Inference In Dynamic Models Research Articles

Dynamic Model Inference of Gene Regulatory Network based on Hybrid Parallel Genetic Algorithm and Threshold Qualification Method

Gene regulation is the process by which various substances in cells regulate the behaviour of gene expression, thereby controlling almost all cellular activities. Therefore, studying gene regulation not only helps to uncover the internal laws governing life processes but also plays a crucial role in predicting, diagnosing, treating, and designing drugs for genetic diseases. By utilizing multi-source biological information such as gene expression profiles, transcription factor information, and protein interaction data, a network model can be developed to depict the regulatory relationships between genes, facilitating further research. To address the limitations of traditional gene regulatory network construction methods, a novel dynamic model has been created by combining hybrid genetics and threshold restriction. This model comprises two parts: solution space reduction and parameter fitting. During solution space reduction, singular value decomposition is employed to define a mathematically feasible gene regulatory network, reducing unnecessary calculations. Subsequently, the control genes of each gene are constrained within a certain range using threshold limitation, enhancing computational efficiency while adhering to bioinformatics principles. In the parameter fitting phase, parallel genetic algorithms are utilized to expediently optimize the entire solution space. The mountain climbing method is then applied to solve problems meticulously within a limited scope, improving calculation accuracy. In this study, this approach was applied to establish genetic regulatory systems for complex skin melanoma and type 2 diabetes. Through comparison with actual networks, the validity of the method was confirmed. Compared to traditional genetic and particle swarm optimization methods, the effectiveness of the proposed method was verified. This paper models the intricate mechanism of gene regulation and elucidates the regulatory process involving genes, proteins, and small biological molecules in greater detail than other models, aligning more closely with intracellular dynamics laws.

Optimal estimating function for weak location‐scale dynamic models

Estimating functions provide a very general framework for the statistical inference of dynamic models under weak assumptions. We consider a class of time series models consisting in the parametrization of the first two conditional moments which – by contrast with classical location‐scale dynamic models – do not impose further constraints on the conditional distribution/moments. Quasi‐likelihood estimators (QLE) are obtained by solving estimating equations deduced from those two conditional moments. Conditions ensuring the existence and asymptotic properties (consistency and asymptotic normality) of such estimators are provided. We propose optimal QLEs in Godambe's sense, deduced from a condition obtained by Chandra and Taniguchi (2001, Annals of the Institute of Statistical Mathematics 53, 125–141). The particular case of the quasi‐maximum likelihood estimators is considered. For pure location models, a data‐driven procedure for optimally choosing the QLE is proposed. Our results are illustrated via Monte Carlo experiments and real financial data.

An Instrumental Variable Approach to Dynamic Models

Abstract We present a new class of methods for identification and inference in dynamic models with serially correlated unobservables, which typically imply that state variables are econometrically endogenous. In the context of Industrial Organization, these state variables often reflect econometrically endogenous market structure. We propose the use of Generalized Instrument Variables methods to identify those dynamic policy functions that are consistent with instrumental variable (IV) restrictions. Extending popular “two-step” methods, these policy functions then identify a set of structural parameters that are consistent with the dynamic model, the IV restrictions and the data. We provide computed illustrations to both single-agent and oligopoly examples. We also present a simple empirical analysis that, among other things, supports the counterfactual study of an environmental policy entailing an increase in sunk costs.

Bias-corrected method of moments estimators for dynamic panel data models

A computationally simple bias correction for linear dynamic panel data models is proposed and its asymptotic properties are studied when the number of time periods is fixed or tends to infinity with the number of panel units. The approach can accommodate both fixed-effects and random-effects assumptions, heteroskedastic errors, as well as higher-order autoregressive models. Panel-corrected standard errors are proposed that allow for robust inference in dynamic models with cross-sectionally correlated errors. Monte Carlo experiments suggest that under the assumption of strictly exogenous regressors the bias-corrected method of moment estimator outperforms popular GMM estimators in terms of efficiency and correctly sized tests.

Separable Nonlinear Least-Squares Parameter Estimation for Complex Dynamic Systems.

