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DAISY: a new software tool to test global identifiability of biological and physiological systems

Bellu, Giuseppina; Saccomani, Maria Pia; Audoly, Stefania; D’Angiò, Leontina
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
EN
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A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a differential algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies...

ON IDENTIFIABILITY OF NONLINEAR ODE MODELS AND APPLICATIONS IN VIRAL DYNAMICS

MIAO, HONGYU; XIA, XIAOHUA; PERELSON, ALAN S.; WU, HULIN
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 01/01/2011 EN
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Ordinary differential equations (ODE) are a powerful tool for modeling dynamic processes with wide applications in a variety of scientific fields. Over the last 2 decades, ODEs have also emerged as a prevailing tool in various biomedical research fields, especially in infectious disease modeling. In practice, it is important and necessary to determine unknown parameters in ODE models based on experimental data. Identifiability analysis is the first step in determing unknown parameters in ODE models and such analysis techniques for nonlinear ODE models are still under development. In this article, we review identifiability analysis methodologies for nonlinear ODE models developed in the past one to two decades, including structural identifiability analysis, practical identifiability analysis and sensitivity-based identifiability analysis. Some advanced topics and ongoing research are also briefly reviewed. Finally, some examples from modeling viral dynamics of HIV, influenza and hepatitis viruses are given to illustrate how to apply these identifiability analysis methods in practice.

An Approach for Identifiability of Population Pharmacokinetic–Pharmacodynamic Models

Shivva, V; Korell, J; Tucker, I G; Duffull, S B
Fonte: Nature Publishing Group Publicador: Nature Publishing Group
Tipo: Artigo de Revista Científica
EN
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Mathematical models are routinely used in clinical pharmacology to study the pharmacokinetic and pharmacodynamic properties of a drug in the body. Identifiability of these models is an important requirement for the success of these clinical studies. Identifiability is classified into two types, structural identifiability related to the structure of the mathematical model and deterministic identifiability which is related to the study design. There are existing approaches for assessment of structural identifiability of fixed-effects models, although their use appears uncommon in the literature. In this study, we develop an informal unified approach for simultaneous assessment of structural and deterministic identifiability for fixed and mixed-effects pharmacokinetic or pharmacokinetic–pharmacodynamic models. This approach uses an information theoretic framework. The method is applied both to simple examples to explore known identifiability properties and to a more complex example to illustrate its utility.

Assessing parameter identifiability for dynamic causal modeling of fMRI data

Arand, Carolin; Scheller, Elisa; Seeber, Benjamin; Timmer, Jens; Klöppel, Stefan; Schelter, Björn
Fonte: Frontiers Media S.A. Publicador: Frontiers Media S.A.
Tipo: Artigo de Revista Científica
Publicado em 20/02/2015 EN
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Deterministic dynamic causal modeling (DCM) for fMRI data is a sophisticated approach to analyse effective connectivity in terms of directed interactions between brain regions of interest. To date it is difficult to know if acquired fMRI data will yield precise estimation of DCM parameters. Focusing on parameter identifiability, an important prerequisite for research questions on directed connectivity, we present an approach inferring if parameters of an envisaged DCM are identifiable based on information from fMRI data. With the freely available “attention to motion” dataset, we investigate identifiability of two DCMs and show how different imaging specifications impact on identifiability. We used the profile likelihood, which has successfully been applied in systems biology, to assess the identifiability of parameters in a DCM with specified scanning parameters. Parameters are identifiable when minima of the profile likelihood as well as finite confidence intervals for the parameters exist. Intermediate epoch duration, shorter TR and longer session duration generally increased the information content in the data and thus improved identifiability. Irrespective of biological factors such as size and location of a region, attention should be paid to densely interconnected regions in a DCM...

On the identifiability of multi-observer hidden Markov models

Nguyen, H.; Roughan, M.
Fonte: IEEE; USA Publicador: IEEE; USA
Tipo: Conference paper
Publicado em //2012 EN
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Most large attacks on the Internet are distributed. As a result, such attacks are only partially observed by any one Internet service provider (ISP). Detection would be significantly easier with pooled observations, but privacy concerns often limit the information that providers are willing to share. Multi-party secure distributed computation provides a means for combining observations without compromising privacy. In this paper, we show the benefits of this approach, the most notable of which is that combinations of observations solve identifiability problems in existing approaches for detecting network attacks.; http://www.icassp2012.com/; Hung X Nguyen and Matthew Roughan

Latino identifiability and public policy: seeking presence and voice in the U.S. civic culture

