Full Bayesian Method Research Articles

Outcome-guided Bayesian clustering for disease subtype discovery using high-dimensional transcriptomic data

Due to the tremendous heterogeneity of disease manifestations, many complex diseases that were once thought to be single diseases are now considered to have disease subtypes. Disease subtyping analysis, that is the identification of subgroups of patients with similar characteristics, is the first step to accomplish precision medicine. With the advancement of high-throughput technologies, omics data offers unprecedented opportunity to reveal disease subtypes. As a result, unsupervised clustering analysis has been widely used for this purpose. Though promising, the subtypes obtained from traditional quantitative approaches may not always be clinically meaningful (i.e. correlate with clinical outcomes). On the other hand, the collection of rich clinical data in modern epidemiology studies has the great potential to facilitate the disease subtyping process via omics data and to discovery clinically meaningful disease subtypes. Thus, we developed an outcome-guided Bayesian clustering (GuidedBayesianClustering) method to fully integrate the clinical data and the high-dimensional omics data. A Gaussian mixed model framework was applied to perform sample clustering; a spike-and-slab prior was utilized to perform gene selection; a mixture model prior was employed to incorporate the guidance from a clinical outcome variable; and a decision framework was adopted to infer the false discovery rate of the selected genes. We deployed conjugate priors to facilitate efficient Gibbs sampling. Our proposed full Bayesian method is capable of simultaneously (i) obtaining sample clustering (disease subtype discovery); (ii) performing feature selection (select genes related to the disease subtype); and (iii) utilizing clinical outcome variable to guide the disease subtype discovery. The superior performance of the GuidedBayesianClustering was demonstrated through simulations and applications of breast cancer expression data and Alzheimer's disease. An R package has been made publicly available on GitHub to improve the applicability of our method.

A modified Huber loss function for continual reassessment methods in clinical trials

In dose-finding (DF) trials, methods for discovering an optimal criterion that controls toxicity while demonstrating a potential for efficacy have been the subject of statistical research. Although continual reassessment methods (CRMs) have been utilized, the consensus among practitioners and clinical trial specialists is that there is always room for improvement with CRMs. Within the paradigm of a full-Bayesian method for CRMs, we examine the performance of dose selection algorithms based on a family of loss functions defined in Huber (The Annals of Mathematical Statistics, vol. 35, issue 1, pp. 73–101, 1964), namely, the Huber loss function, with a special focus on the modified Huber loss function (MHLF). Our exploration suggests that, compared to Bayesian optimal interval design (BOIN) and toxicity interval loss function (TILF), the approach based on the MHLF has been able to select correct doses with fewer average number of patients across the spectrum of dose escalation schemes such as those seen in clinical settings.

Identification of MISO Hammerstein system using sparse multiple kernel-based hierarchical mixture prior and variational Bayesian inference

The Hammerstein model is a cascade composition of a static memoryless nonlinear function followed by a linear time-invariant dynamical subsystem, which is capable of modeling a wide range of nonlinear dynamical systems. Model structural parameter selection (including the model order and the nonlinearity order) and sparse representation of the static nonlinear function are two issues that receive increasing interests in Hammerstein system identification. In this paper, a novel Bayesian sparse multiple kernel-based identification method (BSMKM) for multiple-input single-output (MISO) Hammerstein system is proposed to handle those issues, where the basis-function model and the finite impulse response model are used to represent the nonlinear part and the linear part respectively. Firstly, in order to jointly realize the model parameter estimation, the sparse representation of static nonlinear function (the nonlinearity order selection can also be realized indirectly) and the model order selection of linear dynamical system, a hierarchical prior distribution is constructed based on Gaussian scale mixture model and sparse multiple kernel, which can characterize both inter-group sparsity and intra-group correlation structure. Then, a full Bayesian method based on variational Bayesian inference is proposed to estimate all unknown model parameters, including finite impulse response coefficients, hyperparameters and noise variance. Finally, the performance of the proposed BSMKM identification method is evaluated by numerical experiments using both simulation and real data.

