Deviance Information Criterion Research Articles

Oscillating Dark Energy in Light of the Latest Observations and Its Impact on the Hubble Tension

In this paper, we have performed a comparative study of different types of oscillating dark energy (DE) models using the Metropolis algorithm of Markov Chain Monte Carlo. Eight different oscillating parameterizations are examined herein that have demonstrated considerable ability to fit the overall cosmological observations, including the Pantheon sample of Type Ia supernovae, baryon acoustic oscillations, cosmic chronometer Hubble data, and distance priors of the Planck cosmic microwave background. In order to compare the consistency of these models with observations, we have used both the Akaike and deviance information criteria. Although the values of the Akaike information criterion for different models indicate that there is no support for oscillating DE models, the deviance information criterion showed that there is significant support for some of these models. Our results showed that these models are capable of solving the cosmic coincidence problem and alleviating the Hubble tension. Comparing the H 0 values obtained for different oscillating scenarios with that of ΛCDM, we observed that our oscillating models led to H0¯=69.78 , which is 0.29 greater than H 0,Λ and thus reduces the Hubble tension. Among all of the models, model 1, with H 0 = 70.00 ± 0.71, is the most capable of alleviating the H 0 tension. Furthermore, we examined our models assuming H 0 = 73.0 ± 1.4 from SHoES measurements. We find that adding this data point to our data combination led to a ΔH0¯=0.95 increase in the H 0 value for different models.

A flexible Bayesian tool for CoDa mixed models: logistic-normal distribution with Dirichlet covariance

Compositional Data Analysis (CoDa) has gained popularity in recent years. This type of data consists of values from disjoint categories that sum up to a constant. Both Dirichlet regression and logistic-normal regression have become popular as CoDa analysis methods. However, fitting this kind of multivariate models presents challenges, especially when structured random effects are included in the model, such as temporal or spatial effects. To overcome these challenges, we propose the logistic-normal Dirichlet Model (LNDM). We seamlessly incorporate this approach into the R-INLA package, facilitating model fitting and model prediction within the framework of Latent Gaussian Models. Moreover, we explore metrics like Deviance Information Criteria, Watanabe Akaike information criterion, and cross-validation measure conditional predictive ordinate for model selection in R-INLA for CoDa. Illustrating LNDM through two simulated examples and with an ecological case study on Arabidopsis thaliana in the Iberian Peninsula, we underscore its potential as an effective tool for managing CoDa and large CoDa databases.

Spatial-temporal Bayesian accelerated failure time models for survival endpoints with applications to prostate cancer registry data

Prostate cancer is the most common cancer after non-melanoma skin cancer and the second leading cause of cancer deaths in US men. Its incidence and mortality rates vary substantially across geographical regions and over time, with large disparities by race, geographic regions (i.e., Appalachia), among others. The widely used Cox proportional hazards model is usually not applicable in such scenarios owing to the violation of the proportional hazards assumption. In this paper, we fit Bayesian accelerated failure time models for the analysis of prostate cancer survival and take dependent spatial structures and temporal information into account by incorporating random effects with multivariate conditional autoregressive priors. In particular, we relax the proportional hazards assumption, consider flexible frailty structures in space and time, and also explore strategies for handling the temporal variable. The parameter estimation and inference are based on a Monte Carlo Markov chain technique under a Bayesian framework. The deviance information criterion is used to check goodness of fit and to select the best candidate model. Extensive simulations are performed to examine and compare the performances of models in different contexts. Finally, we illustrate our approach by using the 2004-2014 Pennsylvania Prostate Cancer Registry data to explore spatial-temporal heterogeneity in overall survival and identify significant risk factors.

Comparing Bayesian models for the genetic evaluation of oocytes and embryo counts in Dairy Gir cattle.

