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Open accessJournal ArticleDOI: 10.1080/00273171.2020.1730150

Interpreting the Ising Model: The Input Matters

04 Mar 2021-Multivariate Behavioral Research (Routledge)-Vol. 56, Iss: 2, pp 303-313
Abstract: The Ising model is a model for pairwise interactions between binary variables that has become popular in the psychological sciences. It has been first introduced as a theoretical model for the alig...

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Topics: Ising model (61%), Pairwise comparison (51%), Dynamical systems theory (51%) ... show more

10 results found

Open accessPosted ContentDOI: 10.1037/MET0000303
Abstract: This dissertation deals with the problem of modeling psychopathology. Its first part focuses on statistical (data) models and introduces a number of models for cross-sectional and time series data that can be visualized as a network. This includes Mixed Graphical Models (MGMs), which allow one to include variables of different types in a statistical network model, Moderated Network Models (MNMs) which allow pairwise interactions to be moderated by other variables in the model, and time-varying Vector Autoregressive (VAR) models and MGMs that relax the standard assumption of stationarity. In addition, I discuss several methodological issues related to statistical network models such as the importance of considering predictability, model selection between AR and VAR models, and how the interpretation of the Ising model depends on its domain. The second part focuses on formal theories of psychopathology and how to develop them using data models. I first illustrate the fundamental difficulties in obtaining a formal theory with a purely statistical approach, by trying to recover an assumed bistable system for emotion dynamics with currently popular time series analyses. Next, I present a formal theory of panic disorder, based on an extensive review of the literature on the phenomenology of panic disorder and existing theories. Finally, I discuss three different ways to use data models to construct formal theories about psychopathological phenomena. Based on this discussion, I put forward an abductive framework for constructing formal theories for psychological and psychopathological phenomena.

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Topics: Data modeling (52%), Model selection (52%), Theory (52%) ... show more

35 Citations

Open accessJournal ArticleDOI: 10.1002/PER.2263
Abstract: Network theories have been put forward for psychopathology (in which mental disorders originate from causal relations between symptoms) and for personality (in which personality factors originate f...

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Topics: Personality (60%), Psychopathology (54%), Context (language use) (53%) ... show more

9 Citations

Open accessBook ChapterDOI: 10.1007/978-3-030-18480-3_5
01 Jan 2019-
Abstract: In network psychometrics undirected graphical models—such as the Ising model from statistical physics—are used to characterize the manifest probability distribution of psychometric data. In practice, we often find that it is extremely difficult to apply graphical models as the Ising model to educational data because (i) the model’s likelihood is impossible to compute for the big data that we typically observe in educational measurement, and (ii) the model cannot handle the partially observed data that stem from incomplete test designs. In this chapter, we therefore propose to use a simplified Ising model that is known as the Curie-Weiss model. Unlike the more general Ising model, the Curie-Weiss model is computationally tractable, which makes it suitable for applications in educational measurement. The objective of this chapter is to study the statistical properties of the Curie-Weiss model and discuss its estimation with complete or incomplete data. We demonstrate that our procedures work using a simulated example, and illustrate the analysis of fit of the Curie-Weiss model using real data from the 2012 Cito Eindtoets.

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Topics: Graphical model (57%), Ising model (54%), Rasch model (50%)

4 Citations

Open accessJournal ArticleDOI: 10.3389/FPSYT.2021.640658
Abstract: Inspired by modeling approaches from the ecosystems literature, in this paper, we expand the network approach to psychopathology with risk and protective factors to arrive at an integrated analysis of resilience. We take a complexity approach to investigate the multifactorial nature of resilience and present a system in which a network of interacting psychiatric symptoms is targeted by risk and protective factors. These risk and protective factors influence symptom development patterns and thereby increase or decrease the probability that the symptom network is pulled towards a healthy or disorder state. In this way, risk and protective factors influence the resilience of the network. We take a step forward in formalizing the proposed system by implementing it in a statistical model and translating different influences from risk and protective factors to specific targets on the node and edge parameters of the symptom network. To analyze the behavior of the system under different targets, we present two novel network resilience metrics: Expected Symptom Activity (ESA, which indicates how many symptoms are active or inactive) and Symptom Activity Stability (SAS, which indicates how stable the symptom activity patterns are). These metrics follow standard practices in the resilience literature, combined with ideas from ecology and physics, and characterize resilience in terms of the stability of the system’s healthy state. By discussing the advantages and limitations of our proposed system and metrics, we provide concrete suggestions for the further development of a comprehensive modeling approach to study the complex relationship between risk and protective factors and resilience.

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Topics: Resilience (network) (62%)

3 Citations

Open accessJournal ArticleDOI: 10.3390/MATH9060614
15 Mar 2021-
Abstract: Gini covariance plays a vital role in analyzing the relationship between random variables with heavy-tailed distributions. In this papaer, with the existence of a finite second moment, we establish the Gini–Yule–Walker equation to estimate the transition matrix of high-dimensional periodic vector autoregressive (PVAR) processes, the asymptotic results of estimators have been established. We apply this method to study the Granger causality of the heavy-tailed PVAR process, and the results show that the robust transfer matrix estimation induces sign consistency in the value of Granger causality. Effectiveness of the proposed method is verified by both synthetic and real data.

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Topics: Covariance (57%), Covariance matrix (55%), Autoregressive model (53%) ... show more

1 Citations


27 results found

Open accessJournal ArticleDOI: 10.1214/AOS/1176344136
Abstract: The problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion. These terms are a valid large-sample criterion beyond the Bayesian context, since they do not depend on the a priori distribution.

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Topics: Bayesian information criterion (57%), g-prior (55%), Bayes' theorem (55%) ... show more

35,659 Citations

Open access
01 Jan 2005-
Abstract: The problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion. These terms are a valid large-sample criterion beyond the Bayesian context, since they do not depend on the a priori distribution.

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Topics: Bayes' theorem (56%), Context (language use) (54%), Asymptotic expansion (54%) ... show more

33,801 Citations

Open accessBook
16 Dec 2008-
Abstract: The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide variety of algorithms — among them sum-product, cluster variational methods, expectation-propagation, mean field methods, max-product and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.

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Topics: Variational message passing (62%), Exponential random graph models (61%), Graphical model (58%) ... show more

3,969 Citations

Journal ArticleDOI: 10.1063/1.1703954
Abstract: The individual spins of the Ising model are assumed to interact with an external agency (e.g., a heat reservoir) which causes them to change their states randomly with time. Coupling between the spins is introduced through the assumption that the transition probabilities for any one spin depend on the values of the neighboring spins. This dependence is determined, in part, by the detailed balancing condition obeyed by the equilibrium state of the model. The Markoff process which describes the spin functions is analyzed in detail for the case of a closed N‐member chain. The expectation values of the individual spins and of the products of pairs of spins, each of the pair evaluated at a different time, are found explicitly. The influence of a uniform, time‐varying magnetic field upon the model is discussed, and the frequency‐dependent magnetic susceptibility is found in the weak‐field limit. Some fluctuation‐dissipation theorems are derived which relate the susceptibility to the Fourier transform of the time‐dependent correlation function of the magnetization at equilibrium.

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2,708 Citations

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