A bootstrap-based Markov chain Monte Carlo reliability assessment of crash modification factors calculated by full Bayesian method

A bootstrap-based Markov chain Monte Carlo reliability assessment of crash modification factors calculated by full Bayesian method

Full Bayesian inference in hidden Markov models of plant growth

Accurately modeling the growth process of plants in interaction with their environment is important for predicting their biophysical characteristics, referred to as phenotype prediction. Most models are described by discrete dynamic systems in general state-space representation with important domain-specific characteristics: First, plant model parameters have usually clear functional meanings and may be of genetic origins, thus necessitating a precise estimation. Second, critical growth variables, specifically biomass production and dynamic allocation to organs, are hidden variables not accessible to measure. Finally, the difficulty to assess the local plant environment may imply the introduction of process noises in models. Therefore, a precise understanding of the system’s behavior requires the joint estimation of functional parameters, hidden states, and noise parameters. In this paper we describe how a full Bayesian method of estimation can accurately estimate all these key model variables using Markov chain Monte Carlo (MCMC) techniques. In the presence of both process and observation noises, it requires to use adequate particle MCMC (PMCMC) algorithms to efficiently sample the hidden states which, consequently, allows for a precise estimation of all noise parameters involved. Thanks to the Bayesian framework, appropriate choices of prior distributions for the noise parameters have enabled analytical posterior distributions and only simple updates are required. Furthermore, this estimation strategy can be easily generalized and adapted to different types of plant growth models, such as organ-scale or compartmental, provided that they are formulated as hidden Markov models. Our estimation method improves on those classically used in plant growth modeling in several aspects: First, by building upon a general probabilistic framework the estimation results allow proper statistical analyses. It is useful in prediction, no only for uncertainty and risk analysis (e.g., for crop yield prediction) but also to analyze the results of experimental trials, for example, to compare genotypes in breeding. Moreover, the care taken in the estimation of hidden variables opens new perspectives in the understanding of inner growth processes, notably the balance and interaction between biomass production and allocation (referred to as source-sink dynamics). Applications of this estimation procedure are demonstrated on the GreenLab model for Arabidopsis thaliana and the Log-Normal Allocation and Senescence (LNAS) model for sugar beet, on both synthetic and real data.

Derivation of the Empirical Bayesian method for the Negative Binomial-Lindley generalized linear model with application in traffic safety

The expected crash frequency is the long-term average crash count for a specific site. It is extensively used to systematically evaluate the crash risk associated with roadway elements. To estimate the expected crashes, the Empirical Bayesian (EB) approach is typically employed. The EB method is a computationally convenient approximation to the Full Bayesian (FB) method, which gained popularity due to its simple interpretation, computational efficiency, and the ability to account for the regression to the mean bias. However, the common EB method used in traffic safety analysis is only applicable when the traditional Negative Binomial (NB) model is used. The NB model, however, is not a suitable choice when data is highly dispersed, skewed, or has a large number of zero observations. The Negative Binomial-Lindley (NB-L) model is a mixture of the NB and Lindley distributions and has shown superior fit compared to the NB model, especially when the dataset is characterized by excess zero observations. Even though several studies have used the NB-L in developing crash prediction models, the application of the NB-L in other safety-related tasks (e.g., hot spot identification) is largely neglected. This study proposed a framework to develop the EB method for the NB-L model and subsequently estimate the expected crash values. A comparison between the EB and FB estimates was performed to validate the approximation framework in general. The results indicated that the proposed EB framework is able to estimate expected crashes with comparable precision to the FB estimate, but with much less computational cost. In addition, a site ranking analysis using the EB estimates was conducted to validate the proposed approximation method in safety studies. However, it should be noted that any other type of safety analysis that requires access to the expected crashes can benefit from the proposed EB method. This study concluded that the proposed EB framework can properly approximate the underlying FB approach and can reasonably be considered as an alternative to the traditional EB formula derived from the NB model. The results of this study can help to extend the application of the advanced predictive models beyond predicting crashes to other safety-related tasks, with no additional computational efforts.

Pooled 3-Anatomic-Site Testing for Chlamydia trachomatis and Neisseria gonorrhoeae: A Systematic Review and Meta-Analysis.