Count traits are usually explored in livestock breeding programs, and they usually do not fit into normal distribution, requiring alternatives to adjust the phenotype to estimate accurate genetic parameters and breeding values. Alternatively, distribution such as Poisson can be used to evaluate count traits. This study aimed to compare and discuss the genetic evaluation for oocyte and embryo counts considering Gaussian (untransformed variable - LIN; transformed by logarithm - LOG; transformed by Anscombe - ANS) and Poisson (POI) distributions. The data comprised 11,343 total oocytes(TO), viable oocytes(VO), cleaved embryos(CE), and viable embryo(VE) records of ovum pick-up from 1740 Dairy Gir heifers and cows. The genetic parameters and breeding values were estimated by the MCMCglmm package of the R software. The posterior means of heritability varied from 0.40 (LIN) to 0.49 (POI) for TO, 0.39 (LIN) to 0.49 (POI) for VO, 0.30 (LOG) to 0.41 (POI) for cleaved embryos, and 0.19 (LIN) to 0.32 (POI) for viable embryos. The posterior means of repeatability varied from 0.56 (LIN) to 0.65 (POI) for TO, 0.53 (LOG) to 0.63 (POI) for VO, 0.44 (LOG) to 0.60 (POI) for CE, and 0.36 (LOG) to 0.56 (POI) for VE. Deviance information criterion and mean squared residuals indicated that POI model should be used for the genetic evaluation of embryo and oocyte count traits. Spearman's rank correlation between estimated breeding value (EBV) for embryo and oocyte count traits computed by POI, LOG, and ANS models was high (ranging from 0.77 to 0.99), indicating little reranking among the best animals. The POI model is the most adequate for genetic evaluation, resulting in more reliable EBV of oocyte and embryo count traits for Dairy Gir cattle.

Modeling Factors Influencing Covid-19 Cases in South Sulawesi Using Bayesian Conditional Autoregressive Localised

South Sulawesi Province is listed as the province with the highest number of Covid-19 cases in the Sulawes island. Research on Covid-19 modeling has been carried out by many researchers, but until now, there has been no research using the Bayesian spatial Conditional Autoregressive Localized model which involves a combination of factors such as distance to the provincial capital, population density, and the number of elderly people in each district in South Sulawesi Province. The aim of this research is to get the best Bayesian Conditional Autoregressive Localized model. The best model is based on four criteria, namely: Deviance Information Criteria, Watanabe Akaike Information Criteria, residuals from Modified Moran's I, and the number of areas included in a group. It was found that model with G=3 by including population density covariates was the best model. A significant factor influencing the increase in Covid-19 cases is the population density factor which has a positive effect. This shows that the more densely populated an area is, the greater the chance of being infected with Covid-19. Makassar has the highest relative risk value for Covid-19 followed by Toraja district and Pare-Pare City. Meanwhile, Bone district has the lowest relative risk value for Covid-19, followed by Wajo district and Enrekang district.

Spatially Weighted Multinomial Modelling of Comorbidity of Anaemia and Malaria among Under-Five Children in Nigeria

Children in sub-Saharan African countries, especially Nigeria, continue to suffer increased mortality owing to comorbidity of infections such as anaemia and malaria, which are known to epidemiologically overlap. In order to examine the risk factors and spatial patterns of comorbidity of anaemia and malaria using the 2021 Nigeria Malaria Indicator Survey (NMIS), a multinomial logit model was extended by incorporating a spatially weighted random effect. The impact of climatic variation on the childhood disease comorbidity was explored by weighting the spatial structured component based on the 2021 NMIS average cluster temperature of each state in Nigeria. A number of spatially weighted geo-additive models were fitted and compared using deviance information criterion. Inference was fully Bayesian, and an Intrinsic Conditional Autoregressive prior was used for structured random effects. Based on the map generated from the best-fitted model, which unveiled states that are more susceptible to the risk of disease comorbidity, the average temperature used as a weighting factor, however, has a strong relationship with the spatial pattern of disease comorbidity. States with low temperatures have a higher risk of comorbidity of anaemia and malaria compared to states with higher average temperatures. Area of residence, level of education of the mother, economic status of the mother, and owning mosquito-treated nets were identified as the significant risk factors associated with the disease comorbidity. Findings from this study will be helpful to policymakers and health authorities in their effort to combat the comorbidity of childhood anaemia and malaria, thereby reducing child mortality in Nigeria.

Genetic evaluations of dairy goats with few pedigree data: different approaches to use molecular information.

One of the limitations of implementing animal breeding programs in small-scale or extensive production systems is the lack of production records and genealogical records. In this context, molecular markers could help to gain information for the breeding program. This study addresses the inclusion of molecular data into traditional genetic evaluation models as a random effect by molecular pedigree reconstruction and as a fixed effect by Bayesian clustering. The methods were tested for lactation curve traits in 14 dairy goat herds with incomplete phenotypic data and pedigree information. The results showed an increment of 37.3% of the relationships regarding the originals with MOLCOAN and clustering into five genetic groups. Data leads to estimating additive variance, error variance, and heritability with four different models, including pedigree and molecular information. Deviance Information Criterion (DIC) values demonstrate a greater fitting of the models that include molecular information either as fixed (genetic clusters) or as random (molecular matrix) effects. The molecular information of simple markers can complement genetic improvement strategies in populations with little information.

