Assimilation of GOSAT Methane in the Hemispheric CMAQ; Part II: Results Using Optimal Error Statistics

We applied the parametric variance Kalman filter (PvKF) data assimilation designed in Part I of this two-part paper to GOSAT methane observations with the hemispheric version of CMAQ to obtain the methane field (i.e., optimized analysis) with its error variance. Although the Kalman filter computes error covariances, the optimality depends on how these covariances reflect the true error statistics. To achieve more accurate representation, we optimize the global variance parameters, including correlation length scales and observation errors, based on a cross-validation cost function. The model and the initial error are then estimated according to the normalized variance matching diagnostic, also to maintain a stable analysis error variance over time. The assimilation results in April 2010 are validated against independent surface and aircraft observations. The statistics of the comparison of the model and analysis show a meaningful improvement against all four types of available observations. Having the advantage of continuous assimilation, we showed that the analysis also aims at pursuing the temporal variation of independent measurements, as opposed to the model. Finally, the performance of the PvKF assimilation in capturing the spatial structure of bias and uncertainty reduction across the Northern Hemisphere is examined, indicating the capability of analysis in addressing those biases originated, whether from inaccurate emissions or modelling error.

Credit Risk Volatility: Evidences From the Green Bond Market

The paper is an investigation on the impact of financial markets on the volatility of green bonds credit risk component, measured by the option-adjusted spread/swap curve (OAS) of the Global Bloomberg Barclays MSCI Green Bond Index, for both the non and pandemic periods. For these purpose, after observing the dynamic joint correlations between all the variables through a DCC-GARCH, we adopt GARCH(1,1) and EGARCH(1,1) models, putting the OAS as dependent variable. Our main results show that the conditional variance parameters are significant and persistent in both times, testifying the overall impact of the other markets on the OAS. In more detail, we highlight that the gamma in the two EGARCH models is positive: so the “green” credit risk volatility is more sensitive to positive shocks than negative ones. With reference to the conditional mean, we note that if during the non pandemic time only the stock market is significant, during the pandemic also conventional bonds and gold are impacting. To the best of our knowledge this is the first study that analyzes the specific credit risk component of green bond yields: we deem our findings useful to observe the change of green bonds creditworthiness in a complex market context.

Biases in Maximum Simulated Likelihood Estimation of Bivariate Models

This paper finds that the maximum simulated likelihood (MSL) estimator produces substantial biases when applied to the bivariate normal distribution. A specification of the random parameter bivariate normal model is considered, in which a direct comparison between the MSL and maximum likelihood (ML) estimators is feasible. The analysis shows that MSL produces biased results for the correlation parameter. This paper also finds that the MSL estimator is biased for the bivariate Poisson-lognormal model, developed by Munkin and Trivedi (1999. “Simulated Maximum Likelihood Estimation of Multivariate Mixed-Poisson Regression Models, with Application.” The Econometrics Journal 2: 29–48). A simulation study is conducted, which shows that MSL leads to serious inferential biases, especially large when variance parameters in the true data generating process are small. The MSL estimator produces biases in the estimated marginal effects, conditional means and probabilities of count outcomes.

Gradient Regularization as Approximate Variational Inference

We developed Variational Laplace for Bayesian neural networks (BNNs), which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The Variational Laplace objective is simple to evaluate, as it is the log-likelihood plus weight-decay, plus a squared-gradient regularizer. Variational Laplace gave better test performance and expected calibration errors than maximum a posteriori inference and standard sampling-based variational inference, despite using the same variational approximate posterior. Finally, we emphasize the care needed in benchmarking standard VI, as there is a risk of stopping before the variance parameters have converged. We show that early-stopping can be avoided by increasing the learning rate for the variance parameters.

MixTwice: large-scale hypothesis testing for peptide arrays by variance mixing

Summary Peptide microarrays have emerged as a powerful technology in immunoproteomics as they provide a tool to measure the abundance of different antibodies in patient serum samples. The high dimensionality and small sample size of many experiments challenge conventional statistical approaches, including those aiming to control the false discovery rate (FDR). Motivated by limitations in reproducibility and power of current methods, we advance an empirical Bayesian tool that computes local FDR statistics and local false sign rate statistics when provided with data on estimated effects and estimated standard errors from all the measured peptides. As the name suggests, the MixTwice tool involves the estimation of two mixing distributions, one on underlying effects and one on underlying variance parameters. Constrained optimization techniques provide for model fitting of mixing distributions under weak shape constraints (unimodality of the effect distribution). Numerical experiments show that MixTwice can accurately estimate generative parameters and powerfully identify non-null peptides. In a peptide array study of rheumatoid arthritis, MixTwice recovers meaningful peptide markers in one case where the signal is weak, and has strong reproducibility properties in one case where the signal is strong. Availabilityand implementation MixTwice is available as an R software package https://cran.r-project.org/web/packages/MixTwice/. Supplementary information Supplementary data are available at Bioinformatics online.