Aguirre, Adalberto Jr.; Martínez, Rubén O.
Fonte: Instituto Franklin de Estudios Norteamericanos. Universidad de Alcalá de Henares Publicador: Instituto Franklin de Estudios Norteamericanos. Universidad de Alcalá de Henares
Tipo: Artigo de Revista Científica Formato: application/pdf
SPA
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Public policy initiatives in the U.S. target Latino identifiability in order to constrain its expression in U.S. civic culture. As Latino identifiability increases in U.S. society, so does its perceived threat to valued esources. As a result, public policy initiatives are promoted by the dominant group that seek to constrain the access of Latinos to valued resources. In addition, these public policy initiatives utilize racial profiling to limit the participation of Latinos in other areas of civic life – the right to vote, the freedom to travel, and the privilege of self-identification. A general systems model for Latino identifiability and public policy is presented to illustrate how public policy targets Latinos in the U.S.; Las políticas públicas en los Estados Unidos tienen como objetivo la identificabilidad de los latinos con el fin de limitar su participación en la cultura cívica estadounidense. A medida que aumenta la identificabilidad de los latinos en la sociedad de los Estados Unidos, también lo hace la percepción de amenaza a los recursos valiosos que ellos suponen. Como resultado, las políticas públicas, promovidas por el grupo dominante, buscan limitar el acceso de los latinos a los recursos valiosos. Además...

On identifiability of MAP processes

Ramírez-Cobo, Pepa; Lillo, Rosa E.; Wiper, Michael P.
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /09/2008 SPA
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Two types of transitions can be found in the Markovian Arrival process or MAP: with and without arrivals. In transient transitions the chain jumps from one state to another with no arrival; in effective transitions, a single arrival occurs. We assume that in practice, only arrival times are observed in a MAP. This leads us to define and study the Effective Markovian Arrival process or E-MAP. In this work we define identifiability of MAPs in terms of equivalence between the corresponding E-MAPs and study conditions under which two sets of parameters induce identical laws for the observable process, in the case of 2 and 3-states MAP. We illustrate and discuss our results with examples.

Non-identifiability of the two state Markovian Arrival process

Ramírez-Cobo, Pepa; Lillo, Rosa E.; Wiper, Michael P.
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /11/2009 ENG
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In this paper we consider the problem of identifiability of the two-state Markovian Arrival process (MAP2). In particular, we show that the MAP2 is not identifiable and conditions are given under which two different sets of parameters, induce identical stationary laws for the observable process.

On the identifiability of the two-state BMAP

Rodríguez, Joanna; Lillo, Rosa E.; Ramírez-Cobo, Pepa
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper Formato: application/pdf
Publicado em /05/2012 ENG
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The capability of modeling non-exponentially distributed and dependent inter-arrival times as well as correlated batches makes the Batch Markovian Arrival Processes (BMAP) suitable in different real-life settings as teletraffic, queueing theory or actuarial contexts. An issue to be taken into account for estimation purposes is the identifiability of the process. This is an open problem concerning BMAP-related processes. This paper explores the identifiability issue of the two-state BMAP noted BMAP2(k), where k is the maximum batch arrival size. It is proven that for k = 2 the process cannot be identified, under the assumptions that both the interarrival times and batches sizes are observed. Additionally, a method to obtain an equivalent BMAP2(2) to a given one is provided.; Research partially supported by research grants and projects ECO2011-25706 and MTM2009-14039 (Ministerio de Ciencia e Innovación, Spain) and FQM329 (Junta de Andalucía, Spain), all with EU ERDF funds. The third author was supported by Consolider "Ingenio Mathematica" through her post-doc contract.

Consistency and identifiability in Bayesian analysis

O'Neill, B
Fonte: Universidade Nacional da Austrália Publicador: Universidade Nacional da Austrália
Tipo: Working/Technical Paper Formato: 277648 bytes; 350 bytes; application/pdf; application/octet-stream
EN_AU
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The importance of posterior consistency in the robustness of Bayesian analysis is examined and discussed. The notions of sufficient and minimal sufficient parameters are introduced and important consistency results for such parameters are derived. We see that minimal sufficient parameters are fundamental in characterising the relationship between data and parameters. The concept of identifiability is then introduced and several equivalent definitions are given. The relationship between consistency and identifiability is examined and means of establishing identifiability are examined with a view to finding useful practical tests of identifiability. These results are applied to a simple example involving non response.; no

Parameter identifiability of biochemical reaction networks in systems biology

Geffen, Dara
Fonte: Quens University Publicador: Quens University
Tipo: Tese de Doutorado Formato: 1324816 bytes; application/pdf
EN; EN
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In systems biology, models often contain a large number of unknown or only roughly known parameters that must be estimated through the fitting of data. This work examines the question of whether or not these parameters can in fact be estimated from available measurements. Structural or a priori identifiability of unknown parameters in biochemical reaction networks is considered. Such systems consist of continuous time, nonlinear differential equations. Several methods for analyzing identifiability of such systems exist, most of which restate the question as one of observability by expanding the state space to include parameters. However, these existing methods were not developed with biological systems in mind, so do not necessarily address the specific challenges posed by this type of problem. In this work, such methods are considered for the analysis of a representative biological system, the NF-kappaB signal transduction pathway. It is shown that existing observability-based strategies, which rely on finding an analytical solution, require significant simplifications to be applicable to systems biology problems that are seldom feasible. The analytical nature of the solution imposes restrictions on the size and complexity of systems that these methods can handle. This conflicts with the fact that most currently studied systems biology models are rather large networks containing many states and parameters. In this thesis...