Bayesian Shared Component Spatial Modeling for Assessing the Shared and Age Group-Specific Mental Health Disorder Risk of Young and Old Age Groups: A Case Study of Toronto Neighborhoods, Canada

Mental health disorder risks of young and old age groups hold considerable importance for understanding present and future risk burdens. However, assessing mental health risks is significantly constrained by the influence of shared and age group-specific spatial processes and risk factors. Therefore, this study employed Bayesian shared component spatial modeling (BSCSM) to analyze mental health disorder data obtained from young (20–44 years) and old (65+ years) age groups in Toronto. BSCSM was employed to model the shared and age group-specific disorder risk and to identify hotspot areas. The unmeasured covariates, overdispersion, and latent spatial processes were adjusted using spatial and non-spatial random effect terms. The findings from BSCSM were finally compared with non-shared component modeling approaches. The results suggest that over 60% of variations in mental health disorder risk for both age groups could be explained by the shared component. The high-risk neighborhoods were mainly localized in southern and north-central Toronto for the young and old age groups. Deviance information criterion values suggested that models from BSCSM outperformed non-BSCSM models. BSCSM risk maps were also better at identifying high-risk areas. This work demonstrated that both shared and age group-specific risks are essential for assessing mental health disorder risk and devising targeted interventions.

Modelling spatiotemporal patterns of visceral leishmaniasis incidence in two endemic states in India using environment, bioclimatic and demographic data, 2013-2022.

As of 2021, the National Kala-azar Elimination Programme (NKAEP) in India has achieved visceral leishmaniasis (VL) elimination (<1 case / 10,000 population/year per block) in 625 of the 633 endemic blocks (subdistricts) in four states. The programme needs to sustain this achievement and target interventions in the remaining blocks to achieve the WHO 2030 target of VL elimination as a public health problem. An effective tool to analyse programme data and predict/ forecast the spatial and temporal trends of VL incidence, elimination threshold, and risk of resurgence will be of use to the programme management at this juncture. We employed spatiotemporal models incorporating environment, climatic and demographic factors as covariates to describe monthly VL cases for 8-years (2013-2020) in 491 and 27 endemic and non-endemic blocks of Bihar and Jharkhand states. We fitted 37 models of spatial, temporal, and spatiotemporal interaction random effects with covariates to monthly VL cases for 6-years (2013-2018, training data) using Bayesian inference via Integrated Nested Laplace Approximation (INLA) approach. The best-fitting model was selected based on deviance information criterion (DIC) and Watanabe-Akaike Information Criterion (WAIC) and was validated with monthly cases for 2019-2020 (test data). The model could describe observed spatial and temporal patterns of VL incidence in the two states having widely differing incidence trajectories, with >93% and 99% coverage probability (proportion of observations falling inside 95% Bayesian credible interval for the predicted number of VL cases per month) during the training and testing periods. PIT (probability integral transform) histograms confirmed consistency between prediction and observation for the test period. Forecasting for 2021-2023 showed that the annual VL incidence is likely to exceed elimination threshold in 16-18 blocks in 4 districts of Jharkhand and 33-38 blocks in 10 districts of Bihar. The risk of VL in non-endemic neighbouring blocks of both Bihar and Jharkhand are less than 0.5 during the training and test periods, and for 2021-2023, the probability that the risk greater than 1 is negligible (P<0.1). Fitted model showed that VL occurrence was positively associated with mean temperature, minimum temperature, enhanced vegetation index, precipitation, and isothermality, and negatively with maximum temperature, land surface temperature, soil moisture and population density. The spatiotemporal model incorporating environmental, bioclimatic, and demographic factors demonstrated that the KAMIS database of the national programmme can be used for block level predictions of long-term spatial and temporal trends in VL incidence and risk of outbreak / resurgence in endemic and non-endemic settings. The database integrated with the modelling framework and a dashboard facility can facilitate such analysis and predictions. This could aid the programme to monitor progress of VL elimination at least one-year ahead, assess risk of resurgence or outbreak in post-elimination settings, and implement timely and targeted interventions or preventive measures so that the NKAEP meet the target of achieving elimination by 2030.

