Model misspecification and bias in the least-squares algorithm: Implications for linearized isotropic AVO

2021 ◽  
Vol 40 (9) ◽  
pp. 646-654
Author(s):  
Henning Hoeber
Keyword(s):  
Least Squares ◽  
Model Misspecification ◽  
Forward Model ◽  
Model Parameters ◽  
Omitted Variables ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Omitted Variable Bias ◽  
Least Squares Fit ◽  
Variable Bias

When inversions use incorrectly specified models, the estimated least-squares model parameters are biased. Their expected values are not the true underlying quantitative parameters being estimated. This means the least-squares model parameters cannot be compared to the equivalent values from forward modeling. In addition, the bias propagates into other quantities, such as elastic reflectivities in amplitude variation with offset (AVO) analysis. I give an outline of the framework to analyze bias, provided by the theory of omitted variable bias (OVB). I use OVB to calculate exactly the bias due to model misspecification in linearized isotropic two-term AVO. The resulting equations can be used to forward model unbiased AVO quantities, using the least-squares fit results, the weights given by OVB analysis, and the omitted variables. I show how uncertainty due to bias propagates into derived quantities, such as the χ-angle and elastic reflectivity expressions. The result can be used to build tables of unique relative rock property relationships for any AVO model, which replace the unbiased, forward-model results.

An Empirical Analysis of Model Misspecification in Studies of Valuation of Financial Statement Disclosures

1995 ◽  
Vol 10 (4) ◽  
pp. 719-749 ◽  
Author(s):  
Anne Beatty ◽  
Sandra Chamberlain ◽  
Joseph Magliolo
Keyword(s):  
Measurement Error ◽  
Model Misspecification ◽  
Financial Statement ◽  
Omitted Variables ◽  
Loan Loss ◽  
Share Prices ◽  
Valuation Model ◽  
Omitted Variable Bias ◽  
Weak Evidence ◽  
Variable Bias

A number of studies have examined the correlation between financial statement disclosures and share prices to assess the informativeness of these disclosures. There are several potential econometric problems with analyses of this type, and the interpretations of the results depend critically on the type of econometric problem. For example, the results of these studies should not be used to answer accounting policy questions unless the effect of an omitted variable bias is likely to be minimal. Given potential interpretation problems, we argue that analysis of model misspecification should be performed to isolate the form of misspecification. The contribution of this paper is to suggest a series of tests to perform this task. We use these tests to assess the importance of misspecification in adaptations of Barth's (1994) investment securities valuation model and Beaver et al.'s (1989) model of loan loss valuation. We find compelling evidence of the importance of misspecification apart from measurement error (e.g., omitted variables) in the model of investment securities valuation, but find only weak evidence of any misspecification other than measurement error in the loan loss valuation model.

scholarly journals Omitted Variable Bias in GLMs of Neural Spiking Activity

2018 ◽  
Vol 30 (12) ◽  
pp. 3227-3258 ◽  
Author(s):  
Ian H. Stevenson
Keyword(s):  
Neural Activity ◽  
Single Neuron ◽  
Linear Models ◽  
Theory And Practice ◽  
Parameter Estimates ◽  
Omitted Variables ◽  
History Effects ◽  
Omitted Variable Bias ◽  
Wide Range ◽  
Variable Bias

Generalized linear models (GLMs) have a wide range of applications in systems neuroscience describing the encoding of stimulus and behavioral variables, as well as the dynamics of single neurons. However, in any given experiment, many variables that have an impact on neural activity are not observed or not modeled. Here we demonstrate, in both theory and practice, how these omitted variables can result in biased parameter estimates for the effects that are included. In three case studies, we estimate tuning functions for common experiments in motor cortex, hippocampus, and visual cortex. We find that including traditionally omitted variables changes estimates of the original parameters and that modulation originally attributed to one variable is reduced after new variables are included. In GLMs describing single-neuron dynamics, we then demonstrate how postspike history effects can also be biased by omitted variables. Here we find that omitted variable bias can lead to mistaken conclusions about the stability of single-neuron firing. Omitted variable bias can appear in any model with confounders—where omitted variables modulate neural activity and the effects of the omitted variables covary with the included effects. Understanding how and to what extent omitted variable bias affects parameter estimates is likely to be important for interpreting the parameters and predictions of many neural encoding models.

