An alternative quasi likelihood approach, Bayesian analysis and data-based inference for model specification

RNA-seq has been an increasingly popular high-throughput platform to identify differentially expressed (DE) genes, which is much more reproducible and accurate than the previous microarray technology. Yet, a number of statistical issues remain to be resolved in data analysis, largely due to the high-throughput data volume and over-dispersion of read counts. These problems become more challenging for those biologists who use RNA-seq to measure genome-wide expression profiles in different combinations of sampling resources (species or genotypes) or treatments. In this paper, the author first reviews the statistical methods available for detecting DE genes, which have implemented negative binomial (NB) models and/or quasi-likelihood (QL) approaches to account for the over-dispersion problem in RNA-seq samples. The author then studies how to carry out the DE test in the context of phylogeny, i.e., RNA-seq samples are from a range of species as phylogenetic replicates. The author proposes a computational framework to solve this phylo-DE problem: While an NB model is used to account for data over-dispersion within biological replicates, over-dispersion among phylogenetic replicates is taken into account by QL, plus some special treatments for phylogenetic bias. This work helps to design cost-effective RNA-seq experiments in the field of biodiversity or phenotype plasticity that may involve hundreds of species under a phylogenetic framework.

Appropriate model specification is fundamental to unbiased parameter estimates and accurate model interpretations in structural equation modeling. Thus detecting potential model misspecification has drawn the attention of many researchers. This simulation study evaluates the efficacy of the Bayesian approach (the posterior predictive checking, or PPC procedure) under multilevel bifactor model misspecification (i.e., ignoring a specific factor at the within level). The impact of model misspecification on structural coefficients was also examined in terms of bias and power. Results showed that the PPC procedure performed better in detecting multilevel bifactor model misspecification, when the misspecification became more severe and sample size was larger. Structural coefficients were increasingly negatively biased at the within level, as model misspecification became more severe. Model misspecification at the within level affected the between-level structural coefficient estimates more when data dependency was lower and the number of clusters was smaller. Implications for researchers are discussed.

Quasi Maximum Likelihood Estimation of Value at Risk and Expected Shortfall

It is well known that, in misspecified parametric models, the maximum likelihood estimator (MLE) is consistent for the pseudo-true value and has an asymptotically normal sampling distribution with “sandwich” covariance matrix. Also, posteriors are asymptotically centered at the MLE, normal, and of asymptotic variance that is, in general, different than the sandwich matrix. It is shown that due to this discrepancy, Bayesian inference about the pseudo-true parameter value is, in general, of lower asymptotic frequentist risk when the original posterior is substituted by an artificial normal posterior centered at the MLE with sandwich covariance matrix. An algorithm is suggested that allows the implementation of this artificial posterior also in models with high dimensional nuisance parameters which cannot reasonably be estimated by maximizing the likelihood.

