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Methodology (stat.ME)

Mon, 05 Jun 2023

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1.Truly Multivariate Structured Additive Distributional Regression

Authors:Lucas Kock, Nadja Klein

Abstract: Generalized additive models for location, scale and shape (GAMLSS) are a popular extension to mean regression models where each parameter of an arbitrary distribution is modelled through covariates. While such models have been developed for univariate and bivariate responses, the truly multivariate case remains extremely challenging for both computational and theoretical reasons. Alternative approaches to GAMLSS may allow for higher dimensional response vectors to be modelled jointly but often assume a fixed dependence structure not depending on covariates or are limited with respect to modelling flexibility or computational aspects. We contribute to this gap in the literature and propose a truly multivariate distributional model, which allows one to benefit from the flexibility of GAMLSS even when the response has dimension larger than two or three. Building on copula regression, we model the dependence structure of the response through a Gaussian copula, while the marginal distributions can vary across components. Our model is highly parameterized but estimation becomes feasible with Bayesian inference employing shrinkage priors. We demonstrate the competitiveness of our approach in a simulation study and illustrate how it complements existing models along the examples of childhood malnutrition and a yet unexplored data set on traffic detection in Berlin.

2.A generalization of the CIRCE method for quantifying input model uncertainty in presence of several groups of experiments

Authors:Guillaume Damblin, François Bachoc, Sandro Gazzo, Lucia Sargentini, Alberto Ghione

Abstract: The semi-empirical nature of best-estimate models closing the balance equations of thermal-hydraulic (TH) system codes is well-known as a significant source of uncertainty for accuracy of output predictions. This uncertainty, called model uncertainty, is usually represented by multiplicative (log)-Gaussian variables whose estimation requires solving an inverse problem based on a set of adequately chosen real experiments. One method from the TH field, called CIRCE, addresses it. We present in the paper a generalization of this method to several groups of experiments each having their own properties, including different ranges for input conditions and different geometries. An individual Gaussian distribution is therefore estimated for each group in order to investigate whether the model uncertainty is homogeneous between the groups, or should depend on the group. To this end, a multi-group CIRCE is proposed where a variance parameter is estimated for each group jointly to a mean parameter common to all the groups to preserve the uniqueness of the best-estimate model. The ECME algorithm for Maximum Likelihood Estimation developed in \cite{Celeux10} is extended to the latter context, then applied to a demonstration case. Finally, it is implemented on two experimental setups that differ in geometry to assess uncertainty of critical mass flow.

3.Variational inference based on a subclass of closed skew normals

Authors:Linda S. L. Tan

Abstract: Gaussian distributions are widely used in Bayesian variational inference to approximate intractable posterior densities, but the ability to accommodate skewness can improve approximation accuracy significantly, especially when data or prior information is scarce. We study the properties of a subclass of closed skew normals constructed using affine transformation of independent standardized univariate skew normals as the variational density, and illustrate how this subclass provides increased flexibility and accuracy in approximating the joint posterior density in a variety of applications by overcoming limitations in existing skew normal variational approximations. The evidence lower bound is optimized using stochastic gradient ascent, where analytic natural gradient updates are derived. We also demonstrate how problems in maximum likelihood estimation of skew normal parameters occur similarly in stochastic variational inference and can be resolved using the centered parametrization.

4.Exploiting Intraday Decompositions in Realized Volatility Forecasting: A Forecast Reconciliation Approach

Authors:Massimiliano Caporin, Tommaso Di Fonzo, Daniele Girolimetto

Abstract: We address the construction of Realized Variance (RV) forecasts by exploiting the hierarchical structure implicit in available decompositions of RV. By using data referred to the Dow Jones Industrial Average Index and to its constituents we show that exploiting the informative content of hierarchies improves the forecast accuracy. Forecasting performance is evaluated out-of-sample based on the empirical MSE and QLIKE criteria as well as using the Model Confidence Set approach.