Hierarchical Nonlinear Model Research Articles

Hierarchical game joint optimization for product family-driven modular design

Product family design takes advantage of modularity to enable product variety while maintaining mass production efficiency. Focusing on a set of similar product variants, product family modularity (PFM) is achieved by reusing common components and minimizing fulfillment costs throughout the product realization process. On the other hand, traditional modular design emphasizes technical system modularity (TSM) that focuses on a single product and is geared towards product decomposition in light of technical feasibility. While it is appealing to incorporate product family considerations into the prevailing modularization theories and methods, the key challenge lies in that TSM and PFM are essentially associated with different goals and decision criteria. This leads to a dilemma that TSM and PFM are competing in decision making for identification of modules by grouping similar components. Realizing the importance of game-theoretic decision making underlying product family-driven modular design, this paper proposes to leverage TSM and PFM within a coherent framework of joint optimization. A hierarchical game joint optimization model is developed in line with bilevel programming. A two-dimension evaluation criteria taxonomy is presented for TSM and PFM criteria measure. A bilevel nested genetic algorithm is put forward for efficient solution of the non-linear hierarchical joint optimization model. A case study of robotic vacuum cleaner modular design is reported to gain insight into joint optimization of TSM and PFM. Results and analyses demonstrate that the proposed hierarchical joint optimization model is robust and can empower modular design in cohesion with product family concerns.

Nonlinear hierarchical modeling of experimental infection data

In this paper, we propose a nonlinear hierarchical model (NLHM) for analyzing longitudinal experimental infection (EI) data. The NLHM offers several improvements over commonly used alternatives such as repeated measures analysis of variance (RM-ANOVA) and the linear mixed model (LMM). It enables comparison of relevant biological properties of the course of infection including peak intensity, duration and time to peak, rather than simply comparing mean responses at each observation time. We illustrate the practical benefits of this model and the insights it yields using data from experimental infection studies on equine arteritis virus. Finally, we demonstrate via simulation studies that the NLHM substantially reduces bias and improves the power to detect differences in relevant features of the infection response between two populations. For example, to detect a 20% difference in response duration between two groups (n=15) in which the peak time and peak intensity were identical, the RM-ANOVA test had a power of just 11%, and LMM a power of just 12%. By comparison, the nonlinear model we propose had a power of 58% in the same scenario, while controlling the Type I error rate better than the other two methods.

An Effective Nonlinear Multivariable HMPC for USC Power Plant Incorporating NFN-Based Modeling

The ultra-supercritical (USC) unit is an advanced power generation technology with high plant efficiency, high coal utilization, and low emission. However, it is difficult to realize a coordinate control for the USC unit to achieve fast and stable dynamic response during load tracking and grid frequency disturbances, because it is complex, nonlinear, and large scale. This paper presents a nonlinear hierarchical model predictive control (HMPC) to incorporate both the plant-wide economic process optimization and the regulatory process control into a hierarchical control structure, in which the model predictive control (MPC) technology is utilized to solve the multilayer optimization problem. While the nonlinear HMPC optimization problems can be nonconvex, the neuro-fuzzy network (NFN) modeling on USC is incorporated to facilitate the convex quadratic program (QP) routine. Detailed analysis on load tracking and grid frequency disturbances via simulations has been addressed to demonstrate the effectiveness of the proposed nonlinear HMPC.

Spatial variability of the effect of air pollution on term birth weight: evaluating influential factors using Bayesian hierarchical models.