Constrained nonlinear amplitude variation with offset inversion using Zoeppritz equations

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. R245-R255 ◽  
Author(s):  
Ali Gholami ◽  
Hossein S. Aghamiry ◽  
Mostafa Abbasi
Keyword(s):  
Nonlinear Equations ◽  
Wave Velocity ◽  
Seismic Data ◽  
P Wave ◽  
Simultaneous Estimation ◽  
Model Parameters ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Zoeppritz Equations ◽  
Avo Inversion

The inversion of prestack seismic data using amplitude variation with offset (AVO) has received increased attention in the past few decades because of its key role in estimating reservoir properties. AVO is mainly governed by the Zoeppritz equations, but traditional inversion techniques are based on various linear or quasilinear approximations to these nonlinear equations. We have developed an efficient algorithm for nonlinear AVO inversion of precritical reflections using the exact Zoeppritz equations in multichannel and multi-interface form for simultaneous estimation of the P-wave velocity, S-wave velocity, and density. The total variation constraint is used to overcome the ill-posedness while solving the forward nonlinear model and to preserve the sharpness of the interfaces in the parameter space. The optimization is based on a combination of Levenberg’s algorithm and the split Bregman iterative scheme, in which we have to refine the data and model parameters at each iteration. We refine the data via the original nonlinear equations, but we use the traditional cost-effective linearized AVO inversion to construct the Jacobian matrix and update the model. Numerical experiments show that this new iterative procedure is convergent and converges to a solution of the nonlinear problem. We determine the performance and optimality of our nonlinear inversion algorithm with various simulated and field seismic data sets.

Overburden dependent AVA inversion

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. C15-C23 ◽  
Author(s):  
Lyubov Skopintseva ◽  
Alexey Stovas
Keyword(s):  
Error Estimates ◽  
Velocity Model ◽  
Model Parameters ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Avo Analysis ◽  
Velocity Models ◽  
Model Interpretation

Amplitude-variation-with-offset (AVO) analysis is strongly dependent on interpretation of the estimated traveltime parameters. In practice, we can estimate two or three traveltime parameters that require interpretation within the families of two- or three-parameter velocity models, respectively. Increasing the number of model parameters improves the quality of overburden description and reduces errors in AVO analysis. We have analyzed the effect of two- and three-parameter velocity model interpretation for the overburden on AVO data and have developed error estimates in the reservoir parameters.

Omitted Variables, Intent, and Counterfactuals: A Response to Michael H. Nelson

2007 ◽  
Vol 7 (1) ◽  
pp. 149-158 ◽  
Author(s):  
Allen Hicken
Keyword(s):  
Critical Mass ◽  
Omitted Variables ◽  
Asian Studies ◽  
Political Actors ◽  
Omitted Variable Bias ◽  
Variable Bias ◽  
East Asian Studies ◽  
Political Groups ◽  
Work Knowledge ◽  
Thoughtful Critique

I have written elsewhere: “Where there exists a critical mass of scholars working on similar sets of questions—critiquing and building on one another's work—knowledge accumulation is more likely to occur.”1 It is with this statement in mind that I proceed with my response to Michael Nelson's thoughtful critique on my previous article (see Allen Hicken, “Party Fabrication: Constitutional Reform and the Rise of Thai Rack Thai,” Journal of East Asian Studies 6, no. 3 [2006]: 381–407). Rather than a point-by-point rebuttal, I will focus on three of the most interesting and challenging of Nelson's theoretical critiques. The first substantive issue concerns the charge of omitted variable bias—specifically, in reference to the omission of local political groups from a macro-institutional account. The second and third criticisms are more methodological. First, can we or should we ascribe motives to political actors? Second, how can we use counterfactuals to solve problems of observational equivalence?

scholarly journals Identification of average effects under magnitude and sign restrictions on confounding

10.3982/qe689 ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1619-1657 ◽  
Author(s):  
Karim Chalak
Keyword(s):  
Sensitivity Analysis ◽  
Direct Effect ◽  
Instrumental Variables ◽  
Average Treatment Effect ◽  
Structural Systems ◽  
Omitted Variables ◽  
Average Effect ◽  
Omitted Variable Bias ◽  
Marginal Effects ◽  
Variable Bias

This paper studies measuring various average effects of X on Y in general structural systems with unobserved confounders U, a potential instrument Z, and a proxy W for U. We do not require X or Z to be exogenous given the covariates or W to be a perfect one‐to‐one mapping of U. We study the identification of coefficients in linear structures as well as covariate‐conditioned average nonparametric discrete and marginal effects (e.g., average treatment effect on the treated), and local and marginal treatment effects. First, we characterize the bias, due to the omitted variables U, of (nonparametric) regression and instrumental variables estimands, thereby generalizing the classic linear regression omitted variable bias formula. We then study the identification of the average effects of X on Y when U may statistically depend on X and Z. These average effects are point identified if the average direct effect of U on Y is zero, in which case exogeneity holds, or if W is a perfect proxy, in which case the ratio (contrast) of the average direct effect of U on Y to the average effect of U on W is also identified. More generally, restricting how the average direct effect of U on Y compares in magnitude and/or sign to the average effect of U on W can partially identify the average effects of X on Y. These restrictions on confounding are weaker than requiring benchmark assumptions, such as exogeneity or a perfect proxy, and enable a sensitivity analysis. After discussing estimation and inference, we apply this framework to study earnings equations.

