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Pulmonary hypertension is a cardiovascular disorder manifested by elevated mean arterial blood pressure (>20 mmHg) together with vessel wall stiffening and thickening due to alterations in collagen, elastin, and smooth muscle cells. Hypoxia-induced (type 3) pulmonary hypertension can be studied in animals exposed to a low oxygen environment for prolonged time periods leading to biomechanical alterations in vessel wall structure. This study introduces a novel approach to formulating a reduced order nonlinear elastic structural wall model for a large pulmonary artery. The model relating blood pressure and area is calibrated using ex vivo measurements of vessel diameter and wall thickness changes, under controlled pressure conditions, in left pulmonary arteries isolated from control and hypertensive mice. A two-layer, hyperelastic, and anisotropic model incorporating residual stresses is formulated using the Holzapfel-Gasser-Ogden model. Complex relations predicting vessel area and wall thickness with increasing blood pressure are derived and calibrated using the data. Sensitivity analysis, parameter estimation, subset selection, and physical plausibility arguments are used to systematically reduce the 16-parameter model to one in which a much smaller subset of identifiable parameters is estimated via solution of an inverse problem. Our final reduced one layer model includes a single set of three elastic moduli. Estimated ranges of these parameters demonstrate that nonlinear stiffening is dominated by elastin in the control animals and by collagen in the hypertensive animals. The pressure-area relation developed in this novel manner has potential impact on one-dimensional fluids network models of vessel wall remodeling in the presence of cardiovascular disease.

In addition to the usual slope and location parameters included in a regular two‐parameter logistic model (2PL), the logistic positive exponent (LPE) model incorporates an item parameter that leads to asymmetric item characteristic curves, which have recently been shown to be useful in some contexts. Although this model has been used in some empirical studies, an identifiability analysis (i.e., checking the (un)identified status of a model and searching for identifiablity restrictions to make an unidentified model identified) has not yet been established. In this paper, we formalize the unidentified status of a large class of fixed‐effects item response theory models that includes the LPE model and related versions of it. In addition, we conduct an identifiability analysis of a particular version of the LPE model that is based on the fixed‐effects one‐parameter logistic model (1PL), which we call the 1PL‐LPE model. The main result indicates that the 1PL‐LPE model is not identifiable. Ways to make the 1PL‐LPE useful in practice and how different strategies for identifiability analyses may affect other versions of the model are also discussed. [ABSTRACT FROM AUTHOR]

In behavioral and social research, questionnaires are an important assessment tool, through which individuals can be categorized according to how they classify themselves in respect to a personal trait. One example is the Major Depression Inventory (MDI), which is widely used for the assessment of depression. It can also be used as a depression severity scale, with scores ranging from 0 to 50 constructed considering the same weight for each item in the MDI. However, the dependence among the items of the questionnaire suggests that a score with better properties could be obtained through factor models, which besides allowing to reduce the dimensionality of multivariate data, provides the estimation of common factors and factor loadings that often have an interesting theoretical interpretation. Additionally, auxiliary information could be available and, the effect of these variables in the latent factor could be estimated and provide interesting results. Thus, the main aim of this paper is to propose a factor model for ordered categorical data which incorporates auxiliary variables to explain the latent factors. The proposed model provides an alternative score to MDI based on the estimated latent factors that takes the uncertainty in the data and auxiliary information into account. [ABSTRACT FROM AUTHOR]

In practice, the failure type for some subjects may be missing or uncertain in competing risks data. Analysis of such uncertain failure type in current status data with two competing risks suffers from issues of model identifiability and requires some model assumptions to deal with that (Koley and Dewanji. Journal of Applied Statistics 49(7), (2022)). In this work, we attempt to alleviate this identifiability problem using some additional information and without any such model assumption. In particular, we consider additional information in the form of some prior knowledge on the missing probabilities. Next, we briefly discuss another type of additional information from a validation sample which ascertains failure type. We consider parametric estimation of the model parameters and non-parametric estimation of the sub-distribution functions. We investigate the associated large sample properties theoretically and the finite sample properties through simulation. We also consider analysis of a real data set for the purpose of illustration. [ABSTRACT FROM AUTHOR]

This paper discusses regression analysis of current status data with dependent censoring, a problem that often occurs in many areas such as cross-sectional studies, epidemiological investigations and tumorigenicity experiments. Copula model-based methods are commonly employed to tackle this issue. However, these methods often face challenges in terms of model and parameter identification. The primary aim of this paper is to propose a copula-based analysis for dependent current status data, where the association parameter is left unspecified. Our method is based on a general class of semiparametric linear transformation models and parametric copulas. We demonstrate that the proposed semiparametric model is identifiable under certain regularity conditions from the distribution of the observed data. For inference, we develop a sieve maximum likelihood estimation method, using Bernstein polynomials to approximate the nonparametric functions involved. The asymptotic consistency and normality of the proposed estimators are established. Finally, to demonstrate the effectiveness and practical applicability of our method, we conduct an extensive simulation study and apply the proposed method to a real data example. [ABSTRACT FROM AUTHOR]

