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C.d. Charalambous - One of the best experts on this subject based on the ideXlab platform.
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Exact filters for Newton–Raphson parameter estimation algorithms for continuous-time partially observed stochastic systems☆
Systems & Control Letters, 2001Co-Authors: C.d. Charalambous, J.l. HibeyAbstract:Abstract This paper presents explicit finite-dimensional filters for implementing Newton–Raphson (NR) parameter estimation algorithms. The models which exhibit nonlinear parameter dependence are stochastic, continuous-time and partially observed. The implementation of the NR algorithm requires evaluation of the log-Likelihood gradient and the Fisher information matrix. Fisher information matrices are important in bounding the estimation error from below, via the Cramer–Rao bound. The derivations are based on relations between inComplete and Complete Data, Likelihood, gradient and Hessian Likelihood functions, which are derived using Girsanov's measure transformations.
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Maximum Likelihood parameter estimation from inComplete Data via the sensitivity equations: the continuous-time case
Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251), 1999Co-Authors: C.d. CharalambousAbstract:The problem of estimating the parameters for continuous-time partially observed systems is discussed. New exact filters for obtaining maximum Likelihood (ML) parameter estimates via the expectation maximization algorithm are derived. The methodology exploits relations between inComplete and Complete Data Likelihood and gradient of Likelihood functions, which are derived using Girsanov's measure transformations. The ML parameter estimates are described by a set of Lyapunov sensitivity equations.
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Exact filters for Newton-Raphson parameter estimation algorithms for continuous-time partially observed stochastic systems
Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 1999Co-Authors: C.d. Charalambous, A. Logothetis, J.l. HibeyAbstract:This paper presents explicit finite-dimensional filters for implementing Newton-Raphson (NR) parameter estimation algorithms. The models which exhibit nonlinear parameter dependence are stochastic, continuous-time and partially observed. The implementation of the NR algorithm requires evaluation of the log-Likelihood gradient and the Fisher information matrix. Fisher information matrices are important in bounding the estimation error from below, via the Cramer-Rao bound. The derivations are based on relations between inComplete and Complete Data, Likelihood, gradient and Hessian Likelihood functions, which are derived using Girsanov's measure transformations.
Chris S Elphick - One of the best experts on this subject based on the ideXlab platform.
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application of the Complete Data Likelihood to estimate juvenile and adult survival for the endangered hawaiian stilt
Animal Conservation, 2015Co-Authors: J M Reed, Christopher R Field, Mike Silbernagle, Aaron Nadig, K Goebel, A Dibbenyoung, P Donaldson, Chris S ElphickAbstract:Applied ecologists routinely use demographic models to predict population trajectories. Survival rates throughout the life cycle, which are required for these models, are often difficult to obtain, especially for long-lived or mobile species. Detailed information for pre-adult age classes in particular is often lacking. Using a 20-year Dataset from several hundred individuals, we used Markov chain Monte Carlo methods to fit hierarchical models that describe survival rates for both adult and sub-adult Hawaiian stilts Himantopus mexicanus knudseni, an endangered island endemic. We constructed the Complete-Data Likelihood and used Data augmentation to estimate missing values and incorporate Data that were not collected during formal sampling. Survival estimates were lower and more uncertain during the first 2 months of life compared with the remainder of the first year. The probability of first-year survival averaged 0.55 (95% credibility interval: 0.07–0.90), but varied considerably among cohorts from different years and islands. Probability of adult annual survival differed little between females (0.79; 0.71–0.86) and males (0.80; 0.72–0.87), but increased as birds aged from 1 to 20 years (0.77–0.85). Our analysis confirms that earlier work, despite being based on few Data, provided good point estimates for survival rates. Our new analysis, however, provides the first comprehensive assessment of uncertainty in survival rates and detailed information on the nature of variation in first-year and adult survival. This information will help inform new demographic models and can be used to guide management actions.
