existing methods, yielding acceptable power when 20% of the items were generated from the secondary dimension. Organizational implications and limitations of the study are further discussed.

Understanding the convoluted evolutionary history of the capped-golden langur lineage (Cercopithecidae: Colobinae)†

The phylogenetic position of the capped and golden langur (CG) lineage has been ambiguous owing to the discordance between phylogenies from multiple molecular markers. Previous molecular studies have hypothesised that this discordance likely arises from either a hybridization event that took place between the Indian genus Semnopithecus and the Southeast Asian genus Trachypithecus or from incomplete lineage sorting (ILS). Distinguishing between hybridization and ILS is challenging and these processes can lead to serious difficulties in inferring phylogenies. In this study, we used genetic markers (nine nuclear and eight mitochondrial) in conjunction with coalescent based species tree approach and a test for hybridization using posterior predictive checking to better understand the evolutionary origin of the CG lineage. Both the concatenated nuclear as well as the mitochondrial dataset recovered congruent relationships where CG lineage was sister to Trachypithecus. However, nuclear species tree estimated using different multispecies coalescent methods suggested an opposite result, i.e. CG lineage was sister to Semnopithecus. Hybridization analysis strongly indicates gene flow between Semnopithecus and Trachypithecus that likely gave rise to the hybrid CG lineage. Further, the CG lineage is morphologically intermediate between Semnopithecus and Trachypithecus with respect to skull and body measurements. In light of the above evidences, we argue that the CG lineage needs to be elevated to a new genus of its own. Taxonomic and conservation implications of these results are also discussed.

Analysis of Longitudinal Advice-Seeking Networks Following Implementation of High Stakes Testing

Abstract Teacher interactions around instructional practices have been a topic of study for a long time. Previous studies concerning such interactions have focused on questions pertaining to cross-sectional networks. In fact, very few studies have considered longitudinal networks and still fewer have employed longitudinal network models to study changes in such interactions. We analyse teachers’ advice-seeking networks, observed annually between 2010 and 2013, in schools within a district where several initiatives were implemented starting in 2011. We assess whether formal structures, teaching assignment and leadership position, and teacher characteristics, gender and experience, are associated with advice-seeking ties, and the extent to which these associations change over time. To analyse the advice-seeking networks, we implement a Bayesian longitudinal latent space network model with covariates and random sender-receiver effects. Within the Bayesian framework, we address practical aspects of a principled network analysis such as missing ties and yearly immigration and emigration of teachers. Goodness of model fit assessment is conducted using posterior predictive checks. Our results demonstrate that while some of the associations between observed covariates and teachers’ interactions varied in 2011, most were otherwise stable. In 2011, we found decreases in the associations with same grade assignment, leadership position, and teaching in the same school.

Robustness of Phylogenetic Inference to Model Misspecification Caused by Pairwise Epistasis.

Likelihood-based phylogenetic inference posits a probabilistic model of character state change along branches of a phylogenetic tree. These models typically assume statistical independence of sites in the sequence alignment. This is a restrictive assumption that facilitates computational tractability, but ignores how epistasis, the effect of genetic background on mutational effects, influences the evolution of functional sequences. We consider the effect of using a misspecified site-independent model on the accuracy of Bayesian phylogenetic inference in the setting of pairwise-site epistasis. Previous work has shown that as alignment length increases, tree reconstruction accuracy also increases. Here, we present a simulation study demonstrating that accuracy increases with alignment size even if the additional sites are epistatically coupled. We introduce an alignment-based test statistic that is a diagnostic for pairwise epistasis and can be used in posterior predictive checks.

Robust Bayesian estimator for S-wave spectra, using a combined empirical Green’s function

Summary We propose a new fully automatic and robust Bayesian method to estimate precise and reliable model parameters describing the observed S-wave spectra. All the spectra associated with each event are modelled jointly, using a t-distribution as likelihood function together with informative prior distributions for increased robustness against outliers and extreme values. The model includes the observed noise and a combined empirical Green’s function. It captures source-, receiver-, and path-dependent terms in the description of the observed spectra by combining a physical source and attenuation model with a spatially and event-size dependent empirical compensation. The proposed method propagates estimation uncertainties along the entire processing chain starting from the hypocentre location and delivers reliable uncertainty description of the estimands. The objective is to automatically provide robust and valid descriptions of the observed S-wave spectra generated from an earthquake source in a noisy and heterogeneous environment. The efficiency of the method is tested with synthetic seismograms, and the model is calibrated and cross-validated using 31 640 mining induced seismic events in a iron ore mine (in north of Sweden) with an comprehensive seismic network. The model is evaluated using both posterior predictive checks and residual analysis and we found no evidence that indicates any model deficiencies with respect to central tendency, dispersion, and residual trends.

