Estimates Of Model Parameters Research Articles

A Bayesian hybrid method for the analysis of generalized linear models with missing-not-at-random covariates

Missing data handling is one of the main problems in modelling, particularly if the missingness is of type missing-not-at-random (MNAR) where missingness occurs due to the actual value of the observation. The focus of the current article is generalized linear modelling of fully observed binary response variables depending on at least one MNAR covariate. For the traditional analysis of such models, an individual model for the probability of missingness is assumed and incorporated in the model framework. However, this probability model is untestable, as the missingness of MNAR data depend on their actual values that would have been observed otherwise. In this article, we consider creating a model space that consist of all possible and plausible models for probability of missingness and develop a hybrid method in which a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is combined with Bayesian Model Averaging (BMA). RJMCMC is adopted to obtain posterior estimates of model parameters as well as probability of each model in the model space. BMA is used to synthesize coefficient estimates from all models in the model space while accounting for model uncertainties. Through a validation study with a simulated data set and a real data application, the performance of the proposed methodology is found to be satisfactory in accuracy and efficiency of estimates.

Reliability inference for dual constant-stress accelerated life test with exponential distribution and progressively Type-II censoring

Accelerated life test provides a feasible and effective way to rapidly derive lifetime information by exposing products to higher-than-normal operating conditions. However, most of the previous research on accelerated life test has focused on the application of a single stress factor and a traditional censoring scheme. This article considers the reliability inference for a dual constant-stress accelerated life test model with exponential distribution and progressively Type-II censoring. Point estimates for model parameters are provided using maximum likelihood estimation and the weighted least squares method based on random variable transformation. In addition, we construct asymptotic confidence intervals, approximate confidence intervals, and bootstrap confidence intervals for the parameters of interest. Finally, extensive simulation studies and an illustrative example are presented to investigate the performance of the proposed methods.

A New Multimodal Modification of the Skew Family of Distributions: Properties and Applications to Medical and Environmental Data

The skew distribution has the characteristic of appropriately modeling asymmetric unimodal data. However, in practice, there are several cases in which the data present more than one mode. In the literature, it is possible to find a large number of authors who have studied extensions based on the skew distribution to model this type of data. In this article, a new family is introduced, consisting of a multimodal modification to the family of skew distributions. Using the methodology of the weighted version of a function, we perform the product of the density function of a family of skew distributions with a polynomial of degree 4, thus obtaining a more flexible model that allows modeling data sets, whose distribution contains at most three modes. The density function, some properties, moments, skewness coefficients, and kurtosis of this new family are presented. This study focuses on the particular cases of skew-normal and Laplace distributions, although it can be applied to any other distribution. A simulation study was carried out, to study the behavior of the model parameter estimates. Illustrations with real data, referring to medicine and environmental data, show the practical performance of the proposed model in the two particular cases presented.

Creating cell-specific computational models of stem cell-derived cardiomyocytes using optical experiments.

Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) have gained traction as a powerful model in cardiac disease and therapeutics research, since iPSCs are self-renewing and can be derived from healthy and diseased patients without invasive surgery. However, current iPSC-CM differentiation methods produce cardiomyocytes with immature, fetal-like electrophysiological phenotypes, and the variety of maturation protocols in the literature results in phenotypic differences between labs. Heterogeneity of iPSC donor genetic backgrounds contributes to additional phenotypic variability. Several mathematical models of iPSC-CM electrophysiology have been developed to help to predict cell responses, but these models individually do not capture the phenotypic variability observed in iPSC-CMs. Here, we tackle these limitations by developing a computational pipeline to calibrate cell preparation-specific iPSC-CM electrophysiological parameters. We used the genetic algorithm (GA), a heuristic parameter calibration method, to tune ion channel parameters in a mathematical model of iPSC-CM physiology. To systematically optimize an experimental protocol that generates sufficient data for parameter calibration, we created in silico datasets by simulating various protocols applied to a population of models with known conductance variations, and then fitted parameters to those datasets. We found that calibrating to voltage and calcium transient data under 3 varied experimental conditions, including electrical pacing combined with ion channel blockade and changing buffer ion concentrations, improved model parameter estimates and model predictions of unseen channel block responses. This observation also held when the fitted data were normalized, suggesting that normalized fluorescence recordings, which are more accessible and higher throughput than patch clamp recordings, could sufficiently inform conductance parameters. Therefore, this computational pipeline can be applied to different iPSC-CM preparations to determine cell line-specific ion channel properties and understand the mechanisms behind variability in perturbation responses.