When hybridization or other forms of lateral gene transfer have occurred, evolutionary relationships of species are better represented by phylogenetic networks than by trees. While inference of such networks remains challenging, several recently proposed methods are based on quartet concordance factors—the probabilities that a tree relating a gene sampled from the species displays the possible 4-taxon relationships. Building on earlier results, we investigate what level-1 network features are identifiable from concordance factors under the network multispecies coalescent model. We obtain results on both topological features of the network, and numerical parameters, uncovering a number of failures of identifiability related to 3-cycles in the network. Addressing these identifiability issues is essential for designing statistically consistent inference methods. [ABSTRACT FROM AUTHOR]

In this paper we propose a new parameter estimator that ensures global exponential convergence of linear regression models requiring only the necessary assumption of identifiability of the regression equation, which we show is equivalent to interval excitation of the regressor vector. An extension to – separable and monotonic – nonlinear parameterisations is also given. The estimators are shown to be robust to additive measurement noise and – not necessarily slow-parameter variations. Moreover, a version of the estimator that is robust with respect to sinusoidal disturbances with unknown internal model is given. Simulation results that illustrate the performance of the estimator compared with other algorithms are given. [ABSTRACT FROM AUTHOR]

Nonparametric item response models provide a flexible framework in psychological and educational measurements. Douglas (Psychometrika 66(4):531–540, 2001) established asymptotic identifiability for a class of models with nonparametric response functions for long assessments. Nevertheless, the model class examined in Douglas (2001) excludes several popular parametric item response models. This limitation can hinder the applications in which nonparametric and parametric models are compared, such as evaluating model goodness-of-fit. To address this issue, We consider an extended nonparametric model class that encompasses most parametric models and establish asymptotic identifiability. The results bridge the parametric and nonparametric item response models and provide a solid theoretical foundation for the applications of nonparametric item response models for assessments with many items. [ABSTRACT FROM AUTHOR]

Diagnostic classification models (DCMs) have seen wide applications in educational and psychological measurement, especially in formative assessment. DCMs in the presence of testlets have been studied in recent literature. A key ingredient in the statistical modeling and analysis of testlet-based DCMs is the superposition of two latent structures, the attribute profile and the testlet effect. This paper extends the standard testlet DINA (T-DINA) model to accommodate the potential correlation between the two latent structures. Model identifiability is studied and a set of sufficient conditions are proposed. As a byproduct, the identifiability of the standard T-DINA is also established. The proposed model is applied to a dataset from the 2015 Programme for International Student Assessment. Comparisons are made with DINA and T-DINA, showing that there is substantial improvement in terms of the goodness of fit. Simulations are conducted to assess the performance of the new method under various settings. [ABSTRACT FROM AUTHOR]

Identifiability of a mathematical model plays a crucial role in the parameterization of the model. In this study, we established the structural identifiability of a susceptible-exposedinfected-recovered (SEIR) model given different combinations of input data and investigated practical identifiability with respect to different observable data, data frequency, and noise distributions. The practical identifiability was explored by both Monte Carlo simulations and a correlation matrix approach. Our results showed that practical identifiability benefits from higher data frequency and data from the peak of an outbreak. The incidence data gave the best practical identifiability results compared to prevalence and cumulative data. In addition, we compared and distinguished the practical identifiability by Monte Carlo simulations and a correlation matrix approach, providing insights into when to use which method for other applications. [ABSTRACT FROM AUTHOR]

Ordinal responses often arise from surveys which require respondents to rate items on a Likert scale. Since most surveys contain more than one question, the data collected are multivariate in nature, and the associations between different survey items are usually of considerable interest. In this paper, we focus on a mixture distribution, called the combination of uniform and binomial (CUB), under which each response is assumed to originate from either the respondent's uncertainty or the actual feeling towards the survey item. We extend the CUB model to the bivariate case for modelling two correlated ordinal data without using copula-based approaches. The proposed model allows the associations between the unobserved uncertainty and feeling components of the variables to be estimated, a distinctive feature compared to previous attempts. This article describes the underlying logic and deals with both theoretical and practical aspects of the proposed model. In particular, we will show that the model is identifiable under a wide range of conditions. Practical inferential aspects such as parameter estimation, standard error calculations and hypothesis tests will be discussed through simulations and a real case study. [ABSTRACT FROM AUTHOR]

The crucial role of heavy-tailed distributions in the analysis of financial and extreme value phenomena is widely acknowledged; however, there is a scarcity of probability distributions to accurately model such data. In the pursuit of analyzing financial data, researchers frequently seek out new and optimal statistical models. With a focus on this specific research domain, we present a groundbreaking model known as the new heavy-tailed exponentiated exponential distribution. The new model’s heavy-tailed behaviors are investigated through visual and mathematical methods. Estimation of the new model parameters is done through maximum likelihood estimators. Moreover, a Monte Carlo simulation study is undertaken to analyze the performance of estimators. In our study, we examine two specific data sets pertaining to the price quotations of Yamaha pianos in the United States to present the new distribution. The first set of data focuses on the prices of Yamaha upright pianos, while the second set highlights the prices of Yamaha Clavinova digital pianos. By conducting four evaluation tests, we evaluate the fitting performance of the NHTE-exponential distribution against the rival distributions.