Identifiability Scaling Laws in Bilinear Inverse Problems

Choudhary, Sunav; Mitra, Urbashi
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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A number of ill-posed inverse problems in signal processing, like blind deconvolution, matrix factorization, dictionary learning and blind source separation share the common characteristic of being bilinear inverse problems (BIPs), i.e. the observation model is a function of two variables and conditioned on one variable being known, the observation is a linear function of the other variable. A key issue that arises for such inverse problems is that of identifiability, i.e. whether the observation is sufficient to unambiguously determine the pair of inputs that generated the observation. Identifiability is a key concern for applications like blind equalization in wireless communications and data mining in machine learning. Herein, a unifying and flexible approach to identifiability analysis for general conic prior constrained BIPs is presented, exploiting a connection to low-rank matrix recovery via lifting. We develop deterministic identifiability conditions on the input signals and examine their satisfiability in practice for three classes of signal distributions, viz. dependent but uncorrelated, independent Gaussian, and independent Bernoulli. In each case, scaling laws are developed that trade-off probability of robust identifiability with the complexity of the rank two null space. An added appeal of our approach is that the rank two null space can be partly or fully characterized for many bilinear problems of interest (e.g. blind deconvolution). We present numerical experiments involving variations on the blind deconvolution problem that exploit a characterization of the rank two null space and demonstrate that the scaling laws offer good estimates of identifiability.; Comment: 25 pages...

Identifiability of directed Gaussian graphical models with one latent source

Leung, Dennis; Drton, Mathias; Hara, Hisayuki
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/05/2015
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We study parameter identifiability of directed Gaussian graphical models with one latent variable. In the scenario we consider, the latent variable is a confounder that forms a source node of the graph and is a parent to all other nodes, which correspond to the observed variables. We give a graphical condition that is sufficient for the Jacobian matrix of the parametrization map to be full rank, which entails that the parametrization is generically finite-to-one, a fact that is sometimes also referred to as local identifiability. We also derive a graphical condition that is necessary for such identifiability. Finally, we give a condition under which generic parameter identifiability can be determined from identifiability of a model associated with a subgraph. The power of these criteria is assessed via an exhaustive algebraic computational study on models with 4, 5, and 6 observable variables.

Identifiability in penalized function-on-function regression models

Scheipl, Fabian; Greven, Sonja
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/06/2015
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Regression models with functional responses and covariates constitute a powerful and increasingly important model class. However, regression with functional data poses well known and challenging problems of non-identifiability. This non-identifiability can manifest itself in arbitrarily large errors for coefficient surface estimates despite accurate predictions of the responses, thus invalidating substantial interpretations of the fitted models. We offer an accessible rephrasing of these identifiability issues in realistic applications of penalized linear function-on-function-regression and delimit the set of circumstances under which they are likely to occur in practice. Specifically, non-identifiability that persists under smoothness assumptions on the coefficient surface can occur if the functional covariate's empirical covariance has a kernel which overlaps that of the roughness penalty of the spline estimator. Extensive simulation studies validate the theoretical insights, explore the extent of the problem and allow us to evaluate its practical consequences under varying assumptions about the data generating processes. Based on theoretical considerations and our empirical evaluation, we provide immediately applicable diagnostics for lack of identifiability and give recommendations for avoiding estimation artifacts in practice.; Comment: 20 pages...

Parameter identifiability and redundancy: theoretical considerations

Little, Mark P.; Heidenreich, Wolfgang F.; Li, Guangquan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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In this paper we outline general considerations on parameter identifiability, and introduce the notion of weak local identifiability and gradient weak local identifiability. These are based on local properties of the likelihood, in particular the rank of the Hessian matrix. We relate these to the notions of parameter identifiability and redundancy previously introduced by Rothenberg (Econometrica 39 (1971) 577-591) and Catchpole and Morgan (Biometrika 84 (1997) 187-196). Within the exponential family parameter irredundancy, local identifiability, gradient weak local identifiability and weak local identifiability are shown to be equivalent. We consider applications to a recently developed class of cancer models of Little and Wright (Math Biosciences 183 (2003) 111-134) and Little et al. (J Theoret Biol 254 (2008) 229-238) that generalize a large number of other recently used quasi-biological cancer models, in particular those of Armitage and Doll (Br J Cancer 8 (1954) 1-12) and the two-mutation model (Moolgavkar and Venzon Math Biosciences 47 (1979) 55-77).; Comment: This is now exactly as per the version of the article published in Little et al. (PLoS ONE 2010 5 (1)e8915)