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Application of the Complete‐Data Likelihood to estimate juvenile and adult survival for the endangered Hawaiian stilt
Animal Conservation, 2014Co-Authors: J M Reed, Christopher R Field, Mike Silbernagle, Aaron Nadig, K Goebel, P Donaldson, A. Dibben‐young, Chris S ElphickAbstract:Applied ecologists routinely use demographic models to predict population trajectories. Survival rates throughout the life cycle, which are required for these models, are often difficult to obtain, especially for long-lived or mobile species. Detailed information for pre-adult age classes in particular is often lacking. Using a 20-year Dataset from several hundred individuals, we used Markov chain Monte Carlo methods to fit hierarchical models that describe survival rates for both adult and sub-adult Hawaiian stilts Himantopus mexicanus knudseni, an endangered island endemic. We constructed the Complete-Data Likelihood and used Data augmentation to estimate missing values and incorporate Data that were not collected during formal sampling. Survival estimates were lower and more uncertain during the first 2 months of life compared with the remainder of the first year. The probability of first-year survival averaged 0.55 (95% credibility interval: 0.07–0.90), but varied considerably among cohorts from different years and islands. Probability of adult annual survival differed little between females (0.79; 0.71–0.86) and males (0.80; 0.72–0.87), but increased as birds aged from 1 to 20 years (0.77–0.85). Our analysis confirms that earlier work, despite being based on few Data, provided good point estimates for survival rates. Our new analysis, however, provides the first comprehensive assessment of uncertainty in survival rates and detailed information on the nature of variation in first-year and adult survival. This information will help inform new demographic models and can be used to guide management actions.
Brett T. Mcclintock - One of the best experts on this subject based on the ideXlab platform.
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Capture–recapture abundance estimation using a semi-Complete Data Likelihood approach
The Annals of Applied Statistics, 2016Co-Authors: Ruth King, Brett T. Mcclintock, Darren Kidney, David L. BorchersAbstract:Capture-recapture Data are often collected when abundance estimation is of interest. In the presence of unobserved individual heterogeneity, specified on a continuous scale for the capture probabilities, the Likelihood is not generally available in closed form, but expressible only as an analytically intractable integral. Model-fitting algorithms to estimate abundance most notably include a numerical approximation for the Likelihood or use of a Bayesian Data augmentation technique considering the Complete Data Likelihood. We consider a Bayesian hybrid approach, defining a "semi-Complete" Data Likelihood, composed of the product of a Complete Data Likelihood component for individuals seen at least once within the study and a marginal Data Likelihood component for the individuals not seen within the study, approximated using numerical integration. This approach combines the advantages of the two different approaches, with the semi-Complete Likelihood component specified as a single integral (over the dimension of the individual heterogeneity component). In addition, the models can be fitted within BUGS/JAGS (commonly used for the Bayesian Complete Data Likelihood approach) but with significantly improved computational efficiency compared to the commonly used super-population Data augmentation approaches (between about 10 and 77 times more efficient in the two examples we consider). The semi-Complete Likelihood approach is flexible and applicable to a range of models, including spatially explicit capture-recapture models. The model-fitting approach is applied to two different Datasets corresponding to the closed population model $M_h$ for snowshoe hare Data and a spatially explicit capture-recapture model applied to gibbon Data.
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capture recapture abundance estimation using a semi Complete Data Likelihood approach
The Annals of Applied Statistics, 2016Co-Authors: Ruth King, Brett T. Mcclintock, Darren Kidney, David L. BorchersAbstract:Capture–recapture Data are often collected when abundance estimation is of interest. In this manuscript we focus on abundance estimation of closed populations. In the presence of unobserved individual heterogeneity, specified on a continuous scale for the capture probabilities, the Likelihood is not generally available in closed form, but expressible only as an analytically intractable integral. Model-fitting algorithms to estimate abundance most notably include a numerical approximation for the Likelihood or use of a Bayesian Data augmentation technique considering the Complete Data Likelihood. We consider a Bayesian hybrid approach, defining a “semi-Complete” Data Likelihood, composed of the product of a Complete Data Likelihood component for individuals seen at least once within the study and a marginal Data Likelihood component for the individuals not seen within the study, approximated using numerical integration. This approach combines the advantages of the two different approaches, with the semi-Complete Likelihood component specified as a single integral (over the dimension of the individual heterogeneity component). In addition, the models can be fitted within BUGS/JAGS (commonly used for the Bayesian Complete Data Likelihood approach) but with significantly improved computational efficiency compared to the commonly used superpopulation Data augmentation approaches (between about 10 and 77 times more efficient in the two examples we consider). The semiComplete Likelihood approach is flexible and applicable to a range of models, including spatially explicit capture–recapture models. The model-fitting approach is applied to two different Data sets: the first relates to snowshoe hares where model Mh is applied and the second to gibbons where a spatially explicit capture–recapture model is applied.