BackgroundEpidemiological studies suggest that air pollution is adversely associated with pregnancy outcomes. Such associations may be modified by spatially-varying factors including socio-demographic characteristics, land-use patterns and unaccounted exposures. Yet, few studies have systematically investigated the impact of these factors on spatial variability of the air pollution’s effects. This study aimed to examine spatial variability of the effects of air pollution on term birth weight across Census tracts and the influence of tract-level factors on such variability.MethodsWe obtained over 900,000 birth records from 2001 to 2008 in Los Angeles County, California, USA. Air pollution exposure was modeled at individual level for nitrogen dioxide (NO2) and nitrogen oxides (NOx) using spatiotemporal models. Two-stage Bayesian hierarchical non-linear models were developed to (1) quantify the associations between air pollution exposure and term birth weight within each tract; and (2) examine the socio-demographic, land-use, and exposure-related factors contributing to the between-tract variability of the associations between air pollution and term birth weight.ResultsHigher air pollution exposure was associated with lower term birth weight (average posterior effects: −14.7 (95 % CI: −19.8, −9.7) g per 10 ppb increment in NO2 and −6.9 (95 % CI: −12.9, −0.9) g per 10 ppb increment in NOx). The variation of the association across Census tracts was significantly influenced by the tract-level socio-demographic, exposure-related and land-use factors. Our models captured the complex non-linear relationship between these factors and the associations between air pollution and term birth weight: we observed the thresholds from which the influence of the tract-level factors was markedly exacerbated or attenuated. Exacerbating factors might reflect additional exposure to environmental insults or lower socio-economic status with higher vulnerability, whereas attenuating factors might indicate reduced exposure or higher socioeconomic status with lower vulnerability.ConclusionsOur Bayesian models effectively combined a priori knowledge with training data to infer the posterior association of air pollution with term birth weight and to evaluate the influence of the tract-level factors on spatial variability of such association. This study contributes new findings about non-linear influences of socio-demographic factors, land-use patterns, and unaccounted exposures on spatial variability of the effects of air pollution.Electronic supplementary materialThe online version of this article (doi:10.1186/s12940-016-0112-5) contains supplementary material, which is available to authorized users.

Model-Based Optimisation of Deferoxamine Chelation Therapy.

PurposeHere we show how a model-based approach may be used to provide further insight into the role of clinical and demographic covariates on the progression of iron overload. The therapeutic effect of deferoxamine is used to illustrate the application of disease modelling as a means to characterising treatment response in individual patients.MethodsSerum ferritin, demographic characteristics and individual treatment data from clinical routine practice on 27 patients affected by β-thalassaemia major were used for the purposes of this analysis. The time course of serum ferritin was described by a hierarchical nonlinear mixed effects model, in which compliance was parameterised as a covariate factor. Modelling and simulation procedures were implemented in NONMEM (7.2.0).ResultsA turnover model best described serum ferritin changes over time, with the effect of blood transfusions introduced on the ferritin conversion rate and the effect of deferoxamine on the elimination parameter (Kout) in a proportional manner. The results of the simulations showed that poor quality of execution is preferable over drug holidays; and that independently of the compliance pattern, the therapeutic intervention is not effective if >60% of the doses are missed.ConclusionsModelling of ferritin response enables characterisation of the dynamics of iron overload due to chronic transfusion. The approach can be used to support decision making in clinical practice, including personalisation of the dose for existing and novel chelating agents.Electronic supplementary materialThe online version of this article (doi:10.1007/s11095-015-1805-0) contains supplementary material, which is available to authorised users.

An Integrated Method for Detecting Micro RNA Target Proteins through Reverse-phase Protein Arrays

Objective: Understanding functions of microRNAs (or miRNAs), particularly their effects on protein degradation, is biologically important. Emerging technologies, including the reverse-phase protein array (RPPA) for quantifying protein concentration and RNA-seq for quantifying miRNA expression, provide a unique opportunity to study miRNA-protein regulatory mechanisms. One naive way to analyze such data is to directly examine the correlation between the raw miRNA measurements and protein concentrations estimated from RPPA. However, the uncertainty associated with protein concentration estimates is ignored, which may lead to less accurate results and significant power loss. Methods: We propose an integrated nonlinear hierarchical model for detecting miRNA targets through original RPPA intensity data. This model is fitted within a maximum likelihood framework and the correlation test between miRNA and protein is assessed using Wald tests. We compare this model and the simple method through extensive simulation studies and a real dataset from the Cancer Genome Atlas (TCGA) project. Results: This integrated method is shown to have consistently higher power than the simple method, especially when sample sizes are limited and when the RPPA intensity levels are close to the boundaries of imaging limits. Conclusions: Our proposed method is powerful in detecting miRNA’s protein target through RPPA. We recommend this method in practice.

Termination of Parental Rights for Parents with Substance Use Disorder: For Whom and Then What?

The purpose of this study is to investigate the correlates of termination of parental rights (TPR) for parents with substance use disorder (SUD) and to determine what happens with regard to permanency once a TPR decision is made. Bivariate techniques and hierarchical nonlinear modeling are used. Parents of older youth, boys, and Hispanics were less likely, whereas parents who failed to make progress in substance use treatment and parenting skills are more likely to experience TPR. At follow up, 85% of the children were adopted, 7% remained in a substitute care settings, and 7% were reunified with their parents. Concerns remain for children without a permanent home setting.