Let f be a homogeneous polynomial of even degree d. We study the decompositions f = ∑ i = 1 r f i 2 where deg ⁡ f i = d / 2. The minimal number of summands r is called the 2-rank of f , so that the polynomials having 2-rank equal to 1 are exactly the squares. Such decompositions are never unique and they are divided into O (r) -orbits, the problem becomes counting how many different O (r) -orbits of decomposition exist. We say that f is O (r) -identifiable if there is a unique O (r) -orbit. We give sufficient conditions for generic and specific O (r) -identifiability. Moreover, we show the generic O (r) -identifiability of ternary forms. [ABSTRACT FROM AUTHOR]

Consider a situation where one is interested in estimating the density of a survival time that is subject to random right censoring and measurement errors. This happens often in practice, like in public health (pregnancy length), medicine (duration of infection), ecology (duration of forest fire), among others. We assume a classical additive measurement error model with Gaussian noise and unknown error variance and a random right censoring scheme. Under this setup, we develop minimal conditions under which the assumed model is identifiable when no auxiliary variables or validation data are available, and we offer a flexible estimation strategy using Laguerre polynomials for the estimation of the error variance and the density of the survival time. The asymptotic normality of the proposed estimators is established, and the numerical performance of the methodology is investigated on both simulated and real data on gestational age. [ABSTRACT FROM AUTHOR]

Identifiability of a mathematical model plays a crucial role in the parameterization of the model. In this study, we established the structural identifiability of a susceptible-exposed-infected-recovered (SEIR) model given different combinations of input data and investigated practical identifiability with respect to different observable data, data frequency, and noise distributions. The practical identifiability was explored by both Monte Carlo simulations and a correlation matrix approach. Our results showed that practical identifiability benefits from higher data frequency and data from the peak of an outbreak. The incidence data gave the best practical identifiability results compared to prevalence and cumulative data. In addition, we compared and distinguished the practical identifiability by Monte Carlo simulations and a correlation matrix approach, providing insights into when to use which method for other applications.

AbstractWe are interested in the problem of two-sample network hypothesis testing: given two networks with the same set of nodes, we wish to test whether the underlying Bernoulli probability matrices of the two networks are the same or not. We propose Interlacing Balance Measure (IBM) as a new two-sample testing approach. We consider the Degree-Corrected Mixed-Membership (DCMM) model for undirected networks, where we allow severe degree heterogeneity, mixed-memberships, flexible sparsity levels, and weak signals. In such a broad setting, how to find a test that has a tractable limiting null and optimal testing performances is a challenging problem. We show that IBM is such a test: in a broad DCMM setting with only mild regularity conditions, IBM has N(0,1) as the limiting null and achieves the optimal phase transition.While the above is for undirected networks, IBM is a unified approach and is directly implementable for directed networks. For a broad directed-DCMM (extension of DCMM for directed networks) setting, we show that IBM has N(0,1/2) as the limiting null and continues to achieve the optimal phase transition. We have also applied IBM to the Enron email network and a gene co-expression network, with interesting results. [ABSTRACT FROM AUTHOR]

In this article, we propose a new semiparametric hidden Markov model (HMM) for use in the simultaneous hypothesis testing with dependency. The semi- or non-parametric HMM in the literature requires two conditions for its model identifiability, (a) the latent Markov chain (MC) is ergodic and its transition probability is full rank and (b) the observational distributions of different hidden states are disjoint or linearly independent. Unlike the existing models, our semiparametric HMM with two hidden states makes no assumption on the transition probability of the latent MC but assumes that observational distributions are extremal for the set of all stationary distributions of the model. To estimate the model, we propose a modified expectation-maximization algorithm, whose M-step has an additional purification step to make the observational distribution be extremal one. We numerically investigate the performance of the proposed procedure in the estimation of the model and compare it to two recent existing methods in various multiple testing error settings. In addition, we apply our procedure to analyzing two real data examples, the gas chromatography/mass spectrometry experiment to differentiate the origin of herbal medicine and the epidemiologic surveillance of an influenza-like illness. [ABSTRACT FROM AUTHOR]

Estimating the COVID‐19 infection fatality rate, inferring the latent incidence and predicting the future epidemic evolution are critical to public health surveillance, but often challenging due to limited data availability or quality. Recently, a Bayesian framework combining time series deconvolution of deaths with a parametric Susceptible–Infectious–Recovered (SIR) model was proposed by Irons and Raftery, 2021. We assess the parameter identifiability of the model using the profile likelihood approach and simulations, when only the time series of deaths and seroprevalence survey data are available. The robustness of the model to the more complex but also more realistic Susceptible–Exposed–Infectious–Recovered (SEIR)‐based epidemics is evaluated through simulations; the influence of potential biases in the serosurveys on the inference is also investigated. We use a stationary first‐order autoregressive prior to account for the variability of transmission rate over time. The results suggest that the model is relatively robust to SEIR‐based epidemics, especially when the reproductive number is low, given sufficient information from serosurveys or priors. However, the lack of parameter identifiability under limited data availability cannot be neglected. We apply the model to infer the COVID‐19 infections in Ontario and Quebec, Canada during the Omicron era. [ABSTRACT FROM AUTHOR]