Nonlinear dynamic models are widely used for characterizing processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data collected via high-throughput experiments using methods from molecular biology. While these data are very beneficial, they are typically incomplete and noisy, which renders the inference of parameter values for complex dynamic models challenging. Fortunately, many biological systems have embedded linear mathematical features, which may be exploited, thereby improving fits and leading to better convergence of optimization algorithms. In this paper, we explore options of inference for dynamic models using a novel method of separable nonlinear least-squares optimization and compare its performance to the traditional nonlinear least-squares method. The numerical results from extensive simulations suggest that the proposed approach is at least as accurate as the traditional nonlinear least-squares, but usually superior, while also enjoying a substantial reduction in computational time.

Partial Identification and Inference for Dynamic Models and Counterfactuals

We provide a general framework for investigating partial identification of structural dynamic discrete choice models and their counterfactuals, along with uniformly valid inference procedures. In doing so, we derive sharp bounds for the model parameters, counterfactual behavior, and low-dimensional outcomes of interest, such as the average welfare effects of hypothetical policy interventions. We characterize the properties of the sets analytically and show that when the target outcome of interest is a scalar, its identified set is an interval whose endpoints can be calculated by solving well-behaved constrained optimization problems via standard algorithms. We obtain a uniformly valid inference procedure by an appropriate application of subsampling. To illustrate the performance and computational feasibility of the method, we consider both a Monte Carlo study of firm entry/exit, and an empirical model of export decisions applied to plant-level data from Colombian manufacturing industries. In these applications, we demonstrate how the identified sets shrink as we incorporate alternative model restrictions, providing intuition regarding the source and strength of identification.

An Instrumental Variable Approach to Dynamic Models

We present a new class of methods for identification and inference in dynamic models with serially correlated unobservables, which typically imply that state variables are econometrically endogenous. In the context of Industrial Organization, these state variables often reflect econometrically endogenous market structure. We propose the use of Generalized Instrument Variables methods to identify those dynamic policy functions that are consistent with instrumental variable (IV) restrictions. Extending popular “two-step†methods, these policy functions then identify a set of structural parameters that are consistent with the dynamic model, the IV restrictions and the data. We provide computed illustrations to both single-agent and oligopoly examples. We also present a simple empirical analysis that, among other things, supports the counterfactual study of an environmental policy entailing an increase in sunk costs.

Partial Identification and Inference for Dynamic Models and Counterfactuals

We provide a general framework for investigating partial identification of structural dynamic discrete choice models and their counterfactuals, along with uniformly valid inference procedures. In doing so, we derive sharp bounds for the model parameters, counterfactual behavior, and low-dimensional outcomes of interest, such as the average welfare effects of hypothetical policy interventions. We characterize the properties of the sets analytically and show that when the target outcome of interest is a scalar, its identified set is an interval whose endpoints can be calculated by solving well-behaved constrained optimization problems via standard algorithms. We obtain a uniformly valid inference procedure by an appropriate application of subsampling. To illustrate the performance and computational feasibility of the method, we consider both a Monte Carlo study of firm entry/exit, and an empirical model of export decisions applied to plant-level data from Colombian manufacturing industries. In these applications, we demonstrate how the identified sets shrink as we incorporate alternative model restrictions, providing intuition regarding the source and strength of identification.

A probabilistic approach to joint cell tracking and segmentation in high-throughput microscopy videos.

We present a novel computational framework for the analysis of high-throughput microscopy videos of living cells. The proposed framework is generally useful and can be applied to different datasets acquired in a variety of laboratory settings. This is accomplished by tying together two fundamental aspects of cell lineage construction, namely cell segmentation and tracking, via a Bayesian inference of dynamic models. In contrast to most existing approaches, which aim to be general, no assumption of cell shape is made. Spatial, temporal, and cross-sectional variation of the analysed data are accommodated by two key contributions. First, time series analysis is exploited to estimate the temporal cell shape uncertainty in addition to cell trajectory. Second, a fast marching (FM) algorithm is used to integrate the inferred cell properties with the observed image measurements in order to obtain image likelihood for cell segmentation, and association. The proposed approach has been tested on eight different time-lapse microscopy data sets, some of which are high-throughput, demonstrating promising results for the detection, segmentation and association of planar cells. Our results surpass the state of the art for the Fluo-C2DL-MSC data set of the Cell Tracking Challenge (Maška etal., 2014).