Analysing the influence of factors of birth cohort maturing on geographical distribution of disability risks due to cardio-vascular diseases

We investigated the local regularities of disability incidence due to cardiovascular diseases in Zhytomyr oblast over 1999-2008 by strip-split-plot design. By using geographical mixed model we ascertained the peculiarities of disability distribution among cohorts, age groups and time periods (APC). Data analysis was carried out on the base of hierarchical nonlinear mixed model. Results bear witness to enhanced local heterogeneity in disability rates due to irregularity in distribution of APC factors. Each APC factor rendered significant modification to geographical distribution of disability rates.

Educational Outcomes at Historically Black Colleges and Universities

This study assessed variability in Historically Black Colleges and Universities’ (HBCUs) educational outcomes. Analyses were conducted on two nationally representative databases via hierarchical linear and nonlinear modeling. Intraclass correlation coefficients for HBCUs were compared with those of (a) a random sample—theorized to have no systematic similarity in educational outcomes to HBCUs and (b) a sample of other Predominately Black Institutions (PBIs). Findings indicate that HBCUs’ educational outcomes were generally more cohesive than those of the random sample, and this cohesiveness followed a different pattern than the cohesiveness of outcomes at other PBIs. On the whole, then, this study suggests that educational outcomes at HBCUs are cohesive and distinct from other institutional groups.

Estimation of Daily Milk Yields from AM/PM Milking Records

Daily milk yields on test days were estimated using morning or afternoon partial milk yields collected by official agencies and the accuracy of the estimates was determined. Test-day data for milk yields consisted of 3,156,734 records of AM/PM partial milking measurements of 255,437 milking Holstein cows from 3,708 farms collected from December 2008 to April 2013. A linear regression model (LRM) was applied to estimate daily milk yields using alternate AM/PM milk yield records within lactation stages, milking intervals, and parities on every daily milk yield. The alternate statistical approach was a non-linear hierarchical model (NHM) in which Brody's growth function was implemented by reflecting an animal's physiological milk production cycle. When compared with LRM, daily milk yields predicted by the NHM were assumed to be functionally related to day in milk (or lactation) stage, milking intervals, and partial milk yields. Since the results were in terms of accuracies based on comparisons of different statistical models, accuracies of estimates of daily milk yields by NHM were close to those determined by the LRM. The average of these accuracies was 0.94 for AM partial milk yields and 0.93 for PM partial milk yields for first calving cows. However, the accuracies of AM/PM milk yield estimations from cows under a calving stage higher than the first parity were 0.96 and 0.95, respectively. Correlations between the estimated daily milk yields and the actual daily milk yields ranged from 0.96~ 0.98. These accuracies were lower for unbalanced AM/PM milking intervals and the first calving cows. Overall, prediction of daily milk yields by NHM would be more appropriate than by LRM due to its flexibility under different milk yield-related circumstances, which provides an idea of the functional relationship between milking intervals and days in milk with daily milk yields from statistical viewpoints.

A negative stiffness metamaterial inclusion via small-scale curved structural elements

This work presents a means to produce negative stiffness metamaterial units without employing inherent nonlinear material behavior or dynamic effects, but rather through large deformations of tailored microscale geometry. Specifically, the work of Qiu et al. [J. Microelectromech. Syst. 13, 137–146 (2004)] is generalized to create metamaterial units displaying non-monotonic stress-strain relationships with regions of negative stiffness behavior. These cells are designed to be embedded into a continuous matrix material and negative stiffness is elicited through pre-strain of the metamaterial unit cells brought about by changes in ambient pressure. This work presents a nonlinear hierarchical multiscale material model to estimate the macroscopic stiffness and loss of a composite material containing these pre-strained microscale structured inclusions. The multiscale model consists of two scale transition models: (i) an energy-based nonlinear finite element (FE) method to determine the anisotropic tangent moduli of the inclusion, and (ii) an analytical micromechanical model to determine the effective stiffness and loss tensors due to small perturbations about the local strain state of the metamaterial inclusions. Models and results for various volume fractions are presented and discussed.

Indoor fungal spores of school and current asthma in schoolchildren.