This paper considers the practical and ethical issues related to the death of a sperm donor. It looks at whether sperm banks should check whether the donor is alive at the time the spermatozoa is made available. Knowing that the donor has died in combination with the cause of death can provide important medical information but the chance is very small. However, when the information is available, it may help to decide whether to tell previous recipients and/or to block the remaining samples for future use. A second advantage may be that the donor's offspring can be informed that contact will not be possible and that recipients who are planning to order spermatozoa from an identity‐release donor can be told that the donor has died. However, these advantages presume that identifiable equals contactable while there is no strict link between these two conditions. [ABSTRACT FROM AUTHOR]

In competing risks data, in practice, there may be lack of information or uncertainty about the true failure type, termed as 'missing failure type', for some subjects. We consider a general pattern of missing failure type in which we observe, if not the true failure type, a set of possible failure types containing the true one. In this work, we focus on both parametric and non-parametric estimation based on current status data with two competing risks and the above-mentioned missing failure type. Here, the missing probabilities are assumed to be time-dependent, that is, dependent on both failure and monitoring time points, in addition to being dependent on the true failure type. This makes the missing mechanism non-ignorable. We carry out maximum likelihood estimation and obtain the asymptotic properties of the estimators. Simulation studies are conducted to investigate the finite sample properties of the estimators. Finally, the methods are illustrated through a data set on hearing loss. [ABSTRACT FROM AUTHOR]

We address the semiparametric challenge of identifying and estimating generalized additive partial linear models with nonignorable missingness in the response. Identifiability is ensured under instrumental variable assumption that there is an instrumental covariate related to the prospensity but unrelated to the response variable, or the assumption that the conditional score function is linear in the response variable. We propose a new estimating equation for the prospensity by taking expectation of the unobservable part on a linear combination of all covariates rather than the covariates themselves. This estimating equation does not suffer from the typical curse of dimensionality. Then the unknown nonparametric function is approximated by polynomial spline basis functions and we construct estimating equations for mean of response based on the inverse probability weighting. Under some regular conditions, we establish asymptotic normality of the proposed estimators for parametric components and consistency of the estimators of nonparametric functions. Simulation studies demonstrate that the proposed inference procedure performs well in many settings. The proposed method is applied to analyze the household income dataset from the Chinese Household Income Project Survey 2013. [ABSTRACT FROM AUTHOR]

This paper proposes a multivariate form of generalized information criterion (MGIC) for the multivariate response bridge regression (multi-bridge) model. Also, we prove the identifiability of the multi-bridge as a prerequisite for model selection. We introduce the general form of MGIC for regularization parameter selection in the multi-bridge model. We assess the performance of MGIC variants from three viewpoints: consistency of the obtained models, analysis of high-dimensional data, and comparison to other criteria. Based on the numerical study, we reach better performance for MGIC in comparison to other common criteria (cross-validation and GCV) using simulated and real datasets. [ABSTRACT FROM AUTHOR]

AbstractFunctional data analysis (FDA) is an important modern paradigm for handling infinite-dimensional data. An important task in FDA is clustering, which identifies subgroups based on the shapes of measured curves. Considering that derivatives can provide additional useful information about the shapes of functionals, we propose a novel L2 distance between two random functions by incorporating the functions and their derivative information to determine the dissimilarity of curves under a unified scheme for dense observations. The Karhunen–Loève expansion is used to approximate the curves and their derivatives. Cluster membership prediction for each curve intends to minimize the new distances between the observed and predicted curves through subspace projection among all possible clusters. We provide consistent estimators for the curves, curve derivatives, and the proposed distance. Identifiability issues of the clustering procedure are also discussed. The utility of the proposed method is illustrated via simulation studies and applications to two real datasets. The proposed method can considerably improve cluster performance compared with existing functional clustering methods. Supplementary materials for the article are available online. [ABSTRACT FROM AUTHOR]

Soil constitutive model parameters can be identified from triaxial test data. The identification is frequently performed by fitting a constitutive model to triaxial test data from a purely statistical or probabilistic perspective based on an assumption that measurements are independent. This ignores the sequential attribute of triaxial test data and is, hence, not realistic. In this paper, a probabilistic state space model (SSM) is proposed for undrained triaxial test data analysis, with which the sequential data attribute is explicitly considered and a constitutive model (physics) is linked to the SSM model (statistics) in a natural way. Then, constitutive model parameters can be rigorously learned under a Bayesian framework based on the SSM without artificially augmenting them into hidden variables of SSM. Without loss of generality, the modified Cam Clay (MCC) model is taken as an example to develop the SSM and to demonstrate the proposed Bayesian framework, which is illustrated using simulated and real-life data. Results from the proposed Bayesian framework based on the SSM include not only the best estimates of MCC model parameters but also their posterior distributions for quantifying the identification uncertainty, based on which the identifiability of MCC model parameters is discussed and highlighted. [ABSTRACT FROM AUTHOR]