Exploring the perceived intrusion of mining into the landscape using the fuzzy cognitive mapping approach

Fuzzy Cognitive Mapping (FCM) is a popular method used towards studying the structure and behaviour of complex systems in a wide range of applications. This paper presents the first application of FCM in exploring factors affecting the perceived nuisance caused by the impact of mining projects on the landscape. To this end, a team of experts in mining and landscape engineering was recruited to develop the conceptual model of the “mining-landscape-society” system. The individual Fuzzy Cognitive Maps (FCMs) were not significantly different among the experts, as regards the graph theory indices, and the most central concepts reported were related to the socioeconomic profile of the surrounding area, the characteristics of the mining project, and the characteristics of the landscape. The construction and analysis of the collective FCM offered further insights into the understanding of the system and allowed the analysis of its concepts by means of dynamic model inference. The FCM framework proved to be helpful in identifying and quantifying the factors interacting in the “mining-landscape-society” system and offered the ability to study the role and significance of central concepts in the overall system behaviour. In this sense, it is claimed that FCMs could significantly improve the domain of visual impact assessment related to mining activity. Nevertheless, much work remains to be done in order to improve the model and produce more reliable maps. Future efforts should be built on larger groups of experts from different disciplines as well as on non-experts who influence environmental decision-making.

Combining laboratory and mathematical models to infer mechanisms underlying kinetic changes in macrophage susceptibility to an RNA virus.

BackgroundMacrophages are essential to innate immunity against many pathogens, but some pathogens also target macrophages as routes to infection. The Porcine Reproductive and Respiratory Syndrome virus (PRRSV) is an RNA virus that infects porcine alveolar macrophages (PAMs) causing devastating impact on global pig production. Identifying the cellular mechanisms that mediate PAM susceptibility to the virus is crucial for developing effective interventions. Previous evidence suggests that the scavenger receptor CD163 is essential for productive infection of PAMs with PRRSV. Here we use an integrative in-vitro–in-silico modelling approach to determine whether and how PAM susceptibility to PRRSV changes over time, to assess the role of CD163 expression on such changes, and to infer other potential causative mechanisms altering cell susceptibility.ResultsOur in-vitro experiment showed that PAM susceptibility to PRRSV changed considerably over incubation time. Moreover, an increasing proportion of PAMs apparently lacking CD163 were found susceptible to PRRSV at the later incubation stages, thus conflicting with current understanding that CD163 is essential for productive infection of PAMs with PRRSV. We developed process based dynamic mathematical models and fitted these to the data to assess alternative hypotheses regarding potential underlying mechanisms for the observed susceptibility and biomarker trends. The models informed by our data support the hypothesis that although CD163 may have enhanced cell susceptibility, it was not essential for productive infection in our study. Instead the models promote the existence of a reversible cellular state, such as macrophage polarization, mediated in a density dependent manner by autocrine factors, to be responsible for the observed kinetics in cell susceptibility.ConclusionsOur dynamic model–inference approach provides strong support that PAM susceptibility to the PRRS virus is transient, reversible and can be mediated by compounds produced by the target cells themselves, and that these can render PAMs lacking the CD163 receptor susceptible to PRRSV. The results have implications for the development of therapeutics aiming to boost target cell resistance and prompt future investigation of dynamic changes in macrophage susceptibility to PRRSV and other viruses.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-016-0345-5) contains supplementary material, which is available to authorized users.

The Local Edge Machine: inference of dynamic models of gene regulation.