Background: Visible mold in children’s classroom has been associated with current asthma symptoms in schoolchildren. However, studies on the roles of specific fungal spores on asthma symptoms were limited. Aims:This study aims to assess the relationship between asthmatic conditions and specific airborne fungus in classrooms. Methods: Between April to May 2011, we conducted a cross-sectional survey for allergic diseases in schoolchildren aged 6~15 years in 44 schools in Taiwan.History and current symptoms of allergic diseases were inquired by using questionnaire compatible with International Study of Asthma and Allergies in Childhood (ISAAC). Fungal spores were collected by Burkard Personal Air Sampler in 264 classrooms, and counted by light microscope. Three-level hierarchical non-linear modeling was applied to compare the individual asthmatic conditions to concentration of fungal spores in classrooms. Results: Totally, 6346 of 7154 (88.7%) children’s parents completed the questionnaire. The prevalences of ever-having physician-diagnosed asthma, current asthma, and asthma with symptoms reduced on holidays (ASROH) were 11.7%, 7.5%, and 3.1%, respectively. After adjusting for personal factors, correlated fungal spores and schools, higher prevalence of current asthma and ASROH was found in classrooms with higher levels of aspergillus/penicillium and basidiospores. Conclusions: Indoor fungal spores in classrooms were highly associated with the prevalence of current asthma and ASROH in schoolchildren. Future investigation on potential sources for indoor aspergillus/penicillium and basidiospores may extend the knowledge on causes and environmental remediation of asthma in schools.

Comparison of silvicultural and natural disturbance effects on terrestrial salamanders in northern hardwood forests

In forested ecosystems timber harvesting has the potential to emulate natural disturbances, thereby maintaining the natural communities adapted to particular disturbances. We compared the effects of even-aged (clearcut and patch cut) and uneven-aged (group cut, single-tree selection) timber management techniques with natural ice-storm damage and unmanipulated reference forest sites on red-backed salamanders. We used cover boards and litter searches to survey for salamanders in northern hardwood forests in New Hampshire, USA. We estimated abundance while accounting for detection probability using the Dail–Madsen open population model. We found significant reduction in salamander abundance in recent group cuts, patch cuts, and clearcuts compared to reference forest sites, and significant but less effect of single-tree selection and ice-storm damage. Our results contribute to the evidence of detrimental effects of even-aged harvests on salamander abundance, but in contrast to most previous research, we also found lower abundance in sites following uneven-aged harvest practices when we accounted for detection probability. To more accurately reflect the total effect of harvests on salamanders, we also employed a parametric, nonlinear hierarchical model to estimate edge effects while accounting for imperfect detection. We found that group cut, patch cut, and clearcut logging reduced salamander abundance 34m into the surrounding forest. These edge effects can greatly expand the total area affected by logging, especially in the northeastern US where cuts tend to be relatively small. This novel method for estimating edge effects will allow managers to directly calculate the total effects on populations for various size and shape harvesting plans.

A nonlinear negative stiffness metamaterial unit cell and small-on-large multiscale material model

A persistent challenge in the design of composite materials is the ability to fabricate materials that simultaneously display high stiffness and high loss factors for the creation of structural elements capable of passively suppressing vibro-acoustic energy. Relevant recent research has shown that it is possible to produce composite materials whose macroscopic mechanical stiffness and loss properties surpass those of conventional composites through the addition of trace amounts of materials displaying negative stiffness (NS) induced by phase transformation [R. S. Lakes et al., Nature 410, 565-567 (2001)]. The present work investigates the ability to elicit NS behavior without employing physical phenomena such as inherent nonlinear material behavior (e.g., phase change or plastic deformation) or dynamic effects, but rather the controlled buckling of small-scale structural elements, metamaterials, embedded in a continuous viscoelastic matrix. To illustrate the effect of these buckled elements, a nonlinear hierarchical multiscale material model is derived, which estimates the macroscopic stiffness and loss of a composite material containing pre-strained microscale structured inclusions. The multiscale model consists of two scale transition models, the first being an energy-based nonlinear finite element (FE) method to determine the tangent modulus of the metamaterial unit cell, and the other a classical analytical micromechanical model to determine the effective stiffness and loss tensors of a heterogeneous material for small perturbations from the local strain state of the unit cells. The FE method enables the estimation of an effective nonlinear anisotropic stiffness tensor of a buckled microstructure that produces NS and is sufficiently general to consider geometries different from those given in this work.