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Capture-recapture abundance estimation using a semi-Complete Data Likelihood approach
The Annals of Applied Statistics, 2016Co-Authors: Ruth King, Brett T. Mcclintock, Darren Kidney, David L. BorchersAbstract:Capture-recapture Data are often collected when abundance estimation is of interest. In the presence of unobserved individual heterogeneity, specified on a continuous scale for the capture probabilities, the Likelihood is not generally available in closed form, but expressible only as an analytically intractable integral. Model-fitting algorithms to estimate abundance most notably include a numerical approximation for the Likelihood or use of a Bayesian Data augmentation technique considering the Complete Data Likelihood. We consider a Bayesian hybrid approach, defining a "semi-Complete" Data Likelihood, composed of the product of a Complete Data Likelihood component for individuals seen at least once within the study and a marginal Data Likelihood component for the individuals not seen within the study, approximated using numerical integration. This approach combines the advantages of the two different approaches, with the semi-Complete Likelihood component specified as a single integral (over the dimension of the individual heterogeneity component). In addition, the models can be fitted within BUGS/JAGS (commonly used for the Bayesian Complete Data Likelihood approach) but with significantly improved computational efficiency compared to the commonly used super-population Data augmentation approaches (between about 10 and 77 times more efficient in the two examples we consider). The semi-Complete Likelihood approach is flexible and applicable to a range of models, including spatially explicit capture-recapture models. The model-fitting approach is applied to two different Datasets corresponding to the closed population model $M_h$ for snowshoe hare Data and a spatially explicit capture-recapture model applied to gibbon Data.
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mark resight abundance estimation under inComplete identification of marked individuals
Methods in Ecology and Evolution, 2014Co-Authors: Brett T. Mcclintock, Jason M Hill, Lowell W Fritz, Kathryn Chumbley, Katie Luxa, Duane R DiefenbachAbstract:Summary Often less expensive and less invasive than conventional mark–recapture, so-called 'mark-resight' methods are popular in the estimation of population abundance. These methods are most often applied when a subset of the population of interest is marked (naturally or artificially), and non-invasive sighting Data can be simultaneously collected for both marked and unmarked individuals. However, it can often be difficult to identify marked individuals with certainty during resighting surveys, and inComplete identification of marked individuals is potentially a major source of bias in mark-resight abundance estimators. Previously proposed solutions are ad hoc and will tend to underperform unless marked individual identification rates are relatively high (>90%) or individual sighting heterogeneity is negligible. Based on a Complete Data Likelihood, we present an approach that properly accounts for uncertainty in marked individual detection histories when inComplete identifications occur. The models allow for individual heterogeneity in detection, sampling with (e.g. Poisson) or without (e.g. Bernoulli) replacement, and an unknown number of marked individuals. Using a custom Markov chain Monte Carlo algorithm to facilitate Bayesian inference, we demonstrate these models using two example Data sets and investigate their properties via simulation experiments. We estimate abundance for grassland sparrow populations in Pennsylvania, USA when sampling was conducted with replacement and the number of marked individuals was either known or unknown. To increase marked individual identification probabilities, extensive territory mapping was used to assign inComplete identifications to individuals based on location. Despite marked individual identification probabilities as low as 67% in the absence of this territorial mapping procedure, we generally found little return (or need) for this time-consuming investment when using our proposed approach. We also estimate rookery abundance from Alaskan Steller sea lion counts when sampling was conducted without replacement, the number of marked individuals was unknown, and individual heterogeneity was suspected as non-negligible. In terms of estimator performance, our simulation experiments and examples demonstrated advantages of our proposed approach over previous methods, particularly when marked individual identification probabilities are low and individual heterogeneity levels are high. Our methodology can also reduce field effort requirements for marked individual identification, thus, allowing potential investment into additional marking events or resighting surveys.
Pierre Latouche - One of the best experts on this subject based on the ideXlab platform.