Event Abstract Back to Event 2nd level modelling in fMRI analysis with a clinically depressed sample - Comparisons between classical and Bayesian methods Peter Goodin1, 2*, Joseph Ciorciari1, Susan Rossell1, 2, Matt Hughes1 and Richard Nibbs1 1 Swinburne University, BPsyC, Australia 2 Monash Alfred Psychiatric Research Centre, Australia The use of the Frequentist statistics in fMRI analysis has been the mainstay of the field for the last 25 years. Several other methods have been developed as alternatives, including those based on Bayesian statistics. Bayesian analysis methods have the benefit of allowing interrelation of data through effect size and confidence thresholds, can be more robust to outlier data and may negate the need for stringent multiple comparison correction. When examining functional differences in those with a mental illness , this can lead to detection of more subtle activation that may be of importance. Depression is a disorder that despite a common theme of symptoms is also characterised by functional heterogeneities between individuals, making inferences using Frequentist methods sometimes difficult. Utilising both Frequentist and Bayesian 2nd level analysis methods offered by SPM8 , we examined differences in activation between a healthy control sample and those with major depressive disorder during a novel emotional processing n-back task. Activation using classical methods showed small differences in more posterior visual regions however this was only detectable with liberal thresholding (p = .001 uncorrected, k = 0). In contrast Bayesian analysis (y = 0, 95% confidence) uncovered widespread differences (including overlap with those areas found with the Frequentist method) in multiple regions implicated with the disorder. This suggests that using Bayesian methods in fMRI analysis with a clinical population could be extremely useful in detecting responses that may otherwise go unnoticed or under-represented in more traditional methods, however determination of effect size importance is paramount. Keywords: Depression, fMRI, working memory, Bayesian, Frequentist Conference: XII International Conference on Cognitive Neuroscience (ICON-XII), Brisbane, Queensland, Australia, 27 Jul - 31 Jul, 2014. Presentation Type: Poster Topic: Methods Development Citation: Goodin P, Ciorciari J, Rossell S, Hughes M and Nibbs R (2015). 2nd level modelling in fMRI analysis with a clinically depressed sample - Comparisons between classical and Bayesian methods. Conference Abstract: XII International Conference on Cognitive Neuroscience (ICON-XII). doi: 10.3389/conf.fnhum.2015.217.00203 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 19 Feb 2015; Published Online: 24 Apr 2015. * Correspondence: Mr. Peter Goodin, Swinburne University, BPsyC, Hawthorn, Australia, peter@hitiq.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Peter Goodin Joseph Ciorciari Susan Rossell Matt Hughes Richard Nibbs Google Peter Goodin Joseph Ciorciari Susan Rossell Matt Hughes Richard Nibbs Google Scholar Peter Goodin Joseph Ciorciari Susan Rossell Matt Hughes Richard Nibbs PubMed Peter Goodin Joseph Ciorciari Susan Rossell Matt Hughes Richard Nibbs Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

This chapter studies the estimation problem for a linear model. The first four sections are fairly classical and the presented results are based on the direct analysis of the linear estimation procedures. Sections 4.5 and 4.6 reproduce in a very short form the same results but now based on the likelihood analysis. The presentation is based on the celebrated chi-squared phenomenon which appears to be the fundamental fact yielding the exact likelihood-based concentration and confidence properties. The further sections are complementary and can be recommended for a more profound reading. The issues like regularization, shrinkage, smoothness, and roughness are usually studied within the nonparametric theory; here we try to fit them to the classical linear parametric setup. A special focus is on semiparametric estimation in Sect. 4.9. In particular, efficient estimation and chi-squared result are extended to the semiparametric framework.The main tool of the study is the quasi maximum likelihood method. We especially focus on the validity of the presented results under possible model misspecification. Another important issue is the way of measuring the estimation loss and risk. We distinguish below between response estimation or prediction and the parameter estimation. The most advanced results like chi-squared result in Sect. 4.6 are established under the assumption of a Gaussian noise. However, a misspecification of noise structure is allowed and addressed.

The consistency of propensity score (PS) estimators relies on correct specification of the PS model. The PS is frequently estimated using main-effects logistic regression. However, the underlying model assumptions may not hold. Machine learning methods provide an alternative nonparametric approach to PS estimation. In this simulation study, we evaluated the benefit of using Super Learner (SL) for PS estimation. We created 1,000 simulated data sets (n = 500) under 4 different scenarios characterized by various degrees of deviance from the usual main-term logistic regression model for the true PS. We estimated the average treatment effect using PS matching and inverse probability of treatment weighting. The estimators' performance was evaluated in terms of PS prediction accuracy, covariate balance achieved, bias, standard error, coverage, and mean squared error. All methods exhibited adequate overall balancing properties, but in the case of model misspecification, SL performed better for highly unbalanced variables. The SL-based estimators were associated with the smallest bias in cases of severe model misspecification. Our results suggest that use of SL to estimate the PS can improve covariate balance and reduce bias in a meaningful manner in cases of serious model misspecification for treatment assignment.