Toward a principled Bayesian workflow in cognitive science.

Experiments in research on memory, language, and in other areas of cognitive science are increasingly being analyzed using Bayesian methods. This has been facilitated by the development of probabilistic programming languages such as Stan, and easily accessible front-end packages such as brms. The utility of Bayesian methods, however, ultimately depends on the relevance of the Bayesian model, in particular whether or not it accurately captures the structure of the data and the data analyst's domain expertise. Even with powerful software, the analyst is responsible for verifying the utility of their model. To demonstrate this point, we introduce a principled Bayesian workflow (Betancourt, 2018) to cognitive science. Using a concrete working example, we describe basic questions one should ask about the model: prior predictive checks, computational faithfulness, model sensitivity, and posterior predictive checks. The running example for demonstrating the workflow is data on reading times with a linguistic manipulation of object versus subject relative clause sentences. This principled Bayesian workflow also demonstrates how to use domain knowledge to inform prior distributions. It provides guidelines and checks for valid data analysis, avoiding overfitting complex models to noise, and capturing relevant data structure in a probabilistic model. Given the increasing use of Bayesian methods, we aim to discuss how these methods can be properly employed to obtain robust answers to scientific questions. All data and code accompanying this article are available from https://osf.io/b2vx9/. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Bayesian statistics and modelling

Bayesian statistics is an approach to data analysis based on Bayes’ theorem, where available knowledge about parameters in a statistical model is updated with the information in observed data. The background knowledge is expressed as a prior distribution and combined with observational data in the form of a likelihood function to determine the posterior distribution. The posterior can also be used for making predictions about future events. This Primer describes the stages involved in Bayesian analysis, from specifying the prior and data models to deriving inference, model checking and refinement. We discuss the importance of prior and posterior predictive checking, selecting a proper technique for sampling from a posterior distribution, variational inference and variable selection. Examples of successful applications of Bayesian analysis across various research fields are provided, including in social sciences, ecology, genetics, medicine and more. We propose strategies for reproducibility and reporting standards, outlining an updated WAMBS (when to Worry and how to Avoid the Misuse of Bayesian Statistics) checklist. Finally, we outline the impact of Bayesian analysis on artificial intelligence, a major goal in the next decade. This Primer on Bayesian statistics summarizes the most important aspects of determining prior distributions, likelihood functions and posterior distributions, in addition to discussing different applications of the method across disciplines.

A Bayesian approach to estimating the population prevalence of mood and anxiety disorders using multiple measures.

There is currently no universally accepted measure for population-based surveillance of mood and anxiety disorders. As such, the use of multiple linked measures could provide a more accurate estimate of population prevalence. Our primary objective was to apply Bayesian methods to two commonly employed population measures of mood and anxiety disorders to make inferences regarding the population prevalence and measurement properties of a combined measure. We used data from the 2012 Canadian Community Health Survey - Mental Health linked to health administrative databases in Ontario, Canada. Structured interview diagnoses were obtained from the survey, and health administrative diagnoses were identified using a standardised algorithm. These two prevalence estimates, in addition to data on the concordance between these measures and prior estimates of their psychometric properties, were used to inform our combined estimate. The marginal posterior densities of all parameters were estimated using Hamiltonian Monte Carlo (HMC), a Markov Chain Monte Carlo technique. Summaries of posterior distributions, including the means and 95% equally tailed posterior credible intervals, were used for interpretation of the results. The combined prevalence mean was 8.6%, with a credible interval of 6.8-10.6%. This combined estimate sits between Bayesian-derived prevalence estimates from administrative data-derived diagnoses (mean = 7.4%) and the survey-derived diagnoses (mean = 13.9%). The results of our sensitivity analysis suggest that varying the specificity of the survey-derived measure has an appreciable impact on the combined posterior prevalence estimate. Our combined posterior prevalence estimate remained stable when varying other prior information. We detected no problematic HMC behaviour, and our posterior predictive checks suggest that our model can reliably recreate our data. Accurate population-based estimates of disease are the cornerstone of health service planning and resource allocation. As a greater number of linked population data sources become available, so too does the opportunity for researchers to fully capitalise on the data. The true population prevalence of mood and anxiety disorders may reside between estimates obtained from survey data and health administrative data. We have demonstrated how the use of Bayesian approaches may provide a more informed and accurate estimate of mood and anxiety disorders in the population. This work provides a blueprint for future population-based estimates of disease using linked health data.