Practical limitations of quality and quantity of data can limit the precision of parameter identification in mathematical models. Model-based experimental design approaches have been developed to minimise parameter uncertainty, but the majority of these approaches have relied on first-order approximations of model sensitivity at a local point in parameter space. Practical identifiability approaches such as profile-likelihood have shown potential for quantifying parameter uncertainty beyond linear approximations. This research presents a genetic algorithm approach to optimise sample timing across various parameterisations of a demonstrative PK-PD model with the goal of aiding experimental design. The optimisation relies on a chosen metric of parameter uncertainty that is based on the profile-likelihood method. Additionally, the approach considers cases where multiple parameter scenarios may require simultaneous optimisation. The genetic algorithm approach was able to locate near-optimal sampling protocols for a wide range of sample number (n = 3–20), and it reduced the parameter variance metric by 33–37% on average. The profile-likelihood metric also correlated well with an existing Monte Carlo-based metric (with a worst-case r > 0.89), while reducing computational cost by an order of magnitude. The combination of the new profile-likelihood metric and the genetic algorithm demonstrate the feasibility of considering the nonlinear nature of models in optimal experimental design at a reasonable computational cost. The outputs of such a process could allow for experimenters to either improve parameter certainty given a fixed number of samples, or reduce sample quantity while retaining the same level of parameter certainty. [ABSTRACT FROM AUTHOR]

Identifiability constraints are necessary for parameter estimation when fitting models with nonlinear covariate associations. The choice of constraint affects standard errors of the estimated curve. Centring constraints are often applied by default because they are thought to yield lowest standard errors out of any constraint, but this claim has not been investigated. We show that whether centring constraints are optimal depends on the response distribution and parameterization, and that for natural exponential family responses under the canonical parametrization, centring constraints are optimal only for Gaussian response. [ABSTRACT FROM AUTHOR]

Statistical network analysis primarily focuses on inferring the parameters of an observed network. In many applications, especially in the social sciences, the observed data is the groups formed by individual subjects. In these applications, the network is itself a parameter of a statistical model. Zhao and Weko propose a model-based approach, called the hub model, to infer implicit networks from grouping behavior. The hub model assumes that each member of the group is brought together by a member of the group called the hub. The set of members which can serve as a hub is called the hub set. The hub model belongs to the family of Bernoulli mixture models. Identifiability of Bernoulli mixture model parameters is a notoriously difficult problem. This article proves identifiability of the hub model parameters and estimation consistency under mild conditions. Furthermore, this article generalizes the hub model by introducing a model component that allows hubless groups in which individual nodes spontaneously appear independent of any other individual. We refer to this additional component as the null component. The new model bridges the gap between the hub model and the degenerate case of the mixture model—the Bernoulli product. Identifiability and consistency are also proved for the new model. In addition, a penalized likelihood approach is proposed to estimate the hub set when it is unknown. for this article are available online. [ABSTRACT FROM AUTHOR]

Grade of membership (GoM) models are popular individual-level mixture models for multivariate categorical data. GoM allows each subject to have mixed memberships in multiple extreme latent profiles. Therefore, GoM models have a richer modeling capacity than latent class models that restrict each subject to belong to a single profile. The flexibility of GoM comes at the cost of more challenging identifiability and estimation problems. In this work, we propose a singular value decomposition (SVD)-based spectral approach to GoM analysis with multivariate binary responses. Our approach hinges on the observation that the expectation of the data matrix has a low-rank decomposition under a GoM model. For identifiability, we develop sufficient and almost necessary conditions for a notion of expectation identifiability. For estimation, we extract only a few leading singular vectors of the observed data matrix and exploit the simplex geometry of these vectors to estimate the mixed membership scores and other parameters. We also establish the consistency of our estimator in the double-asymptotic regime where both the number of subjects and the number of items grow to infinity. Our spectral method has a huge computational advantage over Bayesian or likelihood-based methods and is scalable to large-scale and high-dimensional data. Extensive simulation studies demonstrate the superior efficiency and accuracy of our method. We also illustrate our method by applying it to a personality test dataset. [ABSTRACT FROM AUTHOR]

Restricted latent class models (RLCMs) provide an important framework for diagnosing and classifying respondents on a collection of multivariate binary responses. Recent research made significant advances in theory for establishing identifiability conditions for RLCMs with binary and polytomous response data. Multiclass data, which are unordered nominal response data, are also widely collected in the social sciences and psychometrics via forced-choice inventories and multiple choice tests. We establish new identifiability conditions for parameters of RLCMs for multiclass data and discuss the implications for substantive applications. The new identifiability conditions are applicable to a wealth of RLCMs for polytomous and nominal response data. We propose a Bayesian framework for inferring model parameters, assess parameter recovery in a Monte Carlo simulation study, and present an application of the model to a real dataset. [ABSTRACT FROM AUTHOR]