Examining a Home Environmental Strategy to Reduce Availability of Legal Products That Can Be Misused by Youth

This article presents results from a study of a home environmental strategy (HES) designed to reduce availability of harmful legal products (HLPs) in the home that can be used by youth to get high. HLPs include inhalants, prescription and nonprescription drugs, and household products that can be ingested to get high. Availability is one of the most consistent predictors of substance use among youth. Parents of 5th- to 7th-grade students in four Alaskan communities participated in telephone interviews as part of a larger study of a multicomponent Community Prevention Model (CPM) that included a HES. The strategy was designed to encourage parents to reduce availability of HLPs by removing them from the home, and by locking up and monitoring the supplies of HLPs in the home. Data from 402 parents at Wave 1 and 371 parents at Wave 2 were analyzed using Hierarchical Non-Linear Modeling (HNLM). Results show there was a significant decrease in HLPs in the home from Wave 1 to Wave 2, mostly inhalants and prescription and nonprescription drugs. Parents also reported a significant increase in locking up prescription and nonprescription drugs in the home. Parents’ direct exposure to the HES was marginally associated with the change over time in HLP availability in the home. Indirect exposure through others and media was not associated with this change. Study lessons learned and conclusions are highlighted.

Prospects of implant with locking plate in fixation of subtrochanteric fracture: experimental demonstration of its potential benefits on synthetic femur model with supportive hierarchical nonlinear hyperelastic finite element analysis

BackgroundEffective fixation of fracture requires careful selection of a suitable implant to provide stability and durability. Implant with a feature of locking plate (LP) has been used widely for treating distal fractures in femur because of its favourable clinical outcome, but its potential in fixing proximal fractures in the subtrochancteric region has yet to be explored. Therefore, this comparative study was undertaken to demonstrate the merits of the LP implant in treating the subtrochancteric fracture by comparing its performance limits against those obtained with the more traditional implants; angle blade plate (ABP) and dynamic condylar screw plate (DCSP).Materials and MethodsNine standard composite femurs were acquired, divided into three groups and fixed with LP (n = 3), ABP (n = 3) and DCSP (n = 3). The fracture was modeled by a 20 mm gap created at the subtrochanteric region to experimentally study the biomechanical response of each implant under both static and dynamic axial loading paradigms. To confirm the experimental findings and to understand the critical interactions at the boundaries, the synthetic femur/implant systems were numerically analyzed by constructing hierarchical finite element models with nonlinear hyperelastic properties. The predictions from the analyses were then compared against the experimental measurements to demonstrate the validity of each numeric model, and to characterize the internal load distribution in the femur and load bearing properties of each implant.ResultsThe average measurements indicated that the constructs with ABP, DCPS and LP respectively had overall stiffness values of 70.9, 110.2 and 131.4 N/mm, and exhibited reversible deformations of 12.4, 4.9 and 4.1 mm when the applied dynamic load was 400 N and plastic deformations of 11.3, 2.4 and 1.4 mm when the load was 1000 N. The corresponding peak cyclic loads to failure were 1100, 1167 and 1600 N. The errors between the displacements measured experimentally or predicted by the nonlinear hierarchical hyperelastic model were less than 18 %. In the implanted femur heads, the principal stresses were spatially heterogeneous for ABP and DCSP but more homogenous for LP, meaning LP had lower stress concentrations.ConclusionWhen fixed with the LP implant, the synthetic femur model of the subtrochancteric fracture consistently exceeds in the key biomechanical measures of stability and durability. These capabilities suggest increased resistance to fatigue and failure, which are highly desirable features expected of functional implants and hence make the LP implant potentially a viable alternative to the conventional ABP or DCSP in the treatment of subtrochancteric femur fractures for the betterment of clinical outcome.