Phylogenomic species delimitation in the ants of the Temnothorax salvini group (Hymenoptera: Formicidae): an integrative approach

ABSTRACTThe members of the Temnothorax salvini (Forel) species group are rarely collected, arboreally nesting ants of Central American forests. Previously thought to consist of two broadly dispersed species, recent collections have revealed a diversity of specimens that defy the two‐species salvini group concept, but these are difficult to distinguish from each other based solely on morphology. I contrast several model‐based approaches to species delimitation based on target‐enriched genomic data. With molecular data from thousands of ultraconserved elements (UCEs), mitochondrial genome sequences and morphometric data, I use an integrated approach to species delimitation within the salvini group. Morphometric data were analysed using cluster analysis of principal component analysis (PCA) output. I use several popular methods of molecular species delimitation, including bPTP, BPP and STACEY, using a novel approach to filtering UCE data based on posterior predictive checks of nucleotide substitution model adequacy. In addition, I use iBPP to integrate morphometric PCA data and filtered UCE data in a ‘total evidence’ analysis. I use geographical range data for an independent contrast to discriminate among competing species delimitation hypotheses. Furthermore, I investigate the evolutionary timescale and biogeographical history of the group and find that it arose roughly 13 Ma ago in habitats associated with present day mid‐to‐high elevations of the mountain complex spanning southern Mexico to northern Nicaragua. In addition, dispersal of the salvini group into the Southern Sierra Madre in Mexico, lowland habitats and the southern Central American cordilleras in Costa Rica and Panama subsequent to mountain building in southern Central America 5–8 Ma ago appears to follow a taxon‐cycle dynamic, with the lowland‐adapted T. aztecus representing the most recent expansion phase. I find that the salvini group, which previously contained two named species, is composed of nine, all of which are morphologically diagnosable a posteriori.

Per-partnership transmission probabilities for Chlamydia trachomatis infection: evidence synthesis of population-based survey data.

BackgroundChlamydia is the most commonly diagnosed sexually transmitted infection worldwide. Mathematical models used to plan and assess control measures rely on accurate estimates of chlamydia’s natural history, including the probability of transmission within a partnership. Several methods for estimating transmission probability have been proposed, but all have limitations.MethodsWe have developed a new model for estimating per-partnership chlamydia transmission probabilities from infected to uninfected individuals, using data from population-based surveys. We used data on sexual behaviour and prevalent chlamydia infection from the second UK National Study of Sexual Attitudes and Lifestyles (Natsal-2) and the US National Health and Nutrition Examination Surveys 2009–2014 (NHANES) for Bayesian inference of average transmission probabilities, across all new heterosexual partnerships reported. Posterior distributions were estimated by Markov chain Monte Carlo sampling using the Stan software.ResultsPosterior median male-to-female transmission probabilities per partnership were 32.1% [95% credible interval (CrI) 18.4–55.9%] (Natsal-2) and 34.9% (95%CrI 22.6–54.9%) (NHANES). Female-to-male transmission probabilities were 21.4% (95%CrI 5.1–67.0%) (Natsal-2) and 4.6% (95%CrI 1.0–13.1%) (NHANES). Posterior predictive checks indicated a well-specified model, although there was some discrepancy between reported and predicted numbers of partners, especially in women.ConclusionsThe model provides statistically rigorous estimates of per-partnership transmission probability, with associated uncertainty, which is crucial for modelling and understanding chlamydia epidemiology and control. Our estimates incorporate data from several sources, including population-based surveys, and use information contained in the correlation between number of partners and the probability of chlamydia infection. The evidence synthesis approach means that it is easy to include further data as it becomes available.