Cognitive diagnosis models (CDMs) provide a powerful statistical and psychometric tool for researchers and practitioners to learn fine-grained diagnostic information about respondents' latent attributes. There has been a growing interest in the use of CDMs for polytomous response data, as more and more items with multiple response options become widely used. Similar to many latent variable models, the identifiability of CDMs is critical for accurate parameter estimation and valid statistical inference. However, the existing identifiability results are primarily focused on binary response models and have not adequately addressed the identifiability of CDMs with polytomous responses. This paper addresses this gap by presenting sufficient and necessary conditions for the identifiability of the widely used DINA model with polytomous responses, with the aim to provide a comprehensive understanding of the identifiability of CDMs with polytomous responses and to inform future research in this field. [ABSTRACT FROM AUTHOR]

The present work aims at showing that the identification problems (here meant as both issues of empirical indistinguishability and unidentifiability) of some item response theory models are related to the notion of identifiability in knowledge space theory. Specifically, that the identification problems of the 3- and 4-parameter models are related to the more general issues of forward- and backward-gradedness in all items of the power set, which is the knowledge structure associated with IRT models under the assumption of local independence. As a consequence, the identifiability problem of a 4-parameter model is split into two parts: a first one, which is the result of a trade-off between the left-side added parameters and the remainder of the Item Response Function, e.g., a 2-parameter model, and a second one, which is the already well-known identifiability issue of the 2-parameter model itself. Application of the results to the logistic case appears to provide both a confirmation and a generalization of the current findings in the literature for both fixed- and random-effects IRT logistic models. [ABSTRACT FROM AUTHOR]

CD39 (NTPDase1—nucleoside triphosphate diphosphohydrolase 1) is a membrane-tethered ectonucleotidase that hydrolyzes extracellular ATP to ADP and ADP to AMP. This enzyme is expressed in a variety of cell types and tissues and has broadly been recognized within vascular tissue to have a protective role in converting "danger" ligands (ATP) into neutral ligands (AMP). In this study, we investigate the enzyme kinetics of CD39 using a Michaelis–Menten modeling framework. We show how the unique situation of having a reaction product also serving as a substrate (ADP) complicates the determination of the governing kinetic parameters. Model simulations using values for the kinetic parameters reported in the literature do not align with corresponding time-series data. This dissonance is explained by CD39 kinetic parameters previously being determined by graphical/linearization methods, which have been shown to distort the underlying error structure and lead to inaccurate parameter estimates. Modern methods of estimating these kinetic parameters using nonlinear least squares are still challenging due to unidentifiable parameter interactions. We propose a workflow to accurately determine these parameters by isolating the ADPase and ATPase reactions and estimating the respective ADPase parameters and ATPase parameters with independent data sets. Theoretically, this ensures all kinetic parameters are identifiable and reliable for future prospective model simulations involving CD39. These kinds of mathematical models can be used to understand how circulating purinergic nucleotides affect disease etiology and potentially inform the development of corresponding therapies. [ABSTRACT FROM AUTHOR]

We review standard mediation assumptions as they apply to identifying antibody effects in a randomized vaccine trial and propose new study designs to allow the identification of an estimand that was previously unidentifiable. For these mediation analyses, we partition the total ratio effect (one minus the vaccine effect) from a randomized vaccine trial into indirect (effects through antibodies) and direct effects (other effects). Identifying λ\lambda , the proportion of the total effect due to an indirect effect, depends on a cross-world quantity, the potential outcome among vaccinated individuals with antibody levels as if given placebo, or vice versa. We review assumptions for identifying λ\lambda and show that there are two versions of λ\lambda , unless the effect of adding antibodies to the placebo arm is equal in magnitude to the effect of subtracting antibodies from the vaccine arm. We focus on the case when individuals in the placebo arm are unlikely to have the needed antibodies. In that case, if a standard assumption (given confounders the potential mediators and potential outcomes are independent) is true, only one version of λ\lambda is identifiable, and if not neither is identifiable. We propose alternatives for identifying the other version of λ\lambda , using experimental design to identify a formerly cross-world quantity. Two alternative experimental designs use a three-arm trial with the extra arm being passive immunization (administering monoclonal antibodies), with or without closeout vaccination. Another alternative is to combine information from a placebo-controlled vaccine trial with a placebo-controlled passive immunization trial.