A sufficient condition to test identifiability of a nonlinear delayed-differential model with constant delays and multi-inputs

Jauberthie, Carine; Travé-Massuyès, Louise
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/09/2010
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In this paper, an original result in terms of a sufficient condition to test identifiability of nonlinear delayed-differential models with constant delays and multi-inputs is given. The identifiability is studied for the linearized system and a criterion for linear systems with constant delays is provided, from which the identifiability of the original nonlinear system can be proved. This result is obtained by combining a classical identifiability result for nonlinear ordinary differential systems due to M.S. Grewal and K. Glover (1976) with the identifiability of linear delayed-differential models developed by Y. Orlov et al. (2002). This paper is a generalization of the results provided by L. Denis-Vidal, C. Jauberthie, G. Joly-Blanchard (2006), which deal with the specific case of nonlinear delayed-differential models with two delays and a single input.

Causal Inference by Surrogate Experiments: z-Identifiability

Bareinboim, Elias; Pearl, Judea
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/10/2012
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We address the problem of estimating the effect of intervening on a set of variables X from experiments on a different set, Z, that is more accessible to manipulation. This problem, which we call z-identifiability, reduces to ordinary identifiability when Z = empty and, like the latter, can be given syntactic characterization using the do-calculus [Pearl, 1995; 2000]. We provide a graphical necessary and sufficient condition for z-identifiability for arbitrary sets X,Z, and Y (the outcomes). We further develop a complete algorithm for computing the causal effect of X on Y using information provided by experiments on Z. Finally, we use our results to prove completeness of do-calculus relative to z-identifiability, a result that does not follow from completeness relative to ordinary identifiability.; Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (UAI2012)

Generalizing the differential algebra approach to input-output equations in structural identifiability

Eisenberg, Marisa
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/02/2013
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Structural identifiability for parameter estimation addresses the question of whether it is possible to uniquely recover the model parameters assuming noise-free data, making it a necessary condition for successful parameter estimation for real, noisy data. One established approach to this question for nonlinear ordinary differential equation models is via differential algebra, which uses characteristic sets to generate a set of input-output equations which contain complete identifiability information for the model. This paper presents a generalization of this method, proving that identifiability may be determined using more general solution methods such as ad hoc substitution, Groebner bases, and differential Groebner bases, rather than via characteristic sets. This approach is used to examine the structural identifiability of several biological model systems using different solution methods (characteristic sets, Groebner bases, differential Groebner bases, and ad hoc substitution). It is shown that considering a range of approaches can allow for faster computations, which makes it possible to determine the identifiability of models which otherwise would be computationally infeasible.; Comment: Some notes on alternative approaches to finding input-output equations in structural identifiability

A strategic algorithmic tool for doing an a priori identifiability study of dynamical nonlinear models

Verdière, Nathalie; Orange, Sébastien
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/10/2015
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The identifiability's study of a parametrized model is one of the last step of the modeling and consists in insuring that each of its output corresponds to a unique parameter vector. Actually, at our knowledge, no concrete solution or automatic procedure has been proposed in the literature in the case of a non identifiable model. This paper proposes to go further in the identifiability results through the definition of \textit{relative identifiability} that is the determination of the identifiability of any parameter relatively to any set of parameters. We propose an algorithm in order to determine the relative identifiability of any parameter relatively to any list of other parameters. This algorithm takes into account some eventual constraints satisfied by parameters and by its output(s) through the consideration of the initial conditions of the system. It can help an experimenter to elaborate strategies about key parameters that should be estimated and eventually outputs or constraints on parameters that must be added to obtain the identifiability of the model. Three applications of this algorithm are presented to show the relevance of the suggested approach.

Non-identifiability, equivalence classes, and attribute-specific classification in Q-matrix based Cognitive Diagnosis Models

Zhang, Stephanie S.; DeCarlo, Lawrence T.; Ying, Zhiliang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/03/2013
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There has been growing interest in recent years in Q-matrix based cognitive diagnosis models. Parameter estimation and respondent classification under these models may suffer due to identifiability issues. Non-identifiability can be described by a partition separating attribute profiles into groups of those with identical likelihoods. Marginal identifiability concerns the identifiability of individual attributes. Maximum likelihood estimation of the proportion of respondents within each equivalence class is consistent, making possible a new measure of assessment quality reporting the proportion of respondents for whom each individual attribute is marginally identifiable. Arising from this is a new posterior-based classification method adjusting for non-identifiability.