Pooled testing for Chlamydia trachomatis (CT) and Neisseria gonorrhoeae (NG) may be a cost-saving solution to increase screening by simplifying testing procedures and reducing resource burdens. We conducted a systematic review and meta-analysis to examine the performance of pooled 3-anatomic-site testing (pharyngeal, rectal, and urogenital sites) for CT and NG in comparison with single-anatomic-site testing. We conducted a systematic literature search in PubMed, Embase, and Web of Science to identify original evaluation studies of the performance of pooled testing for CT and NG infections and identified 14 studies for inclusion. Each study was systematically evaluated for bias. We conducted bivariate fixed-effects and random-effects meta-analyses using a full Bayesian method of the positive percent agreement and negative percent agreement. The combined positive percent agreement for CT was 93.11% (95% confidence interval [CI], 91.51%-94.55%), and the negative percent agreement was 99.44% (95% CI, 99.18%-99.65%). For NG, the combined positive percent agreement was 93.80% (95% CI, 90.26%-96.61%), and the negative percent agreement was 99.73% (95% CI, 99.30%-99.97%). We found that pooled 3-anatomic-site tests performed similarly to single-anatomic-site tests for the detection of CT and NG. The pooled 3-anatomic-site tests have the added potential benefit of reduced cost and resource requirement, which could lead to improved testing access and screening uptake.

Meso-level hotspot identification for suburban arterials

Accurate identification of crash hotspots forms the foundation of roadway safety improvement. The Highway Safety Manual micro-level approach uses individual intersections and road segments as analysis units, and correspondingly identifies some isolated road entities as hotspots. However, because traffic police and administrative agencies routinely conduct safety improvement based on multiple continuous segments and intersections, the identification of hotspots at the micro-level is inefficient for field application. To better meet this need, this study proposes a new meso-level approach to identify hotspots, specifically on suburban arterials. Meso-level analysis units of three different configurations (201, 150, and 100 units) were obtained by combining a set number of intersections and their adjacent segments according to crash distribution and homogeneity. Their influence areas were determined according to the proportion of urbanized land in areas perpendicularly adjacent to the arterials. Three Bayesian Poisson-lognormal conditional autoregressive models (PLN-CAR) considering spatial correlations were developed for each unit configuration, using the full Bayesian (FB) method to ameliorate random fluctuation in crash counts. Potential for safety improvement (PSI) values were calculated based on the modeling results and were used to identify hotspots. Two measures, i.e., the concentrated degree of hotspots (CDH) and the hotspot identification accuracy (HIA), were proposed to make a quantitative and comparative evaluation. Results showed that 1) arterials with more parallel roads suffer lower crash risk, and 2) considering both the hotspot distribution and the identification accuracy, the 150 meso-level unit configuration was the best. The proposed meso-level hotspot identification method promises to be adaptive to safety improvement practices on suburban arterials.

A review of h‐likelihood and hierarchical generalized linear model

AbstractFisher's classical likelihood has become the standard procedure to make inference for fixed unknown parameters. Recently, inferences of unobservable random variables, such as random effects, factors, missing values, etc., have become important in statistical analysis. Because Fisher's likelihood cannot have such unobservable random variables, the full Bayesian method is only available for inference. An alternative likelihood approach is proposed by Lee and Nelder. In the context of Fisher likelihood, the likelihood principle means that the likelihood function carries all relevant information regarding the fixed unknown parameters. Bjørnstad extended the likelihood principle to extended likelihood principle; all information in the observed data for fixed unknown parameters and unobservables are in the extended likelihood, such as the h‐likelihood. However, it turns out that the use of extended likelihood for inferences is not as straightforward as the Fisher likelihood. In this paper, we describe how to extract information of the data from the h‐likelihood. This provides a new way of statistical inferences in entire fields of statistical science.This article is categorized under: Statistical Models > Generalized Linear Models Algorithms and Computational Methods > Maximum Likelihood Methods

Spatial quantile regression with application to high and low child birth weight in Malawi

BackgroundChild low and high birth weight are important public health problems. Many studies have looked at factors of low and high birth weight using mean regression. This study aimed at using quantile regression to find out determinants of low and high birth weight.MethodsSpatial quantile regression models at 0.05 and 0.95 percentiles of birth weight were fitted to 13,087 children birth weight in kilograms using Malawi demographic health survey data of 2010 study. Full Bayesian method by integrated nested Laplace approximations (INLA) was used to estimate the model. Second order random walk priors were assigned for mother age and antenatal visits for pregnancy while Gaussian markov random field prior was used for district of the child.ResultsResidual spatial patterns reveal areas in the southern region promoting high birth weight while areas in the central and northern region promote low birth weight. Most fixed effects findings are consistent with the literature. Richest family, normal mother body mass index (BMI), mother over weight (BMI > 25 kg/m2), birth order 2–3, mother secondary education and height (≥150 cm) negate low birth weight while weight 45–70 kg promote low birth weight. Birth order category 6+, mother height (≥150 cm) and poor wealth quintile, promote high birth weight, while richer and richest wealth quintiles and education categories: primary, secondary, and higher, and mother overweight (BMI > 25 kg/m2) reduce high birth weight. Antenatal visits for pregnancy reduce both low and high birth weight.ConclusionStrategies to reduce low and high birth weight should simultaneously address mother education, weight gain during pregnancy and poverty while targeting areas increasing low and high birth weight.