Evaluating the Performance of Mixed Zero-Inflated Poisson Regression Models with Time-dependent and Time-independent Covariates

One of the issues that researchers may encounter in count data is having many zeros. One of the solutions to model these data is using zero-inflated Poisson (ZIP) regression models. Recently, researchers have started to model longitudinal count data with time-dependent covariates. However, it has not been considered whether a model with time-dependent covariates provides a better fit than a model with time-independent covariates. In this paper, the fit between a mixed ZIP model with time-dependent covariates and a mixed ZIP model with time-independent covariates is compared using simulation. Using the deviance information criterion as a measure of fit, we found that the model with time-dependent covariates exhibits a better fit than the model with time-independent covariates. KEYWORDS correlated data, count data, excess zeros, longitudinal, mixed models, model fit

Uncertainly Analysis of Prior Distribution in Accelerated Degradation Testing Bayesian Evaluation Method Based on Deviance Information Criterion

Uncertainly Analysis of Prior Distribution in Accelerated Degradation Testing Bayesian Evaluation Method Based on Deviance Information Criterion

Improved Method to Estimating Parameters of a Poisson Hidden Markov Model Using Bayesian Approach

Expectation-Maximization (EM) is a popular method for estimating parameters of the Poisson-Hidden Markov Model (P-HMM). However, over-dispersion in comparison to the Poisson distribution remains a concern. This study developed a Bayesian method to Poisson count models. The study compares the Mean Square Errors and sufficiency of the EM to the Gibbs sampler technique using Akaike Information Criterion, Bayesian Information Criterion, and Deviance Information Criterion as model selectors. The Maximum Likelihood Estimates and Maximum a \textit{posteriori} were calculated using both simulated and real data in this case. The study&amp;#39;s findings indicate that using any of the two approaches depends on the data type and the sample size. Whereas the Poisson Hidden Markov model, which uses the EM algorithm is preferred when using Zero-inflated data with a sample size&amp;nbsp; n &amp;le; 20 , the Bayesian Poisson-Hidden Markov Model, which uses a Gibbs sampler is better used for Heavy and Mixture data types irrespective of the sample size. The model predicted parameters of simulated data with remarkable accuracy and produced some unique statistical property results. This method is applicable to Poisson-hidden Markov models with homogeneous time series.

Comparison performance of the Bayesian Approach with the Weibull and Birnbaum-Saunders distributions in imputation of time-to-event censors.

Almost all survival data is censored, and censor imputation is necessary. This study aimed to investigate the performance of the Bayesian Approach (BA) in the imputation of censored records in simulated and Breast Cancer (BC) data. Due to the difference in the distribution of time to event in survival analysis, two well-known the Weibull and Birnbaum-Saunders (BS) distributions have been used to test the performance of the BA. For each of the censored, 10,000 times were simulated using the BA in R and BUGS software, and their median or mean was imputed instead of each censor. The eligibility of both imputation methods was investigated using different curves, different censoring percentages, and sample sizes, as well as the Deviance Information Criteria (DIC), Effective Sample Size, and the Geweke diagnostic in simulated and especially real BC data. The BC data, which contains 220 patients who were identified and followed up between 2015 and 2023, was made accessible on February 1, 2023. The Kaplan-Meier, the BA, and other survival curves were drawn for the observed times. Findings indicated that the performance of the BA under the Weibull and BS distributions in simulated data is similar. The DIC index in the BC data under the BS distribution (1510) is less than the Weibull distribution (1698). Therefore, the BS distribution is preferred over the Weibull for imputation of censoring times in real BC data.

Incorporating Road Network Connectivity in Neighboring Structures for Crash Prediction Models at the Area Level

Spatial correlation models have been traditionally used in road safety to account for spatial effects resulting from unmeasured or unknown risk factors that induce spatial correlation between neighboring areas. In transportation, the interaction between neighboring areas is highly influenced by the number of roads that connect those areas and the importance of those roads. This paper proposes an approach in which the weights of the spatial interaction (and therefore the spatial correlation) between areas depends on the number of road connections between those areas and the importance of those connections. The results using districts in Costa Rica show that the inclusion of road network connectivity in the models of spatial correlation significantly improves model fit, even after accounting for model complexity using the deviance information criterion (DIC) and widely applicable information criterion (WAIC). The inclusion of higher weights for national roads compared to municipal or local roads further improved the model fit. The best three models with respect to the posterior deviance, DIC, and WAIC are those that give at least three times more weight to national roads compared to local roads. With respect to site ranking, those three models present similar results, which also highlights the consistency among those models.