The Influence of Local Food Environments on Adolescents’ Food Purchasing Behaviors

This study examined the relationship between the neighborhood food environment and the food purchasing behaviors among adolescents. Grade 7 and 8 students (n = 810) at 21 elementary schools in London, Ontario, Canada completed a questionnaire assessing their food purchasing behaviors. Parents of participants also completed a brief questionnaire providing residential address and demographic information. A Geographic Information System (GIS) was used to assess students’ home and school neighborhood food environment and land use characteristics. Logistic regression analysis was conducted to assess the influence of the home neighborhood food environment on students’ food purchasing behaviors, while two-level Hierarchical Non-Linear Regression Models were used to examine the effects of school neighborhood food environment factors on students’ food purchasing behaviors. The study showed that approximately 65% of participants reported self-purchasing foods from fast-food outlets or convenience stores. Close proximity (i.e., less than 1 km) to the nearest fast-food outlet or convenience store in the home neighborhood increased the likelihood of food purchasing from these food establishments at least once per week by adolescents (p < 0.05). High fast-food outlet density in both home and school neighborhoods was associated with increased fast-food purchasing by adolescents (i.e., at least once per week; p < 0.05). In conclusion, macro-level regulations and policies are required to amend the health-detracting neighborhood food environment surrounding children and youth’s home and school.

Living on Three Time Scales: The Dynamics of Plasma Cell and Antibody Populations Illustrated for Hepatitis A Virus

Understanding the mechanisms involved in long-term persistence of humoral immunity after natural infection or vaccination is challenging and crucial for further research in immunology, vaccine development as well as health policy. Long-lived plasma cells, which have recently been shown to reside in survival niches in the bone marrow, are instrumental in the process of immunity induction and persistence. We developed a mathematical model, assuming two antibody-secreting cell subpopulations (short- and long-lived plasma cells), to analyze the antibody kinetics after HAV-vaccination using data from two long-term follow-up studies. Model parameters were estimated through a hierarchical nonlinear mixed-effects model analysis. Long-term individual predictions were derived from the individual empirical parameters and were used to estimate the mean time to immunity waning. We show that three life spans are essential to explain the observed antibody kinetics: that of the antibodies (around one month), the short-lived plasma cells (several months) and the long-lived plasma cells (decades). Although our model is a simplified representation of the actual mechanisms that govern individual immune responses, the level of agreement between long-term individual predictions and observed kinetics is reassuringly close. The quantitative assessment of the time scales over which plasma cells and antibodies live and interact provides a basis for further quantitative research on immunology, with direct consequences for understanding the epidemiology of infectious diseases, and for timing serum sampling in clinical trials of vaccines.

CYP2A6 genetic variation and dexmedetomidine disposition

There is a large interindividual variability in dexmedetomidine dose requirements for sedation of patients in intensive care units (ICU). Cytochrome P450 2A6 (CYP2A6) mediates an important route of dexmedetomidine metabolism, and genetic variation in CYP2A6 affects the clearance of other substrate drugs. We examined whether CYP2A6 genotypes affect dexmedetomidine disposition. In 43 critically ill ICU patients receiving dexmedetomidine infusions adjusted to achieve the desired level of sedation, we determined a median of five plasma dexmedetomidine concentrations each. Forty subjects were genotyped for five common CYP2A6 alleles and grouped into normal (n = 33), intermediate (n = 5), and slow metabolizers (n = 2). Using a Bayesian hierarchical nonlinear mixture model, estimated dexmedetomidine clearance was 49.1L/h (posterior mean; 95% credible interval 41.4-57.6L/h). There were no significant differences in dexmedetomidine clearance among normal, intermediate, and slow CYP2A6 metabolizer groups. Genetic variation in CYP2A6 does not appear to be an important determinant of dexmedetomidine clearance in ICU patients.

A Bayesian Non-Linear Model for Forecasting Insurance Loss Payments

SummaryWe propose a Bayesian non-linear hierarchical model that addresses some of the major challenges that non-life insurance companies face when forecasting the outstanding claim amounts for which they will ultimately be liable. This approach is distinctive in several ways. First, data from individual companies are treated as repeated measurements of various cohorts of claims, thus respecting the correlation between successive observations. Second, non-linear growth curves are used to model the loss development process in a way that is intuitively appealing and facilitates prediction and extrapolation beyond the range of the available data. Third, a hierarchical structure is employed to reflect the natural variation of major parameters between the claim cohorts, accounting for their heterogeneity. This approach enables us to carry out inference at the level of industry, company and/or accident year, based on the full posterior distribution of all quantities of interest. In addition, prior experience and expert opinion can be incorporated in the analyses through judgementally selected prior probability distributions. The ability of the Bayesian framework to carry out simultaneous inference based on the joint posterior is of great importance for insurance solvency monitoring and industry decision making.