Shared features of economic and climate time series imply that tools for empirically modeling nonstationary economic outcomes are also appropriate for studying many aspects of observational climate-change data. Greenhouse gas emissions, such as carbon dioxide, nitrous oxide, and methane, are a major cause of climate change as they cumulate in the atmosphere and reradiate the sun’s energy. As these emissions are currently mainly due to economic activity, economic and climate time series have commonalities, including considerable inertia, stochastic trends, and distributional shifts, and hence the same econometric modeling approaches can be applied to analyze both phenomena. Moreover, both disciplines lack complete knowledge of their respective data-generating processes (DGPs), so model search retaining viable theory but allowing for shifting distributions is important. Reliable modeling of both climate and economic-related time series requires finding an unknown DGP (or close approximation thereto) to represent multivariate evolving processes subject to abrupt shifts. Consequently, to ensure that DGP is nested within a much larger set of candidate determinants, model formulations to search over should comprise all potentially relevant variables, their dynamics, indicators for perturbing outliers, shifts, trend breaks, and nonlinear functions, while retaining well-established theoretical insights. Econometric modeling of climate-change data requires a sufficiently general model selection approach to handle all these aspects. Machine learning with multipath block searches commencing from very general specifications, usually with more candidate explanatory variables than observations, to discover well-specified and undominated models of the nonstationary processes under analysis, offers a rigorous route to analyzing such complex data. To do so requires applying appropriate indicator saturation estimators (ISEs), a class that includes impulse indicators for outliers, step indicators for location shifts, multiplicative indicators for parameter changes, and trend indicators for trend breaks. All ISEs entail more candidate variables than observations, often by a large margin when implementing combinations, yet can detect the impacts of shifts and policy interventions to avoid nonconstant parameters in models, as well as improve forecasts. To characterize nonstationary observational data, one must handle all substantively relevant features jointly: A failure to do so leads to nonconstant and mis-specified models and hence incorrect theory evaluation and policy analyses.

Parsimonious estimation of high-dimensional covariance matrices is of fundamental importance in multivariate statistics. Typical examples occur in finance, where the instantaneous dependence among several asset returns should be taken into account. Multivariate GARCH processes have been established as a standard approach for modelling such data. However, the majority of GARCH-type models are either based on strong assumptions that may not be realistic or require restrictions that are often too hard to be satisfied in practice. We consider two alternative decompositions of time-varying covariance matrices [Formula: see text]. The first is based on the modified Cholesky decomposition of the covariance matrices and second relies on the hyperspherical parametrization of the standard Cholesky factor of their correlation matrices [Formula: see text]. Then, we combine each Cholesky factor with the log-GARCH models for the corresponding time–varying volatilities and use a quasi maximum likelihood approach to estimate the parameters. Using log-GARCH models is quite natural for achieving the positive definiteness of [Formula: see text] and this is a novelty of this work. Application of the proposed methodologies to two real financial datasets reveals their usefulness in terms of parsimony, ease of implementation and stresses the choice of the appropriate models using familiar data-driven processes such as various forms of the exploratory data analysis and regression.

Two competitive analytical approaches, namely, the generalized method of moments (GMM) and quasi-maximum likelihood (QML) are widely used in statistics and econometrics literature for inferences in stochastic volatility models (SVMs). Alternative numerical approaches such as monte carlo markov chain (MCMC), simulated maximum likelihood (SML) and Bayesian approaches are also available. All these later approaches are, however, based on simulations. In this paper, we revisit the analytical estimation approaches and briefly demonstrate that the existing GMM approach is unnecessarily complicated. Also, the asymptotic properties of the likelihood approximation based QML approach are unknown and the finite sample based QML estimators can be inefficient. We then develop a precise set of moment estimating equations and demonstrate that the proposed method of moments (MM) estimators are easy to compute and they perform well in estimating the parameters of the SVMs in both small and large time series set up. A ‘working’ generalized quasi-likelihood (WGQL) estimation approach is also considered. Estimation methods are illustrated by reanalyzing a part of the Swiss-Franc and U.S. dollar exchange rates data.