We present a novel approach, the Local Edge Machine, for the inference of regulatory interactions directly from time-series gene expression data. We demonstrate its performance, robustness, and scalability on in silico datasets with varying behaviors, sizes, and degrees of complexity. Moreover, we demonstrate its ability to incorporate biological prior information and make informative predictions on a well-characterized in vivo system using data from budding yeast that have been synchronized in the cell cycle. Finally, we use an atlas of transcription data in a mammalian circadian system to illustrate how the method can be used for discovery in the context of large complex networks.Electronic supplementary materialThe online version of this article (doi:10.1186/s13059-016-1076-z) contains supplementary material, which is available to authorized users.

Combined Parameter and State Estimation Problem in a Complex Domain: RF Hyperthermia Treatment Using Nanoparticles

The particle filter methods have been widely used to solve inverse problems with sequential Bayesian inference in dynamic models, simultaneously estimating sequential state variables and fixed model parameters. This methods are an approximation of sequences of probability distributions of interest, that using a large set of random samples, with presence uncertainties in the model, measurements and parameters. In this paper the main focus is the solution combined parameters and state estimation in the radiofrequency hyperthermia with nanoparticles in a complex domain. This domain contains different tissues like muscle, pancreas, lungs, small intestine and a tumor which is loaded iron oxide nanoparticles. The results indicated that excellent agreements between estimated and exact value are obtained.

Optimal Inference in Dynamic Models with Conditional Moment Restrictions

By an application of the theory of optimal estimating function, optimal instruments for dynamic models with conditional moment restrictions are derived. The general efficiency bound is provided, along with estimators attaining the bound. It is demonstrated that the optimal estimators are always at least as efficient as the traditional optimal generalized method of moments estimator, and usually more efficient. The form of our optimal instruments resembles that from Newey (1990), but involves conditioning on the history of the stochastic process. In the special case of i.i.d. observations, our optimal estimator reduces to Newey’s. Specification and hypothesis testing in our framework are introduced. We derive the theory of optimal instruments and the associated asymptotic distribution theory for general cases including non-martingale estimating functions and general history dependence. Examples involving time-varying conditional volatility and stochastic volatility are offered.

A maximum entropy approach to estimation and inference in dynamic models or Counting fish in the sea using maximum entropy

In this paper we consider estimation problems based on dynamic discrete time models. The first problem involves noisy state observations, where the state equation and the observation equation are nonlinear. The objective is to estimate the unknown parameters of the state and observation equations and the unknown values of the state variable. Next we consider the problem of estimating the parameters of the objective function and of the state equation in a linear-quadratic control problem. In each case, given time series observations, we suggest a nonlinear inversion procedure that permits the unknown underlying parameters to be estimated. Examples are presented to suggest the operational nature of the results.

Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances

We study the properties of the quasi-maximum likelihood estimator (QMLE) and related test statistics in dynamic models that jointly parameterize conditional means and conditional covariances, when a normal log-likelihood os maximized but the assumption of normality is violated. Because the score of the normal log-likelihood has the martingale difference property when the forst two conditional moments are correctly specified, the QMLE is generally Consistent and has a limiting normal destribution. We provide easily computable formulas for asymptotic standard errors that are valid under nonnormality. Further, we show how robust LM tests for the adequacy of the jointly parameterized mean and variance can be computed from simple auxiliary regressions. An appealing feature of these robyst inference procedures is that only first derivatives of the conditional mean and variance functions are needed. A monte Carlo study indicates that the asymptotic results carry over to finite samples. Estimation of several AR and AR-GARCH time series models reveals that in most sotuations the robust test statistics compare favorably to the two standard (nonrobust) formulations of the Wald and IM tests. Also, for the GARCH models and the sample sizes analyzed here, the bias in the QMLE appears to be relatively small. An empirical application to stock return volatility illustrates the potential imprtance of computing robust statistics in practice.

Inference in dynamic models containing ‘surprise’ variables

Abstract Some new results on calculating moving average representation (MAR) coefficients and their limiting distribution from estimated vector ARMA processes are presented. The technique is applied to the problem of estimating the coefficients of unanticipated or ‘surprise’ variables in a single equation for a multi-period expectations horizon. The method naturally conditions the expectations on all past values of the process and avoids the necessity of using two-step regression procedures and adjusting the resulting standard errors.