Statistical analysis of multivariate binary time series based on a neural network model

This article is devoted to the statistical analysis of multivariate binary time series. For solving this problem a parsimonious neural network model of Markov’s ergodic chain of order s was determined. Consistent statistical estimators for model parameters and estimation algorithms of parameters and forecasting algorithms of future states of time series were developed. The results of computer experiments on simulated and real data are presented.

Determinants influencing alcohol-related two-vehicle crash severity: A multivariate Bayesian hierarchical random parameters correlated outcomes logit model

Alcohol-related driving remains a significant concern due to its profound association with the likelihood of traffic crashes and the severity of resulting injuries, especially between two vehicles. To investigate the determinants influencing the alcohol-related two-vehicle crash severity, a foundational framework employed was a multinomial logit model. Meanwhile, by incorporating random intercept from individual case and vehicle levels to accommodate unobserved heterogeneity, and covariance matrices to underscore correlated outcomes, a multivariate hierarchical random parameters correlated outcomes logit model was proposed. Additionally, to further explore the potential temporal instability of explanatory variables, a random slope from a per-year indicator was introduced into the model. Crash data from the US Statewide Integrated Traffic Records System (SWITRS) database spanning from January 1, 2016, to December 31, 2021, was used. Three crash injury severity categories were examined, encompassing severe injury, minor injury, and no injury, with characteristics related to the driver, vehicle, road, environment, crash, and time serving as explanatory variables. The model results highlighted significant heterogeneity, with each case and vehicle accounting for 56.9% of the total variance for minor injuries and 50.8% for severe injuries. Furthermore, a significant negative correlation was explicitly exhibited between minor injury and severe injury outcomes at the case level. In terms of potential temporal instability, we provided per-year (2016–2019) parameter estimates and identified significant instability for indicators such as non-intersection, broadside and head-on collisions, cloudy weather conditions, and drivers who had been drinking but were not under the influence. Considering the impact of the COVID-19 pandemic, we divided the accident time into pre-COVID and during-COVID periods, modeling parameter estimates for both periods. This analysis revealed significant instability in several factors influenced by the pandemic. Additionally, noteworthy disparities in the estimated results of explanatory variables emerged in comparison to those general two-vehicle crashes or alcohol-related crashes, providing valuable insights. For instance, drivers who had been drinking but were not under the influence were less likely to sustain severe injuries, but the probability of minor injuries increased. These findings underscore the significance of thorough investigations into the determinants of injury severity in alcohol-impaired two-vehicle crash severity, along with the temporal instability of such factors. They hold important implications for effective traffic safety management and the formulation of prohibitive countermeasures.

Addressing Autocorrelation, Multicollinearity, and Heavy-Tail Errors in the Linear Regression Model

The most popular estimator for estimating parameters of linear regression models is the Ordinary Least Squares (OLS) Estimator. The OLS is considered the best linear unbiased estimator when certain assumptions are not violated. However, when autocorrelation, multicollinearity, and heavy-tail error are jointly present in the dataset, the OLS estimator is inefficient and imprecise. In this paper, we developed an estimator of linear regression model parameters that jointly handle multicollinearity, autocorrelation, and heavy tail errors. The new estimator, LADHLKL, was derived by combining the Hildreth-Lu (HL), the Kibria Lukman (KL), and the Least Absolute Deviation (LAD) estimators. The LADHLKL poses both the characteristics of the LAD, HL, and KL estimators which makes it resistant to both problems. We examined the properties of the proposed estimator and compared its performance with other existing estimators in terms of mean square error. An application to real-life data and simulation study revealed that the proposed estimator dominates other estimators in all the considered conditions in terms of mean square error.