We tested whether it is beneficial for the accuracy of phylogenetic inference to sample characters that are evolving under different sets of parameters, using both Bayesian MCMC (Markov chain Monte Carlo) and parsimony approaches. We examined differential rates of evolution among characters, differential character-state frequencies and character-state space, and differential relative branch lengths among characters. We also compared the relative performance of parsimony and Bayesian analyses by progressively incorporating more of these heterogeneous parameters and progressively increasing the severity of this heterogeneity. Bayesian analyses performed better than parsimony when heterogeneous simulation parameters were incorporated into the substitution model. However, parsimony outperformed Bayesian MCMC when heterogeneous simulation parameters were not incorporated into the Bayesian substitution model. The higher the rate of evolution simulated, the better parsimony performed relative to Bayesian analyses. Bayesian and parsimony analyses converged in their performance as the number of simulated heterogeneous model parameters increased. Up to a point, rate heterogeneity among sites was generally advantageous for phylogenetic inference using both approaches. In contrast, branch-length heterogeneity was generally disadvantageous for phylogenetic inference using both parsimony and Bayesian approaches. Parsimony was found to be more conservative than Bayesian analyses, in that it resolved fewer incorrect clades.

We consider a model for a multivariate time series where the conditional covariance matrix is a function of a finite-dimensional parameter and the innovation distribution is nonparametric. The semiparametric lower bound for the estimation of the euclidean parameter is characterized, and it is shown that adaptive estimation without reparametrization is not possible. Based on a consistent first-stage estimator (such as quasi maximum likelihood), we propose a semiparametric estimator that estimates the efficient influence function using kernel estimators. We state conditions under which the estimator attains the semiparametric lower bound. For particular models such as the constant conditional correlation model, adaptive estimation of the dynamic part of the model is shown to be possible. To avoid the curse of dimensionality one can, e.g., restrict the multivariate density to the class of spherical distributions, for which we also derive the semiparametric efficiency bound and an estimator that attains this bound. A simulation experiment demonstrates the efficiency gain of the proposed estimator compared with quasi maximum likelihood estimation.Rombouts work was supported by the Centre for Research on e-Finance, HEC Montreal. Hafner gratefully acknowledges financial support by the Fonds Sp ciaux de Recherche (FSR 05) of the Universit catholique de Louvain. The authors thank three anonymous referees for valuable comments and suggestions and Luc Bauwens, Geert Dhaene, Feico Drost, Wolfgang H rdle, Douglas Hodgson, Jens Peter Kreiss, Oliver Linton, and Bas Werker for helpful discussions. We also thank participants of the CORE econometrics seminar, the York annual meeting in econometrics, the annual econometric study group meeting 2002 in Bristol, the 2003 workshop The Art of Semiparametrics in Berlin, and the statistics seminar of the Stockholm School of Economics for valuable comments.

This paper examines the estimation of the Stochastic Conditional Duration model by the empirical characteristic function and the generalized method of moments when maximum likelihood is unavailable. The joint characteristic function for the durations along with general expressions for the moments are derived, leading naturally to estimation via the empirical characteristic function and generalized method of moments. In a Monte Carlo study as well as an empirical application, these alternative methods are compared with quasi maximum likelihood. These experiments reveal that the empirical characteristic function approach outperforms the quasi maximum likelihood and generalized method of moments in terms of both bias and root mean square error. Copyright The Author(s). Journal compilation Royal Economic Society 2008

Contributors

Traditionally, reliability assessment of devices has been based on (accelerated) life tests. However, for highly reliable products, little information about reliability is provided by life tests in which few or no failures are typically observed. Since most failures arise from a degradation mechanism at work for which there are characteristics that degrade over time, one alternative is monitor the device for a period of time and assess its reliability from the changes in performance (degradation) observed during that period. The goal of this article is to illustrate how degradation data can be modeled and analyzed by using "classical" and Bayesian approaches. Four methods of data analysis based on classical inference are presented. Next we show how Bayesian methods can also be used to provide a natural approach to analyzing degradation data. The approaches are applied to a real data set regarding train wheels degradation.