Addressing Heteroscedasticity in Correlated Binary Data: A Bayesian Mixed Effects Location Scale Approach

Introduction: The mixed effects logistic regression model is a common model for analysing correlated binary data as longitudinal data. The between and within subject variances are typically considered to be homogeneous but longitudinal data often show heterogeneity in these variances. This study proposes a Bayesian mixed effects location scale model to accommodate heteroscedasticity in binary data analysis.&#x0D; Methods: This study was carried out in two stages; first, the simulation study was used to evaluate the accuracy of the proposed model with the Bayesian approach and then the proposed model was applied to a real data. In simulation study, the data were generated from the mixed effects location scale model with different correlations between the random location effect and random scale effect and different sample sizes. In order to evaluate the accuracy of the estimations, the Root Mean Square Error, bias and Coverage Probability were calculated and the deviance information criterion was used to select the appropriate model. At the end we utilized this model to analyse uric acid levels of patients with haematological disorders.&#x0D; Results: The simulation results show the accuracy of model parameter estimates as well as the correlation between random location and scale effects. They also display that if a random scale effect is present in the data, it should be accounted for in model. Otherwise, the model is forced to assign the within subject variation due to these subject random effects to the error term. The results of real data are also in line with this. The odds of having normal UA levels increases by a factor of 26% per week. Due to the positive value of the covariance parameter, patients with higher mean of UA levels show higher variation in UA levels. Furthermore, the significance of the covariates in the between subject and within subject variances model, as well as the significance of the random scale variance determines the heterogeneity across subjects.&#x0D; Conclusion: Bayesian mixed effects location scale model provides a useful tool for analysing correlated binary data with heteroscedasticity because it considers data correlation and modelling mean and variance simultaneously. Furthermore, it improves the accuracy of statistical inference in longitudinal studies compared to classic mixed effects models.

How to Model in Zoology: Basic Concepts and Explanations

The information criteria used for biologists-zoologists when comparing statistical models are summarized. The three criteria summarizes the quality (Akaike Information Criterion, AIC), complexity (Bayesian Information Criterion, BIC) and finally the reliability, fiability or accuracy (Deviance Information Criterion, DIC) of a model.

Covariate-guided Bayesian mixture of spline experts for the analysis of multivariate high-density longitudinal data.

With rapid development of techniques to measure brain activity and structure, statistical methods for analyzing modern brain-imaging data play an important role in the advancement of science. Imaging data that measure brain function are usually multivariate high-density longitudinal data and are heterogeneous across both imaging sources and subjects, which lead to various statistical and computational challenges. In this article, we propose a group-based method to cluster a collection of multivariate high-density longitudinal data via a Bayesian mixture of smoothing splines. Our method assumes each multivariate high-density longitudinal trajectory is a mixture of multiple components with different mixing weights. Time-independent covariates are assumed to be associated with the mixture components and are incorporated via logistic weights of a mixture-of-experts model. We formulate this approach under a fully Bayesian framework using Gibbs sampling where the number of components is selected based on a deviance information criterion. The proposed method is compared to existing methods via simulation studies and is applied to a study on functional near-infrared spectroscopy, which aims to understand infant emotional reactivity and recovery from stress. The results reveal distinct patterns of brain activity, as well as associations between these patterns and selected covariates.

Genomic analysis of feed efficiency traits in beef cattle using random regression models.