Likelihood-based inference for semi-parametric transformation cure models with interval censored data

A simple yet effective way of modeling survival data with cure fraction is by considering Box-Cox transformation cure model (BCTM) that unifies mixture and promotion time cure models. In this article, we numerically study the statistical properties of the BCTM when applied to interval censored data. Time-to-events associated with susceptible subjects are modeled through proportional hazards structure that allows for non-homogeneity across subjects, where the baseline hazard function is estimated by distribution-free piecewise linear function with varied degrees of non-parametricity. Due to missing cured statuses for right censored subjects, maximum likelihood estimates of model parameters are obtained by developing an expectation-maximization (EM) algorithm. Under the EM framework, the conditional expectation of the complete data log-likelihood function is maximized by considering all parameters (including the Box-Cox transformation parameter α) simultaneously, in contrast to conventional profile-likelihood technique of estimating α. The robustness and accuracy of the model and estimation method are established through a detailed simulation study under various parameter settings, and an analysis of real-life data obtained from a smoking cessation study.

General quasi-equilibrium multivalent binding model to study diverse and complex drug-receptor interactions of biologics.

Pharmacokinetics and pharmacodynamics of many biologics are influenced by their complex binding to biological receptors. Biologics consist of diverse groups of molecules with different binding kinetics to its receptors including IgG with simple one-to-one drug receptor bindings, bispecific antibody (BsAb) that binds to two different receptors, and antibodies that can bind to six or more identical receptors. As the binding process is typically much faster than elimination (or internalization) and distribution processes, quasi-equilibrium (QE) binding models are commonly used to describe drug-receptor binding kinetics of biologics. However, no general QE modeling framework is available to describe complex binding kinetics for diverse classes of biologics. In this paper, we describe novel approaches of using differential algebraic equations (DAE) to solve three QE multivalent drug-receptor binding (QEMB) models. The first example describes the binding kinetics of three-body equilibria of BsAb that binds to 2 different receptors for trimer formation. The second example models an engineered IgG variant (Multabody) that can bind to 24 identical target receptors. The third example describes an IgG with modified neonatal Fc receptor (FcRn) binding affinity that competes for the same FcRn receptor as endogenous IgG. The model parameter estimates were obtained by fitting the model to all data simultaneously. The models allowed us to study potential roles of cooperative binding on bell-shaped drug exposure-response relationships of BsAb, and concentration-depended distribution of different drug-receptor complexes for Multabody. This DAE-based QEMB model platform can serve as an important tool to better understand complex binding kinetics of diverse classes of biologics.

Predicting the incidence of rifampicin resistant tuberculosis in Yunnan, China: a seasonal time series analysis based on routine surveillance data

BackgroundRifampicin resistant tuberculosis (RR-TB) poses a growing threat to individuals and communities. This study utilized a seasonal autoregressive integrated moving average (SARIMA) model to quantitatively predict the monthly incidence of RR-TB in Yunnan Province which could guide government health administration departments and the centers for disease control and prevention (CDC) in preventing and controlling the RR-TB epidemic.MethodsThe study utilized routine surveillance reporting data from the infectious Disease Network Surveillance and Reporting System. Monthly incidence rates of RR-TB were collected from January 2019 to December 2022. A time series SARIMA model was used to predict the number of monthly RR-TB cases in Yunnan Province in 2023, and the model was validated using time series plots, seasonal and non-seasonal differencing, autocorrelation and partial autocorrelation analysis, and white noise tests.ResultsFrom 2019 to 2022, the incidence of RR-TB decreases as the incidence of all TB decreases (P < 0.05). There was no significant change in the proportion of RR-TB among all TB cases, which remained within 2.5% (P>0.05). The time series decomposition shows that it presented obvious seasonality, periodicity and randomness after being decomposed. Time series analysis was performed on the original series after 1 non-seasonal difference and 1 seasonal difference, the ADF test showed P < 0.05. According to ACF and PACF, the SARIMA (1, 1, 1) (1, 1, 0)12 model was chosen and statistically significant model parameter estimates (P < 0.05). The predicted seasonal trend of RR-TB incidence in 2019 to 2023 was similar to the actual data. The percentage accuracy in the prediction excesses 80% in 2019 to 2022 and is all within 95% CI. However there was a certain gap between the actual incidence and the predicted value in 2023, and the acutual incidence had increased by 12.4% compared to 2022. The percentage of accuracy in the prediction was only 70% in 2023.ConclusionsWe found the incidence of RR-TB was based on that of all TB in Yunnan. The SARIMA model successfully predicted the seasonal incidence trend of RR-TB in Yunnan Province in 2019 to 2023, but the prediction precision could be influenced by factors such as new infectious disease outbreaks or pandemics, social issues, environmental challenges or other unknown risks. Hence CDCs should pay special attention to the post epidemic effects of new infectious disease outbreaks or pandemics, carry out monitoring and early warning, and better optimize disease prediction models.

