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A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph visualizing and clustering. A latent space model of particular interest is the Random Dot Product Graph (RDPG), which can be fit using an efficient spectral method; however, this method is based on a heuristic that can fail, even in simple cases. Here, we consider a closely related latent space model, the Logistic RDPG, which uses a logistic link function to map from latent positions to edge likelihoods. Over this model, we show that asymptotically exact maximum likelihood inference of latent position vectors can be achieved using an efficient spectral method. Our method involves computing top eigenvectors of a normalized adjacency matrix and scaling eigenvectors using a regression step. The novel regression scaling step is an essential part of the proposed method. In simulations, we show that our proposed method is more accurate and more robust than common practices. We also show the effectiveness of our approach over standard real networks of the karate club and political blogs.

An empirical approach to model estimation and evaluation based on Bayesian Maximum Likelihood is introduced to the post-Keynesian literature. To illustrate the method, it is applied to a neo-Kaleckian type of model of Euro Area business cycle fluctuations including endogenous fiscal and monetary policy as well as endogenous wage formation. To evaluate its empirical performance, the marginal likelihood and impulse-responses conditional on the proposed model are contrasted to those conditional on the corresponding Bayesian vector auto-regression models after relaxing the theory-implied cross-coefficient restrictions. The estimated parameter distributions are broadly in line with the empirical literature. Yet, a Bayesian vector auto-regression with loose theory-implied restrictions on the prior outperforms the neo-Kaleckian model considerably indicating misspecification. Further, a baseline Dynamic Stochastic General Equilibrium model is superior in terms of the marginal likelihood. Comparative impulse-response analysis indicates a failure of the neo-Kaleckian model to satisfyingly capture the fiscal and monetary policy transmission mechanisms. ; Ein bayesianischer Maximum-Likelihood-Ansatz zur Modellschätzung und -evaluierung wird in die postkeynesianische Literatur eingeführt. Um die Methode zu illustrieren, wird sie an einem neokaleckianischen Konjunkturzyklusmodell für die Eurozone inklusive Fiskalpolitik, Geldpolitik sowie einer endogenen Lohnbestimmung angewandt. Um die empirische Leistungsfähigkeit des Modells zu evaluieren, werden die marginale Verteilung und Impuls-Reaktionen bedingt auf das vorgeschlagene Model jenen gegenübergestellt, die auf die entsprechenden bayesianischen Vektor-Autoregressionen nach Lockerung der theorie-induzierten Parameterrestriktionen bedingt sind. Die geschätzten Parameterverteilungen stehen weitgehend im Einklang mit der empirischen Literatur. Dennoch übertreffen die bayesianischen Vektor-Autoregressionen mit nur losen theorie-induzierten Parameterrestriktionen der a-priori Wahrscheinlichkeiten das neokaleckianische Model erheblich, was eine Fehlspezifikation des letzteren anzeigt. Darüber hinaus ist ein einfaches Allgemeines Gleichgewichtsmodell überlegen, gemessen an der marginalen Verteilung. Eine vergleichende Analyse der Impuls-Reaktionen suggeriert, dass ein großer Teil der Fehlspezifikation des neokaleckianischen Modells darin begründet liegt, dass es die fiskal- und geldpolitischen Transmissionsmechanismen nicht zufriedenstellend erfassen kann.

Networks of social and economic interactions are often influenced by unobserved structures among the nodes. Based on a simple model of how an unobserved community structure generates networks of interactions, we axiomatize a method of detecting the latent community structures from network data. The method is based on maximum likelihood estimation.

This is the author's version of a work that was accepted for publication in Signal Processing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Signal Processing, volume 175, october 2020, 107661; DOI 10.1016/j.sigpro.2020.107661. ; [EN] Hard-Output Maximum Likelihood (ML) detection for Generalized Spatial Modulation (GSM) systems involves obtaining the ML solution of a number of different MIMO subproblems, with as many possible antenna configurations as subproblems. Obtaining the ML solution of all of the subproblems has a large computational complexity, especially for large GSM MIMO systems. In this paper, we present two techniques for reducing the computational complexity of GSM ML detection. The first technique is based on computing a box optimization bound for each subproblem. This, together with sequential processing of the subproblems, allows fast discarding of many of these subproblems. The second technique is to use a Sphere Detector that is based on box optimization for the solution of the subproblems. This Sphere Detector reduces the number of partial solutions explored in each subproblem. The experiments show that these techniques are very effective in reducing the computational complexity in large MIMO setups. ; This work has been partially supported by Spanish Ministry of Science, Innovation and Universities and by European Union through grant RTI2018-098085-BC41 (MCUI/AEI/FEDER), by GVA through PROMETEO/2019/109 and by Catedra Telefonica-UPV through SSENCE project. ; García Mollá, VM.; Martínez Zaldívar, FJ.; Simarro, MA.; Gonzalez, A. (2020). Maximum likelihood low-complexity GSM detection for large MIMO systems. Signal Processing. 175:1-11. https://doi.org/10.1016/j.sigpro.2020.107661 ; S ; 1 ; 11 ; 175

Based on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood/Fisherian method of taking account of uncertainty when studying a statistical problem. It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference. Every likelihood concept is illustrated by realistic examples, which are not compromised by computational problems. Examples range from asimile comparison of two accident rates, to complex studies that require generalised linear or semiparametric mode

In this article, we construct two likelihood‐based confidence intervals (CIs) for a binomial proportion parameter using a double‐sampling scheme with misclassified binary data. We utilize an easy‐to‐implement closed‐form algorithm to obtain maximum likelihood estimators of the model parameters by maximizing the full‐likelihood function. The two CIs are a naïve Wald interval and a modified Wald interval. Using simulations, we assess and compare the coverage probabilities and average widths of our two CIs. Finally, we conclude that the modified Wald interval, unlike the naïve Wald interval, produces close‐to‐nominal CIs under various simulations and, thus, is preferred in practice. Utilizing the expressions derived, we also illustrate our two CIs for a binomial proportion parameter using real‐data example.

Quantitative comparative social scientists have long worried about the performance of multilevel models when the number of upper-level units is small. Adding to these concerns, an influential Monte Carlo study by Stegmueller (2013) suggests that standard maximum-likelihood (ML) methods yield biased point estimates and severely anti-conservative inference with few upper-level units. In this article, the authors seek to rectify this negative assessment. First, they show that ML estimators of coefficients are unbiased in linear multilevel models. The apparent bias in coefficient estimates found by Stegmueller can be attributed to Monte Carlo Error and a flaw in the design of his simulation study. Secondly, they demonstrate how inferential problems can be overcome by using restricted ML estimators for variance parameters and a t-distribution with appropriate degrees of freedom for statistical inference. Thus, accurate multilevel analysis is possible within the framework that most practitioners are familiar with, even if there are only a few upper-level units.