Feed efficiency plays a major role in the overall profitability and sustainability of the beef cattle industry, as it is directly related to the reduction of the animal demand for input and methane emissions. Traditionally, the average daily feed intake and weight gain are used to calculate feed efficiency traits. However, feed efficiency traits can be analysed longitudinally using random regression models (RRMs), which allow fitting random genetic and environmental effects over time by considering the covariance pattern between the daily records. Therefore, the objectives of this study were to: (1) propose genomic evaluations for dry matter intake (DMI), body weight gain (BWG), residual feed intake (RFI) and residual weight gain (RWG) data collected during an 84-day feedlot test period via RRMs; (2) compare the goodness-of-fit of RRM using Legendre polynomials (LP) and B-spline functions; (3) evaluate the genetic parameters behaviour for feed efficiency traits and their implication for new selection strategies. The datasets were provided by the EMBRAPA-GENEPLUS beef cattle breeding program and included 2920 records for DMI, 2696 records for BWG and 4675 genotyped animals. Genetic parameters and genomic breeding values (GEBVs) were estimated by RRMs under ssGBLUP for Nellore cattle using orthogonal LPs and B-spline. Models were compared based on the deviance information criterion (DIC). The ranking of the average GEBV of each test week and the overall GEBV average were compared by the percentage of individuals in common and the Spearman correlation coefficient (top 1%, 5%, 10% and 100%). The highest goodness-of-fit was obtained with linear B-Spline function considering heterogeneous residual variance. The heritability estimates across the test period for DMI, BWG, RFI and RWG ranged from 0.06 to 0.21, 0.11 to 0.30, 0.03 to 0.26 and 0.07 to 0.27, respectively. DMI and RFI presented within-trait genetic correlations ranging from low to high magnitude across different performance test-day. In contrast, BWG and RWG presented negative genetic correlations between the first 3 weeks and the other days of performance tests. DMI and RFI presented a high-ranking similarity between the GEBV average of week eight and the overall GEBV average, with Spearman correlations and percentages of individuals selected in common ranging from 0.95 to 1.00 and 93 to 100, respectively. Week 11 presented the highest Spearman correlations (ranging from 0.94 to 0.98) and percentages of individuals selected in common (ranging from 85 to 94) of BWG and RWG with the average GEBV of the entire period of the test. In conclusion, the RRM using linear B-splines is a feasible alternative for the genomic evaluation of feed efficiency. Heritability estimates of DMI, RFI, BWG and RWG indicate enough additive genetic variance to achieve a moderate response to selection. A new selection strategy can be adopted by reducing the performance test to 56 days for DMI and RFI selection and 77 days for BWG and RWG selection.

Prevalence and determinants of adequate postnatal care in Ethiopia: evidence from 2019 Ethiopia mini demographic and health survey

BackgroundThe postpartum period is critical for both the mother's and newborn child's health and survival. Rising morbidity and mortality are usually the consequence of absence of adequate, suitable, or timely care during that time period. There is lack of information on the adequacy of postnatal care in Ethiopia and this study was aimed to investigate adequacy of postnatal care and its determinants in the study area.MethodsIn this study, we used a cross-sectional dataset from the 2019 Ethiopia Mini Demographic and Health Survey. A multistage stratified clustered design applied and survey weights were used to take into account the complicated sample design. A multilevel mixed effects logistic regression was fitted on 3772 women who were nested within 305 clusters. The fixed effect models were fitted and expressed as adjusted odds ratios with 95% confidence intervals, while intra-class correlation coefficients, median odds ratio, and proportional change in variance explained measures of variation. As model fitness criteria, the deviance information criterion and the Akaike information criterion were used.ResultsThis study found that only 563(16.14%, 95% CI: 16.05–16.24) women had adequate post natal care. Age of between 25–35 years old (AOR = 1.55, 95%CI = 1.04–2.31), secondary level of education (AOR = 2.23, 95%CI = 1.43–3.45), Having parity of between two and four had (AOR = 0.62, 95%CI = 0.42 0.93), having ANC follow up four and above (AOR = 1.74, 95%CI = 1.31–2.33), being residents of Oromia region (AOR = 0.10, 95CI = 0.02- 0.43) were strong predictors of adequate postnatal care.ConclusionThe study found that prevalence of adequate PNC in Ethiopia was significantly low. To increase postnatal care adequacy, it was recommended to reinforce existing policies and strategies such as increasing number of antenatal care follow up, and scheduling mothers based on the national postnatal care follow-up protocol.

Bayesian CART models for insurance claims frequency

The accuracy and interpretability of a (non-life) insurance pricing model are essential qualities to ensure fair and transparent premiums for policy-holders, that reflect their risk. In recent years, classification and regression trees (CARTs) and their ensembles have gained popularity in the actuarial literature, since they offer good prediction performance and are relatively easy to interpret. In this paper, we introduce Bayesian CART models for insurance pricing, with a particular focus on claims frequency modelling. In addition to the common Poisson and negative binomial (NB) distributions used for claims frequency, we implement Bayesian CART for the zero-inflated Poisson (ZIP) distribution to address the difficulty arising from the imbalanced insurance claims data. To this end, we introduce a general MCMC algorithm using data augmentation methods for posterior tree exploration. We also introduce the deviance information criterion (DIC) for tree model selection. The proposed models are able to identify trees which can better classify the policy-holders into risk groups. Simulations and real insurance data will be used to illustrate the applicability of these models.