QPRF: A system to accelerate population receptive field decoding.

Patterns of BOLD response can be decoded using the population receptive field (PRF) model to reveal how visual input is represented on the cortex (Dumoulin and Wandell, 2008). The time cost of evaluating the PRF model is high, often requiring days to decode BOLD signals for a small cohort of subjects. We introduce the qPRF, an efficient method for decoding that reduced the computation time by a factor of 1436 when compared to another widely available PRF decoder (Kay, Winawer, Mezer and Wandell, 2013) on a benchmark of data from the Human Connectome Project (HCP; Van Essen, Smith, Barch, Behrens, Yacoub and Ugurbil, 2013). With a specially designed data structure and an efficient search algorithm, the qPRF optimizes the five PRF model parameters according to a least-squares criterion. To verify the accuracy of the qPRF solutions, we compared them to those provided by Benson, Jamison, Arcaro, Vu, Glasser, Coalson, Van Essen, Yacoub, Ugurbil, Winawer and Kay (2018). Both hemispheres of the 181 subjects in the HCP data set (a total of 10,753,572 vertices, each with a unique BOLD time series of 1800 frames) were decoded by qPRF in 15.2 hours on an ordinary CPU. The absolute difference in reported by Benson et al. and achieved by the qPRF was negligible, with a median of 0.39% ( units being between 0% and 100%). In general, the qPRF yielded a slightly better fitting solution, achieving a greater on 99.7% of vertices. The qPRF may facilitate the development and computation of more elaborate models based on the PRF framework, as well as the exploration of novel clinical applications.

New orders of 2k factorial designs generated by simulated annealing adapted to optimality criteria

Excessive changes in factor levels can lead to a high cost in practice and hinder the conduction of experiments, in addition to adding a higher computational cost and loss of the orthogonality property, resulting in numerical problems in estimating the parameters of a model. The sequential specification of experimental points, seen as treatments in a 2k factorial design, results in a high-order bias in some factors, which is caused by the accumulation of −1 or +1 signals. This study aimed to propose new designs generated by the simulated annealing technique, respecting the main A-optimal and D-optimal optimality criteria as random execution orders that minimize the order bias. This approach allowed the generation of 24 and 25 factorials, which were compared to the designs in standard order. The simulated annealing technique is a viable method to generate optimal designs with the same efficiency as the usual designs to obtain A-optimal and D-optimal designs with new execution orders, which minimize the effect of order bias relative to standard order designs. Regarding efficiency, the generated designs were precise in the variance of model parameter estimates, similar to the original designs.

Abstract We014: Creating Cell-specific Computational Models of Stem Cell-derived Cardiomyocytes Using Optical Experiments

Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) have gained traction as a powerful model in cardiac disease and therapeutics research, since iPSCs are self-renewing and can be derived from healthy and diseased patients without invasive surgery. However, current iPSC-CM differentiation methods produce cardiomyocytes with immature, fetal-like electrophysiological phenotypes, and the variety of maturation protocols in the literature results in phenotypic differences between labs. Heterogeneity of iPSC donor genetic backgrounds contributes to additional phenotypic variability. Several mathematical models of iPSC-CM electrophysiology have been developed to help understand the ionic underpinnings of, and to simulate, various cell responses, but these models individually do not capture the phenotypic variability observed in iPSC-CMs. Here, we tackle these limitations by developing a computational pipeline to calibrate cell preparation-specific iPSC-CM electrophysiological parameters. We used the genetic algorithm (GA), a heuristic parameter calibration method, to tune ion channel parameters in a mathematical model of iPSC-CM physiology. To systematically optimize an experimental protocol that generates sufficient data for parameter calibration, we created simulated datasets by applying various protocols to a population of in silico cells with known conductance variations, and we fitted to those datasets. We found that calibrating models to voltage and calcium transient data under 3 varied experimental conditions, including electrical pacing combined with ion channel blockade and changing buffer ion concentrations, improved model parameter estimates and model predictions of unseen channel block responses. This observation held regardless of whether the fitted data were normalized, suggesting that normalized fluorescence recordings, which are more accessible and higher throughput than patch clamp recordings, could sufficiently inform conductance parameters. Therefore, this computational pipeline can be applied to different iPSC-CM preparations to determine cell line-specific ion channel properties and understand the mechanisms behind variability in perturbation responses.