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exact icl maximization in a non stationary temporal extension of the stochastic block model for dynamic networks
Neurocomputing, 2016Co-Authors: Marco Corneli, Pierre Latouche, Fabrice RossiAbstract:The stochastic block model (SBM) is a flexible probabilistic tool that can be used to model interactions between clusters of nodes in a network. However, it does not account for interactions of time varying intensity between clusters. The extension of the SBM developed in this paper addresses this shortcoming through a temporal partition: assuming interactions between nodes are recorded on fixed-length time intervals, the inference procedure associated with the model we propose allows to cluster simultaneously the nodes of the network and the time intervals. The number of clusters of nodes and of time intervals, as well as the memberships to clusters, are obtained by maximizing an exact integrated Complete-Data Likelihood, relying on a greedy search approach. Experiments on simulated and real Data are carried out in order to assess the proposed methodology.
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Model selection and clustering in stochastic block models based on the exact integrated Complete Data Likelihood
Statistical Modelling: An International Journal, 2015Co-Authors: E. Côme, Pierre LatoucheAbstract:The stochastic block model (SBM) is a mixture model for the clustering of nodes in networks. The SBM has now been employed for more than a decade to analyze very different types of networks in many...
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Variational Bayesian Inference and Complexity Control for Stochastic Block Models
arXiv: Applications, 2009Co-Authors: Pierre Latouche, Etienne Birmelé, Christophe AmbroiseAbstract:It is now widely accepted that knowledge can be acquired from networks by clustering their vertices according to connection profiles. Many methods have been proposed and in this paper we concentrate on the Stochastic Block Model (SBM). The clustering of vertices and the estimation of SBM model parameters have been subject to previous work and numerous inference strategies such as variational Expectation Maximization (EM) and classification EM have been proposed. However, SBM still suffers from a lack of criteria to estimate the number of components in the mixture. To our knowledge, only one model based criterion, ICL, has been derived for SBM in the literature. It relies on an asymptotic approximation of the Integrated Complete-Data Likelihood and recent studies have shown that it tends to be too conservative in the case of small networks. To tackle this issue, we propose a new criterion that we call ILvb, based on a non asymptotic approximation of the marginal Likelihood. We describe how the criterion can be computed through a variational Bayes EM algorithm.
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Bayesian methods for graph clustering
2009Co-Authors: Pierre Latouche, Etienne Birmelé, Christophe AmbroiseAbstract:It is now widely accepted that knowledge can be acquired from networks by clustering their vertices according to connection profiles. Many methods have been proposed and in this paper we concentrate on the Stochastic Block Model (SBM). The clustering of vertices and the estimation of SBM model parameters have been subject to previous work and numerous inference strategies such as variational Expectation Maximization (EM) and classification EM have been proposed. However, SBM still suffers from a lack of criteria to estimate the number of components in the mixture. To our knowledge, only one model based criterion, ICL, has been derived for SBM in the literature. It relies on an asymptotic approximation of the Integrated Complete-Data Likelihood and recent studies have shown that it tends to be too conservative in the case of small networks. To tackle this issue, we propose a new criterion that we call ILvb, based on a non asymptotic approximation of the marginal Likelihood. We describe how the criterion can be computed through a variational Bayes EM algorithm.
Zheng Wang - One of the best experts on this subject based on the ideXlab platform.
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Community Detection in Signed Networks Based on the Signed Stochastic Block Model and Exact ICL
IEEE Access, 2019Co-Authors: Shuqiu Ping, Dayou Liu, Bo Yang, Yungang Zhu, Hechang Chen, Zheng WangAbstract:There has been an increasing interest in detecting community in signed networks because signed networks contain more information (both positive and negative edges) than unsigned networks (only positive edges). Many methods have been proposed to find communities in signed networks; however, most of them can be regarded as the discriminative methods that do not concern with how the signed networks are generated so that they are usually difficult to characterize accurately the intrinsic community structure. The existing method SSL which is based on a generative model can achieve high accuracy in community detection in signed networks. However, SSL needs to estimate the models in the possible space one by one, which requires a large amount of calculation. In view of this, we propose a method to find community in signed networks, in which the exact integrated Complete Data Likelihood (ICLex) for the signed stochastic block model proposed in SSL is derived and a greedy search is employed to optimize the value of the derived ICLex for signed networks to find communities. Our method has a rigorous probabilistic interpretation and does not need to estimate the models one by one from the possible space. The knowledge on hyper-parameters of our model is not necessary. In the experiments, the proposed method is tested on the synthetic and real-world networks and compared with several current methods. The experimental results show that our method can find the communities in signed networks more accurately than these current methods and more efficiently than SSL.