scholarly journals Bayesian graph selection consistency under model misspecification

Bernoulli ◽  
2021 ◽  
Vol 27 (1) ◽  
pp. 637-672
Author(s):  
Yabo Niu ◽  
Debdeep Pati ◽  
Bani K. Mallick
Keyword(s):  
Model Misspecification ◽  
Selection Consistency

scholarly journals Use of the Lagrange Multiplier Test for Assessing Measurement Invariance Under Model Misspecification

2021 ◽  
pp. 001316442110203
Author(s):  
Lucia Guastadisegni ◽  
Silvia Cagnone ◽  
Irini Moustaki ◽  
Vassilis Vasdekis
Keyword(s):  
Lagrange Multiplier ◽  
False Positive ◽  
Latent Variable ◽  
Model Misspecification ◽  
Cross Product ◽  
Small Sample ◽  
Type I ◽  
Local Dependence ◽  
Lagrange Multiplier Test ◽  
Product Approach

This article studies the Type I error, false positive rates, and power of four versions of the Lagrange multiplier test to detect measurement noninvariance in item response theory (IRT) models for binary data under model misspecification. The tests considered are the Lagrange multiplier test computed with the Hessian and cross-product approach, the generalized Lagrange multiplier test and the generalized jackknife score test. The two model misspecifications are those of local dependence among items and nonnormal distribution of the latent variable. The power of the tests is computed in two ways, empirically through Monte Carlo simulation methods and asymptotically, using the asymptotic distribution of each test under the alternative hypothesis. The performance of these tests is evaluated by means of a simulation study. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the tests performance deteriorates, especially for false positive rates under local dependence and power for small sample size under misspecification of the latent variable distribution. In general, the Lagrange multiplier test computed with the Hessian approach and the generalized Lagrange multiplier test have better performance in terms of false positive rates while the Lagrange multiplier test computed with the cross-product approach has the highest power for small sample sizes. The asymptotic power turns out to be a good alternative to the classic empirical power because it is less time consuming. The Lagrange tests studied here have been also applied to a real data set.

scholarly journals Distance-Based Estimation Methods for Models for Discrete and Mixed-Scale Data

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 107
Author(s):  
Elisavet M. Sofikitou ◽  
Ray Liu ◽  
Huipei Wang ◽  
Marianthi Markatou
Keyword(s):  
Data Model ◽  
Null Hypothesis ◽  
Model Misspecification ◽  
Asymptotic Properties ◽  
Estimation Methods ◽  
Measurement Scale ◽  
Interval Scale ◽  
Pearson Residuals ◽  
Using Data ◽  
Scale Data

Pearson residuals aid the task of identifying model misspecification because they compare the estimated, using data, model with the model assumed under the null hypothesis. We present different formulations of the Pearson residual system that account for the measurement scale of the data and study their properties. We further concentrate on the case of mixed-scale data, that is, data measured in both categorical and interval scale. We study the asymptotic properties and the robustness of minimum disparity estimators obtained in the case of mixed-scale data and exemplify the performance of the methods via simulation.

scholarly journals PAC-Bayes Bounds on Variational Tempered Posteriors for Markov Models

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 313
Author(s):  
Imon Banerjee ◽  
Vinayak A. Rao ◽  
Harsha Honnappa
Keyword(s):  
Markov Model ◽  
Markov Models ◽  
Model Misspecification ◽  
Dependence Structure ◽  
Posterior Distributions ◽  
Ergodic Properties ◽  
Variational Approximations ◽  
Popular View ◽  
Probably Approximately Correct ◽  
Risk Bounds

Datasets displaying temporal dependencies abound in science and engineering applications, with Markov models representing a simplified and popular view of the temporal dependence structure. In this paper, we consider Bayesian settings that place prior distributions over the parameters of the transition kernel of a Markov model, and seek to characterize the resulting, typically intractable, posterior distributions. We present a Probably Approximately Correct (PAC)-Bayesian analysis of variational Bayes (VB) approximations to tempered Bayesian posterior distributions, bounding the model risk of the VB approximations. Tempered posteriors are known to be robust to model misspecification, and their variational approximations do not suffer the usual problems of over confident approximations. Our results tie the risk bounds to the mixing and ergodic properties of the Markov data generating model. We illustrate the PAC-Bayes bounds through a number of example Markov models, and also consider the situation where the Markov model is misspecified.

scholarly journals Inference for copula modeling of discrete data: a cautionary tale and some facts

2017 ◽  
Vol 5 (1) ◽  
pp. 121-132 ◽  
Author(s):  
Olivier P. Faugeras
Keyword(s):  
Model Misspecification ◽  
Discrete Data ◽  
Cautionary Tale ◽  
Copula Models ◽  
Problematic Use ◽  
Copula Modeling ◽  
Copula Parameter ◽  
Parametric Copula

AbstractIn this note, we elucidate some of the mathematical, statistical and epistemological issues involved in using copulas to model discrete data. We contrast the possible use of (nonparametric) copula methods versus the problematic use of parametric copula models. For the latter, we stress, among other issues, the possibility of obtaining impossible models, arising from model misspecification or unidentifiability of the copula parameter.

Using management strategy evaluation to establish indicators of changing fisheries

2019 ◽  
Vol 76 (9) ◽  
pp. 1653-1668 ◽  
Author(s):  
T.R. Carruthers ◽  
A.R. Hordyk
Keyword(s):  
Management Strategy ◽  
Statistical Power ◽  
Stock Assessment ◽  
Model Misspecification ◽  
Management Approach ◽  
Data Types ◽  
Quality Of Data ◽  
Management Strategy Evaluation ◽  
Strategy Evaluation ◽  
Management Procedures

A new indicator is described that uses multivariate posterior predictive data arising from management strategy evaluation (MSE) to detect operating model misspecification (exceptional circumstances) due to changing system dynamics. The statistical power of the indicator was calculated for five case studies for which fishery stock assessments have estimated changes in recruitment, natural mortality rate, growth, fishing efficiency, and size selectivity. The importance of the component data types that inform the indicator was also calculated. The indicator was tested for multiple types of management procedures (e.g., catch limits by stock assessment, size limits, spatial closures) given varying qualities of data. The statistical power of the indicator could be high even over short time periods and depended on the type of system change and quality of data. Statistical power depended strongly on the type of management approach, suggesting that indicators should be established that rigorously account for feedbacks between proposed management and observed data. MSE processes should use alternative operating models to evaluate protocols for exceptional circumstances to ensure they are of acceptable statistical power.

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