Evaluating the robustness of parameter estimates in cognitive models: A meta-analytic review of multinomial processing tree models across the multiverse of estimation methods.

Researchers have become increasingly aware that data-analysis decisions affect results. Here, we examine this issue systematically for multinomial processing tree (MPT) models, a popular class of cognitive models for categorical data. Specifically, we examine the robustness of MPT model parameter estimates that arise from two important decisions: the level of data aggregation (complete-pooling, no-pooling, or partial-pooling) and the statistical framework (frequentist or Bayesian). These decisions span a multiverse of estimation methods. We synthesized the data from 13,956 participants (164 published data sets) with a meta-analytic strategy and analyzed the magnitude of divergence between estimation methods for the parameters of nine popular MPT models in psychology (e.g., process-dissociation, source monitoring). We further examined moderators as potential sources of divergence. We found that the absolute divergence between estimation methods was small on average (<.04; with MPT parameters ranging between 0 and 1); in some cases, however, divergence amounted to nearly the maximum possible range (.97). Divergence was partly explained by few moderators (e.g., the specific MPT model parameter, uncertainty in parameter estimation), but not by other plausible candidate moderators (e.g., parameter trade-offs, parameter correlations) or their interactions. Partial-pooling methods showed the smallest divergence within and across levels of pooling and thus seem to be an appropriate default method. Using MPT models as an example, we show how transparency and robustness can be increased in the field of cognitive modeling. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Antibacterial action of penicillin against Mycobacterium avium complex.

β-lactam antibiotics are promising treatments for Mycobacterium avium complex (MAC) lung disease. We hypothesized that benzylpenicillin has efficacy against MAC. Benzylpenicillin lung concentration-time profiles of seven doses in three dosing schedules were administered for 28 days using the hollow fiber system model of intracellular MAC (HFS-MAC). Data were analyzed using the inhibitory sigmoid maximal effect (Emax) model for each sampling day, while two ordinary differential equations (ODEs) were used for the wild-type and penicillin-resistant mutants. Benzylpenicillin killed >2.1 log10 colony-forming unit (CFU)/mL below Day 0, better than azithromycin, ethambutol, and rifabutin. Efficacy was terminated by acquired resistance. Sigmoid Emax parameter estimates significantly differed between sampling days and were a poor fit. However, ODE model parameter estimates vs. exposure were a better fit. The exposure mediating Emax was 84.6% (95% CI 76.91-82.98) of time concentration exceeded the minimum inhibitory concentration (MIC). In Monte Carlo experiments, 24 million international units of benzylpenicillin continuous infusion achieved the target exposure in lungs of >90% of 10,000 subjects until an MIC of 64 mg/L, designated the susceptibility breakpoint. Benzylpenicillin demonstrated a better bactericidal effect against MAC than guideline-recommended drugs before the development of resistance. Its role in combination therapy with other drugs with better efficacy than guideline-recommended drugs should be explored.

Modeling Glucose, Insulin, C-Peptide, and Lactate Interplay in Adolescents During an Oral Glucose Tolerance Test.