High-Resolution Bistatic ISAR Imaging of a Space Target with Sparse Aperture

Due to the large size of space targets, migration through resolution cells (MTRC) are induced by a rotational motion in high-resolution bistatic inverse synthetic aperture radar (Bi-ISAR) systems. The inaccurate correction of MTRC degrades the quality of Bi-ISAR images. However, it is challenging to correct the MTRC where sparse aperture data exists for Bi-ISAR systems. A joint approach of MTRC correction and sparse high-resolution imaging for Bi-ISAR systems is presented in this paper. First, a Bi-ISAR imaging sparse model-related to MTRC is established based on compress sensing (CS). Second, the target image elements and noise are modeled as the complex Laplace prior, and the Gaussian prior, respectively. Finally, the high-resolution, well-focused image is obtained by the full Bayesian inference method, without manual adjustments of unknown parameters. Simulated results verify the effectiveness and robustness of the proposed algorithm.

Segmented Bayesian calibration approach for estimating age in forensic science.

Forensic age estimation is receiving growing attention from researchers in the last few years. Accurate estimates of age are needed both for identifying real age in individuals without any identity document and assessing it for human remains. The methods applied in such context are mostly based on radiological analysis of some anatomical districts and entail the use of a regression model. However, estimating chronological age by regression models leads to overestimated ages in younger subjects and underestimated ages in older ones. We introduced a full Bayesian calibration method combined with a segmented function for age estimation that relied on a Normal distribution as a density model to mitigate this bias. In this way, we were also able to model the decreasing growth rate in juveniles. We compared our new Bayesian-segmented model with other existing approaches. The proposed method helped producing more robust and precise forecasts of age than compared models while exhibited comparable accuracy in terms of forecasting measures. Our method seemed to overcome the estimation bias also when applied to a real data set of South-African juvenilesubjects.

Comparison of Bayesian techniques for the before–after evaluation of the safety effectiveness of short 2+1 road sections

In evaluating the effectiveness of a road safety treatment, the regression to the mean phenomenon is a cause for concern because of a possible overestimation of benefits. Therefore, Bayesian approaches are usually suggested as the most appropriate methodologies for before—after studies as they account for regression to the mean effects. The empirical Bayes (EB) methodology examines the estimation of the expected number of crashes that would have occurred without treatment and compares them with the crashes observed at the treated sites. Even if there is no significant regression to the mean bias, the EB technique requires a reliable and large dataset with sufficient years of observation and number of treated sites, adequate for estimating the safety effects of a treatment with acceptable standard errors. In this framework, a full Bayesian (FB) approach can mitigate the problem of using small datasets by providing more detailed causal inferences and more flexibility in selecting crash count distributions, acknowledging that a more complex methodology must be applied. With the aim of estimating the safety improvements of new, short 2 + 1 road sections in Poland limited by the existing road network, EB and FB estimations are compared and different safety performance function (SPF) model forms are used in order to evaluate the performance of the two methodologies. Results indicated that, even if crash modification factors (CMFs) resulted in similar average values, the EB trend is to underestimate CMFs compared with the more complex methodology, while overall the FB approach provided a lower standard deviation. The differences are more pronounced between the EB and FB approaches when a simple SPF model form is used for the analysed dataset. Moreover, for this specific dataset, the difference between the FB method and the EB method using a refined regression model with more variables was negligible.

Meta-analysis of the Cepheid Xpert® CT/NG assay for extragenital detection of Chlamydia trachomatis (CT) and Neisseria gonorrhoeae (NG) infections.