Summary: The right to privacy refers to an individual's decision about how personal information can be gathered, utilized, and disseminated. Individual consent and openness are the most important foundations for gaining consumers' confidence, and this pushes businesses to use privacy‐enhancing techniques while developing systems. The purpose of a privacy‐aware design is to safeguard data in such a manner that it does not expand an adversary's current understanding of an individual beyond what would be permitted. When these data pieces are coupled with the plethora of source data accessible outside the system to identify a user, this becomes crucial. Individual privacy is protected by privacy rules all around the globe, but they are often complicated and ambiguous, making their translation into practical and technologically privacy‐friendly structures difficult. The main contribution of this article is that we use Shannon's entropy (SE) to construct an objective measure that may guide our major technical design choices. And for privacy‐aware architecture, simplifying the state‐of‐the‐art security approaches given in the literature. [ABSTRACT FROM AUTHOR]

Voltage‐clamp experiments are commonly utilised to characterise cellular ion channel kinetics. In these experiments, cells are stimulated using a known time‐varying voltage, referred to as the voltage protocol, and the resulting cellular response, typically in the form of current, is measured. Parameters of models that describe ion channel kinetics are then estimated by solving an inverse problem which aims to minimise the discrepancy between the predicted response of the model and the actual measured cell response. In this paper, a novel framework to evaluate the information content of voltage‐clamp protocols in relation to ion channel model parameters is presented. Additional quantitative information metrics that allow for comparisons among various voltage protocols are proposed. These metrics offer a foundation for future optimal design frameworks to devise novel, information‐rich protocols. The efficacy of the proposed framework is evidenced through the analysis of seven voltage protocols from the literature. By comparing known numerical results for inverse problems using these protocols with the information‐theoretic metrics, the proposed approach is validated. The essential steps of the framework are: (i) generate random samples of the parameters from chosen prior distributions; (ii) run the model to generate model output (current) for all samples; (iii) construct reduced‐dimensional representations of the time‐varying current output using proper orthogonal decomposition (POD); (iv) estimate information‐theoretic metrics such as mutual information, entropy equivalent variance, and conditional mutual information using non‐parametric methods; (v) interpret the metrics; for example, a higher mutual information between a parameter and the current output suggests the protocol yields greater information about that parameter, resulting in improved identifiability; and (vi) integrate the information‐theoretic metrics into a single quantitative criterion, encapsulating the protocol's efficacy in estimating model parameters. [ABSTRACT FROM AUTHOR]

Missing data problems arise in randomized trials, which complicates the inference of causal effects if the missing mechanism is non-ignorable. We tackle the challenge of identifying and estimating the complier average causal effect parameters under non-ignorable missingness by increasing the covariates to mitigate the sensitivity to the violation of specific identification assumptions. The missing data mechanism is assumed to follow a logistic model, wherein the absence of the outcome is explained by the outcome itself, the treatment received, and the covariates. We establish the identifiability of the models under mild conditions by assuming that the outcome follows a normal distribution. We develop a computational method to estimate model parameters through a two-step likelihood estimation approach, employing subgroup analysis. The bootstrap method is employed for variance estimation, and the effectiveness of our approach is confirmed through simulation. We applied the proposed method to analyze the household income dataset from the Chinese Household Income Project Survey 2013. [ABSTRACT FROM AUTHOR]

Measurement errors are often encountered in several continuous variables in a data set, and various methods have been proposed to handle these measurement errors when they are supposed to be independent. Recently, Kekeç and Van Keilegom (Electron J Stat 16(1):1831–1854, 2022) considered bivariate classical measurement error models with correlated measurement errors, and estimated their variance matrix when no validation data nor auxiliary variables are available. However, in practice, one often observes more than two variables with correlated measurement errors. In this paper, we introduce a flexible and practical method to estimate the variance matrix of multivariate classical additive Gaussian measurement errors, without additional information. We show that the error variance matrix is identifiable under certain circumstances and introduce an estimation method of the variance matrix and of the multivariate density of the variables of interest by means of Bernstein polynomials. Asymptotic properties and finite sample characteristics of the proposed methodology are also examined. Furthermore, we consider in a simulation study a multiple linear regression model with measurement errors in multiple covariates, and use the proposed estimator of the variance matrix to estimate the model parameters by means of the simulation extrapolation (SIMEX) algorithm. Finally, the method is illustrated on a dataset on fetal biometry measurements. [ABSTRACT FROM AUTHOR]

AbstractHigh-dimensional compositional data are prevalent in many applications. The simplex constraint poses intrinsic challenges to inferring the conditional dependence relationships among the components forming a composition, as encoded by a large precision matrix. We introduce a precise specification of the compositional precision matrix and relate it to its basis counterpart, which is shown to be asymptotically identifiable under suitable sparsity assumptions. By exploiting this connection, we propose a composition adaptive regularized estimation (CARE) method for estimating the sparse basis precision matrix. We derive rates of convergence for the estimator and provide theoretical guarantees on support recovery and data-driven parameter tuning. Our theory reveals an intriguing tradeoff between identification and estimation, thereby highlighting the blessing of dimensionality in compositional data analysis. In particular, in sufficiently high dimensions, the CARE estimator achieves minimax optimality and performs as well as if the basis were observed. We further discuss how our framework can be extended to handle data containing zeros, including sampling zeros and structural zeros. The advantages of CARE over existing methods are illustrated by simulation studies and an application to inferring microbial ecological networks in the human gut. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