Lactate is not considered just a "waste product" of anaerobic glycolysis anymore. It has been proved to play a key role in several metabolic diseases, such as in the metabolic dysfunction-associated steatotic liver disease, obesity, and diabetes. The capability of simulating glucose-insulin-lactate interaction would be useful to design and test drugs targeting lactate metabolism in such pathological conditions. Minimal models are available, which describe and quantify glucose-lactate interaction but models to simulate postprandial glucose-insulin-C-peptide-lactate time courses are missing. The aim of this study is to fill this gap. Starting from the Padova Type 2 Diabetes Simulator (T2DS), we first added a description of glucose-lactate kinetics and then created a population of 100 in silico subjects to match glucose-insulin-C-peptide-lactate data of 44 adolescents with/without obesity who underwent a standard oral glucose tolerance test (OGTT) of 75 g. The developed model accurately predicts all molecules time courses, guaranteeing precise model parameter estimates (percent coefficient of variation [CV%] median [25th-75th percentile] = 19 [9-29]%). The generated in silico population shows good agreement with the clinical data in terms of area under the curve (AUC) (P = .6, .6, .9, .6 for glucose, insulin, C-peptide, and lactate, respectively) and parameter distributions (P > .1). We have developed a simulator to describe glucose, insulin, C-peptide, and lactate kinetics during an OGTT, which captures the behavior of a real population of adolescents with/without obesity both in terms of average and intersubject variability. Such simulator can be used to investigate the pharmacodynamics of drugs targeting lactate metabolic pathway in various pathological conditions.

Achieving Occam's razor: Deep learning for optimal model reduction.

All fields of science depend on mathematical models. Occam's razor refers to the principle that good models should exclude parameters beyond those minimally required to describe the systems they represent. This is because redundancy can lead to incorrect estimates of model parameters from data, and thus inaccurate or ambiguous conclusions. Here, we show how deep learning can be powerfully leveraged to apply Occam's razor to model parameters. Our method, FixFit, uses a feedforward deep neural network with a bottleneck layer to characterize and predict the behavior of a given model from its input parameters. FixFit has three major benefits. First, it provides a metric to quantify the original model's degree of complexity. Second, it allows for the unique fitting of data. Third, it provides an unbiased way to discriminate between experimental hypotheses that add value versus those that do not. In three use cases, we demonstrate the broad applicability of this method across scientific domains. To validate the method using a known system, we apply FixFit to recover known composite parameters for the Kepler orbit model and a dynamic model of blood glucose regulation. In the latter, we demonstrate the ability to fit the latent parameters to real data. To illustrate how the method can be applied to less well-established fields, we use it to identify parameters for a multi-scale brain model and reduce the search space for viable candidate mechanisms.

Different Statistical Inference Algorithms for the New Pareto Distribution Based on Type-II Progressively Censored Competing Risk Data with Applications

In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples.

Modeling and Optimal Control of Infectious Diseases

We propose a stochastic model of infectious disease transmission that is more realistic than those found in the literature. The model is based on jump-diffusion processes. However, it is defined in such a way that the number of people susceptible to be infected decreases over time, which is the case for a population of fixed size. Next, we consider the problem of finding the optimal control of the proposed model. The dynamic programming equation satisfied by the value function is derived. Estimators of the various model parameters are obtained.

A hierarchical Bayesian approach for parameter identification in structural deterioration models using probabilistic surrogate models

Most structural systems currently in operation are subjected to potentially multiple deterioration processes, for which different models exist to describe their evolution in time. The quantities of interest (QoIs) involved in them are often directly unobservable. However, advances in Structural Health Monitoring (SHM) have enabled gathering structural response data which can be used to indirectly make inferences on unobservable (state) quantities through Bayesian inference. Obtaining updated estimates of deterioration model parameters, given observed data, enables them to be used to predict future health states of interest for the structure, which constitutes a core tenet of condition-based maintenance (CBM). Key to obtaining robust parameter estimates is accounting for different uncertain quantities involved in the model that transforms unobservable quantities to observable ones, which in a Bayesian context is achieved through the likelihood function. This work presents an offline, flexible hierarchical framework to tackle this problem that employs probabilistic reduced order models (ROMs) in the construction of the likelihood function, that enable marginalizing out these uncertain quantities. The approximate likelihood function is then used within a typical Markov Chain Monte Carlo (MCMC) setting for parameter estimation. The framework is demonstrated in applications related to deterioration processes common to ship structures.