Modeling inter-trial variability of pointing movements during visuomotor adaptation

Trial-to-trial variability during visuomotor adaptation is usually explained as the result of two different sources, planning noise and execution noise. The estimation of the underlying variance parameters from observations involving varying feedback conditions cannot be achieved by standard techniques (Kalman filter) because they do not account for recursive noise propagation in a closed-loop system. We therefore developed a method to compute the exact likelihood of the output of a time-discrete and linear adaptation system as has been used to model visuomotor adaptation (Smith et al. in PLoS Biol 4(6):e179, 2006), observed under closed-loop and error-clamp conditions. We identified the variance parameters by maximizing this likelihood and compared the model prediction of the time course of variance and autocovariance with empiric data. The observed increase in variability during the early training phase could not be explained by planning noise and execution noise with constant variances. Extending the model by signal-dependent components of either execution noise or planning noise showed that the observed temporal changes of the trial-to-trial variability can be modeled by signal-dependent planning noise rather than signal-dependent execution noise. Comparing the variance time course between different training schedules showed that the signal-dependent increase of planning variance was specific for the fast adapting mechanism, whereas the assumption of constant planning variance was sufficient for the slow adapting mechanisms.

Power formulas for mixed effects models with random slope and intercept comparing rate of change across groups

We have previously derived power calculation formulas for cohort studies and clinical trials using the longitudinal mixed effects model with random slopes and intercepts to compare rate of change across groups [Ard & Edland, Power calculations for clinical trials in Alzheimer’s disease. J Alzheim Dis 2011;21:369–77]. We here generalize these power formulas to accommodate 1) missing data due to study subject attrition common to longitudinal studies, 2) unequal sample size across groups, and 3) unequal variance parameters across groups. We demonstrate how these formulas can be used to power a future study even when the design of available pilot study data (i.e., number and interval between longitudinal observations) does not match the design of the planned future study. We demonstrate how differences in variance parameters across groups, typically overlooked in power calculations, can have a dramatic effect on statistical power. This is especially relevant to clinical trials, where changes over time in the treatment arm reflect background variability in progression observed in the placebo control arm plus variability in response to treatment, meaning that power calculations based only on the placebo arm covariance structure may be anticonservative. These more general power formulas are a useful resource for understanding the relative influence of these multiple factors on the efficiency of cohort studies and clinical trials, and for designing future trials under the random slopes and intercepts model.

Variance constraints strongly influenced model performance in growth mixture modeling: a simulation and empirical study

Background Growth Mixture Modeling (GMM) is commonly used to group individuals on their development over time, but convergence issues and impossible values are common. This can result in unreliable model estimates. Constraining variance parameters across classes or over time can solve these issues, but can also seriously bias estimates if variances differ. We aimed to determine which variance parameters can best be constrained in Growth Mixture Modeling. Methods To identify the variance constraints that lead to the best performance for different sample sizes, we conducted a simulation study and next verified our results with the TRacking Adolescent Individuals’ Lives Survey (TRAILS) cohort. Results If variance parameters differed across classes and over time, fitting a model without constraints led to the best results. No constrained model consistently performed well. However, the model that constrained the random effect variance and residual variances across classes consistently performed very poorly. For a small sample size (N = 100) all models showed issues. In TRAILS, the same model showed substantially different results from the other models and performed poorly in terms of model fit. Conclusions If possible, a Growth Mixture Model should be fit without any constraints on variance parameters. If not, we recommend to try different variance specifications and to not solely rely on the default model, which constrains random effect variances and residual variances across classes. The variance structure must always be reported Researchers should carefully follow the GRoLTS-Checklist when analyzing and reporting trajectory analyses.

Bayesian multilevel structural equation modeling: An investigation into robust prior distributions.

Bayesian estimation of multilevel structural equation models (MLSEMs) offers advantages in terms of sample size requirements and computational feasibility, but does require careful specification of the prior distribution especially for the random effects variance parameters. The traditional “non-informative” conjugate choice of an inverse- Gamma prior with small hyperparameters has been shown time and again to be problematic. In this paper, we investigate alternative, more robust prior distributions. In contrast to multilevel models without latent variables, MLSEMs have multiple random effects variance parameters, both for the multilevel structure and for the latent variable structure. It is therefore even more important to construct reasonable priors for these parameters. We find that, although the robust priors outperform the traditional inverse-Gamma prior, their hyperparameters do require careful consideration.