Survival analysis studies time to event data, also called survival data in biomedical research. The main challenge in the analysis of survival data is to develop inferential methods that take into account the incomplete information contained in censored observations. The seminal paper of Kaplan and Meier (J Am Stat Assoc 53:457–481,1958) gave a boost to the development of statistical methods for time to event data subject to right censoring; methods that have been applied in a broad variety of scientific fields including health, engineering and economy. A basic quantity in survival analysis is the survival distribution: S (t) = P (T > t) , with T the time to event or, in case of a bivariate vector of lifetimes (T 1 , T 2) , S (t 1 , t 2) = P (T 1 > t 1 , T 2 > t 2 ). Nonparametric estimation of these basic quantities received, since Kaplan and Meier (J Am Stat Assoc 53:457–481,1958), considerable attention resulting in many publications scattered over a large period of time and a large field of applications. The purpose of this paper is to review, in a unified way, nonparametric estimation of S(t) and S (t 1 , t 2) for time to event data subject to right censoring. Interesting to realize is that, in the multivariate setting, the form of the nonparametric estimator for S (t 1 , t 2) is determined by the actual censoring scheme. In this survey we focus, for the proposed (implicitly) existing or new nonparametric estimators, on the asymptotic normality. By doing so we fill some gaps in the literature by introducing some new estimators and by providing explicit expressions for the asymptotic variances often not yet available for some of the existing estimators. [ABSTRACT FROM AUTHOR]

In ecology, the observation process (how we collect data) can be as complex as the biological process we are investigating. Failure to account for complex observation processes leads to uncertainty, biased inference and poor predictions, resulting in misleading research results. Often, field scientists are best placed to describe observation problems that occur but are excluded from discussions about how to tackle these problems statistically. Statisticians are often unaware of the nuances of observation processes leading to the problems being ignored, or tackled on a case-by-case basis. We propose a typology of observation problems and inferential solutions, hence facilitating the linkages between field protocols and statistical treatments. Advances in statistics mean that it is now possible to tackle increasingly sophisticated observation processes. The intricacies and ambitious scale of modern data collection techniques mean that this is now essential. Methodological research to make inference about the biological process while accounting for the observation process has expanded dramatically, but solutions are often presented in field-specific terms, limiting our ability to identify commonalities between methods. We suggest a typology of observation processes that could improve translation between fields and aid methodological synthesis. We propose the LIES framework (defining observation processes in terms of issues of Latency, Identifiability, Effort and Scale) and illustrate its use with both simple examples and more complex case studies. [ABSTRACT FROM AUTHOR]

This paper presents classification and analysis of the mathematical models of the spread of COVID-19 in different groups of population such as family, school, office (3–100 people), town (100–5000 people), city, region (0.5–15 million people), country, continent, and the world. The classification covers major types of models (time-series, differential, imitation ones, neural networks models and their combinations). The time-series models are based on analysis of time series using filtration, regression and network methods. The differential models are those derived from systems of ordinary and stochastic differential equations as well as partial differential equations. The imitation models include cellular automata and agent-based models. The fourth group in the classification consists of combinations of nonlinear Markov chains and optimal control theory, derived by methods of the mean-field game theory. COVID-19 is a novel and complicated disease, and the parameters of most models are, as a rule, unknown and estimated by solving inverse problems. The paper contains an analysis of major algorithms of solving inverse problems: stochastic optimization, nature-inspired algorithms (genetic, differential evolution, particle swarm, etc.), assimilation methods, big-data analysis, and machine learning. [ABSTRACT FROM AUTHOR]

In this paper, the identifiability and the estimability of a particular phase-type ageing model (PTAM) are investigated. We consider a PTAM that is shown to be identifiable, although it has poor estimability when the only observation is the time until absorption. We use a data-cloning method to assess model estimability, which is also analysed visually via contour plots and marginal likelihood functions. The PTAM's estimability under different scenarios is compared, from the best scenario of a fully observable Markov process for each individual to the worst scenario wherein the only observation is the time until absorption for each individual. Some in-between scenarios are also studied and include the situations where the state could be observed every several years and the state could be measured with some error. Certain conditions are provided regarding the state of the Markov chain that improves the PTAM's estimability. [ABSTRACT FROM AUTHOR]

This paper focuses on the uses of the definite marker -tì in Longxi Qiang, a Tibeto-Burman language. Although the selection of referring expressions made by speakers is based on referent accessibility or cognitive status, at the same time, referring expressions have pragmatic and interactive dimensions. The concept of identifiability can account for the uses of the definite marker -tì; however, this concept is not sufficient to explain the selection of -tì in certain discourse contexts. Accordingly, this paper discusses the discourse uses of non-referential definite noun phrases. In addition to encoding definiteness, -tì serves as a prominence marker to trigger the interpretation that an entity, an action or a property is prominent, and the speaker intended to highlight the topicality. With respect to discourse functions, -tì is attached not only to noun phrases but also to verb and adjective phrases, fillers and connectors. These uses of -tì have been expanded into Wenchuan Mandarin. [ABSTRACT FROM AUTHOR]