The literature indexed on PubMed.gov was searched. Included studies were those that were an evaluation of the Xpert CT/NG assay with rectal and/or pharyngeal specimen types compared with another nucleic acid amplification test (NAAT), the Aptima transcription mediated amplification assay. A full Bayesian method was used for bivariate fixed-effect meta-analysis of positive and negative per cent agreement and pooled estimates (and 95% confidence intervals (CI)) were presented for each. The pooled positive and negative per cent agreement for detection of CT in rectal specimens was 89.72% (95% CI: 84.97%, 93.64%) and 99.23% (95% CI: 98.74%, 99.60%), and in pharyngeal specimens, they were 89.96% (95% CI: 66.38%, 99.72%) and 99.62% (95% CI: 98.95%, 99.95%) respectively. For NG detection in rectal specimens, the pooled positive and negative per cent agreement was 92.75% (95% CI: 87.91%, 96.46%) and 99.75% (95% CI: 99.46%, 99.93%), and in pharyngeal specimens, they were 92.51% (95% CI: 85.84%, 97.18%) and 98.56% (95% CI: 97.69%, 99.23%) respectively. It was found that the Xpert CT/NG assay performed similarly to the Aptima transcription mediated amplification assay for the detection of CT and NG in extragenital specimens. The Xpert assay has the benefit of providing faster results at the point-of-care, thus reducing the turnaround time for results, potentially enabling same-day treatment.

A generalized exponential link function to map a conflict indicator into severity index within safety continuum framework

Traffic conflict indicators measure the temporal and spatial proximity of conflict-involved road users. These indicators can reflect the severity of traffic conflicts to a reliable extent. Instead of using the indicator value directly as a severity index, many link functions have been developed to map the conflict indicator to a severity index. However, little information is available about the choice of a particular link function. To guard against link misspecification or subjectivity, a generalized exponential link function was developed. The severity index generated by this link was introduced to a parametric safety continuum model which objectively models the centre and tail regions. An empirical method, together with full Bayesian estimation method was adopted to estimate model parameters. The safety implication of return level was calculated based on the model parameters. The proposed approach was applied to the conflict and crash data collected from 21 segments from three freeways located in Guangdong province, China. The Pearson’s correlation test between return levels and observed crashes showed that a θ value of 1.2 was the best choice of the generalized parameter for current data set. This provides statistical support for using the generalized exponential link function. With the determined generalized exponential link function, the visualization of parametric safety continuum was found to be a gyroscope-shaped hierarchy.

Evaluating Safety Benefits of the Insurance Corporation of British Columbia Road Improvement Program Using a Full Bayes Approach

The objective of this study was to conduct a time-series (before-to-after) evaluation of the safety performance of a sample of locations that have been improved under the Insurance Corporation of British Columbia (ICBC) Road Improvement Program. The program started in 1989 when ICBC established partnerships with local road authorities in British Columbia, Canada, and works cooperatively to make sound investments in road safety improvements. The overall effectiveness of the road improvement program was assessed by determining whether the frequency or severity of collisions at the improvement sites has been reduced after implementation of the improvement, and by quantifying the program costs versus the economic safety benefits to determine the return on ICBC’s road safety investment. Seventy-two urban intersections were included in the evaluation. The methodology adopted for estimating the safety benefits was a before–after study with the full Bayesian method, while the benefit–cost analysis was carried out by using two indicators: net present value and benefit–cost ratio (B/C) with a payback period of 5 years. Overall, the total reductions of severe (fatal plus injury) and nonsevere (property damage only) collision frequency for intersections with new pedestrian signal installations were found equal to −24.54% and −6.21%, respectively; −22.95% and −10.78%, respectively, for intersections with geometric design improvements; and −13.76% and −5.04%, respectively, for intersections with traffic signal upgrades. Finally, an overall B/C ratio of 4.32:1 was achieved.

Age estimation in children by measurement of open apices in teeth with Bayesian calibration approach

Age estimation from teeth by radiological analysis, in both children and adolescents, has wide applications in several scientific and forensic fields. In 2006, Cameriere et al. proposed a regression method to estimate chronological age in children, according to measurements of open apices of permanent teeth.Although several regression models are used to analyze the relationship between age and dental development, one serious limitation is the unavoidable bias in age estimation when regression models are used.The aim of this paper is to develop a full Bayesian calibration method for age estimation in children according to the sum of open apices, S, of the seven left permanent mandibular teeth.This cross-sectional study included 2630 orthopantomographs (OPGs) from healthy living Italian subjects, aged between 4 and 17 years and with no obvious developmental abnormalities. All radiographs were in digital format and were processed by the ImageJ computer-aided drawing program. The distance between the inner side of the open apex was measured for each tooth. Dental maturity was then evaluated according to the sum of normalized open apices (S).Intra- and inter-observer agreement was satisfactory, according to an intra-class correlation coefficient of S on 50 randomly selected OPGs. Mean absolute errors were 0.72 years (standard deviation 0.60) and 0.73 years (standard deviation 0.61) in boys and girls, respectively. The mean interquartile range (MIQR) of the calibrating distribution was 1.37 years (standard deviation 0.46) and 1.51 years (standard deviation 0.52) in boys and girls, respectively. Estimate bias was βERR=−0.005 and 0.003 for boys and girls, corresponding to a bias of a few days for all individuals in the sample. Neither of the βERR values was significantly different from 0 (p>0.682).In conclusion, the Bayesian calibration method overcomes problems of bias in age estimation when regression models are used, and appears to be suitable for assessing both age and age distribution in children according to tooth maturity.