scholarly journals Improving the Accuracy of Model-based Quantitative NMR

2020 ◽  
Author(s):  
Yevgen Matviychuk ◽  
Ellen Steimers ◽  
Erik von Harbou ◽  
Daniel J. Holland
Keyword(s):  
Least Squares ◽  
Model Misspecification ◽  
Optimization Criterion ◽  
Model Fit ◽  
Accuracy Improvement ◽  
Adjustment Procedure ◽  
Model Based ◽  
Nmr Data ◽  
Least Squares Fit ◽  
Useful Signal

Abstract. We proposed an effective and computationally simple mechanism to improve the accuracy of model-based quantification in NMR data analysis. The proposed adjustment procedure aims to account for all useful signal left in the residual after the usual least squares fit, which can signify a case of model misspecification – a problem notoriously difficult to avoid in most model-based qNMR methods. Our alternative optimization criterion explicitly relies on the denoising of residual and smoothing the remaining baseline and is particularly effective in correcting errors in spectrum phasing. The results of analysis of experimental datasets obtained with high and medium field spectrometers indicate the accuracy improvement by 20–40 % compared to the usual least-squares model fit.

scholarly journals Omitted variable bias in GLMs of neural spiking activity

2018 ◽  
Author(s):  
Ian H. Stevenson
Keyword(s):  
Neural Activity ◽  
Single Neuron ◽  
Linear Models ◽  
Theory And Practice ◽  
Parameter Estimates ◽  
Omitted Variables ◽  
History Effects ◽  
Omitted Variable Bias ◽  
Wide Range ◽  
Variable Bias

AbstractGeneralized linear models (GLMs) have a wide range of applications in systems neuroscience describing the encoding of stimulus and behavioral variables as well as the dynamics of single neurons. However, in any given experiment, many variables that impact neural activity are not observed or not modeled. Here we demonstrate, in both theory and practice, how these omitted variables can result in biased parameter estimates for the effects that are included. In three case studies, we estimate tuning functions for common experiments in motor cortex, hippocampus, and visual cortex. We find that including traditionally omitted variables changes estimates of the original parameters and that modulation originally attributed to one variable is reduced after new variables are included. In GLMs describing single-neuron dynamics, we then demonstrate how post-spike history effects can also be biased by omitted variables. Here we find that omitted variable bias can lead to mistaken conclusions about the stability of single neuron firing. Omitted variable bias can appear in any model with confounders – where omitted variables modulate neural activity and the effects of the omitted variables covary with the included effects. Understanding how and to what extent omitted variable bias affects parameter estimates is likely to be important for interpreting the parameters and predictions of many neural encoding models.

Flexibly preconditioned extended least-squares migration in shot-record domain

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. S299-S315 ◽  
Author(s):  
Yin Huang ◽  
Rami Nammour ◽  
William Symes
Keyword(s):  
Least Squares ◽  
Conjugate Gradient ◽  
Numerical Experiments ◽  
Computational Effort ◽  
Amplitude Variation ◽  
Image Stack ◽  
Amplitude Variation With Offset ◽  
Image Volume ◽  
Spatially Varying ◽  
Least Squares Migration

We have developed a method for accelerating the convergence of iterative least-squares migration. The algorithm uses a pseudodifferential scaling (dip and spatially varying filter) preconditioner together with a variant of conjugate gradient (CG) iteration with iterate-dependent (flexible) preconditioning. The migration is formulated without the image stack, thus producing a shot-dependent image volume that retains offset information useful for velocity updating and amplitude variation with offset analysis. Numerical experiments indicate that flexible preconditioning with pseudodifferential scaling not only attains considerably smaller data misfit and gradient error for a given computational effort, but also produces higher resolution image volumes with more balanced amplitude and fewer artifacts than is achieved with a nonpreconditioned CG method.

Parameter Estimation and Sensitivity Analysis of a Nonlinearly Elastic Static Lung Model

1985 ◽  
Vol 107 (4) ◽  
pp. 315-320 ◽  
Author(s):  
J. R. Ligas ◽  
G. M. Saidel ◽  
F. P. Primiano
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Least Squares ◽  
Static Pressure ◽  
Optimal Parameter ◽  
Elastic Strain Energy ◽  
Lung Model ◽  
Model Parameters ◽  
Least Squares Fit ◽  
Parameter Values

A model for the static pressure-volume behavior of the lung parenchyma based on a pseudo-elastic strain energy function was tested. Values of the model parameters and their variances were estimated by an optimal least-squares fit of the model-predicted pressures to the corresponding data from excised, saline-filled dog lungs. Although the model fit data from twelve lungs very well, the coefficients of variation for parameter values differed greatly. To analyze the sensitivity of the model output to its parameters, we examined an approximate Hessian, H, of the least-squares objective function. Based on the determinant and condition number of H, we were able to set formal criteria for choosing the most reliable estimates of parameter values and their variances. This in turn allowed us to specify a normal range of parameter values for these dog lungs. Thus the model not only describes static pressure-volume data, but also uses the data to estimate parameters from a fundamental constitutive equation. The optimal parameter estimation and sensitivity analysis developed here can be widely applied to other physiologic systems.

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