Spatial Analysis of Common Gastrointestinal Tract Cancers in Counties of Iran

Gastrointestinal tract cancers are among the most common cancers in Iran and comprise approximately 38% of all the reported cases of cancer. This study aimed to describe the epidemiology and to investigate spatial clustering of common cancers of the gastrointestinal tract across the counties of Iran using full Bayesian smoothing and Moran I Index statistics. The data of the national registry cancer were used in this study. Besides, indirect standardized rates were calculated for 371 counties of Iranand smoothed using Winbug 1.4 software with a full Bayesian method. Global Moran I and local Moran I were also used to investigate clustering. According to the results, 75,644 new cases of cancer were nationally registered in Iran among which 18,019 cases (23.8%) were esophagus, gastric, colorectal, and liver cancers. The results of Global Moran's I test were 0.60 (P=0.001), 0.47 (P=0.001), 0.29 (P=0.001), and 0.40 (P=0.001) for esophagus, gastric, colorectal, and liver cancers, respectively. This shows clustering of the four studied cancers in Iran at the national level. High level clustering of the cases was seen in northern, northwestern, western, and northeastern areas for esophagus, gastric, and colorectal cancers. Considering liver cancer, high clustering was observed in some counties in central, northeastern, and southern areas.

Full Bayesian evaluation of the safety effects of reducing the posted speed limit in urban residential area

Full Bayesian (FB) before–after evaluation is a newer approach than the empirical Bayesian (EB) evaluation in traffic safety research. While a number of earlier studies have conducted univariate and multivariate FB before–after safety evaluations and compared the results with the EB method, often contradictory conclusions have been drawn. To this end, the objectives of the current study were to (i) perform a before–after safety evaluation using both the univariate and multivariate FB methods in order to enhance our understanding of these methodologies, (ii) perform the EB evaluation and compare the results with those of the FB methods and (iii) apply the FB and EB methods to evaluate the safety effects of reducing the urban residential posted speed limit (PSL) for policy recommendation. In addition to three years of crash data for both the before and after periods, traffic volume, road geometry and other relevant data for both the treated and reference sites were collected and used. According to the model goodness-of-fit criteria, the current study found that the multivariate FB model for crash severities outperformed the univariate FB models. Moreover, in terms of statistical significance of the safety effects, the EB and FB methods led to opposite conclusions when the safety effects were relatively small with high standard deviation. Therefore, caution should be taken in drawing conclusions from the EB method. Based on the FB method, the PSL reduction was found effective in reducing crashes of all severities and thus is recommended for improving safety on urban residential collector roads.

Bayesian calibration for forensic age estimation.

Forensic medicine is increasingly called upon to assess the age of individuals. Forensic age estimation is mostly required in relation to illegal immigration and identification of bodies or skeletal remains. A variety of age estimation methods are based on dental samples and use of regression models, where the age of an individual is predicted by morphological tooth changes that take place over time. From the medico-legal point of view, regression models, with age as the dependent random variable entail that age tends to be overestimated in the young and underestimated in the old. To overcome this bias, we describe a new full Bayesian calibration method (asymmetric Laplace Bayesian calibration) for forensic age estimation that uses asymmetric Laplace distribution as the probability model. The method was compared with three existing approaches (two Bayesian and a classical method) using simulated data. Although its accuracy was comparable with that of the other methods, the asymmetric Laplace Bayesian calibration appears to be significantly more reliable and robust in case of misspecification of the probability model. The proposed method was also applied to a real dataset of values of the pulp chamber of the right lower premolar measured on x-ray scans of individuals of known age.