Cheating with Models

Beliefs and decisions are often based on confronting models with data. What is the largest “fake” correlation that a misspecified model can generate, even when it passes an elementary misspecification test? We study an “analyst” who fits a model, represented by a directed acyclic graph, to an objective (multivariate) Gaussian distribution. We characterize the maximal estimated pairwise correlation for generic Gaussian objective distributions, subject to the constraint that the estimated model preserves the marginal distribution of any individual variable. As the number of model variables grows, the estimated correlation can become arbitrarily close to one regardless of the objective correlation. (JEL D83, C13, C46, C51)

Novel Data Augmentation Employing Multivariate Gaussian Distribution for Neural Network-Based Blood Pressure Estimation

In this paper, we propose a novel data augmentation technique employing multivariate Gaussian distribution (DA-MGD) for neural network (NN)-based blood pressure (BP) estimation, which incorporates the relationship between the features in a multi-dimensional feature vector to describe the correlated real-valued random variables successfully. To verify the proposed algorithm against the conventional algorithm, we compare the results in terms of mean error (ME) with standard deviation and Pearson correlation using 110 subjects contributed to the database (DB) which includes the systolic BP (SBP), diastolic BP (DBP), photoplethysmography (PPG) signal, and electrocardiography (ECG) signal. For each subject, 3 times (or 6 times) measurements are accomplished in which the PPG and ECG signals are recorded for 20 s. And, to compare with the performance of the BP estimation (BPE) using the data augmentation algorithms, we train the BPE model using the two-stage system, called the stacked NN. Since the proposed algorithm can express properly the correlation between the features than the conventional algorithm, the errors turn out lower compared to the conventional algorithm, which shows the superiority of our approach.

Parametric Estimation of Long Memory Multivariate Gaussian random fields

The aim of this paper is to make a theoretically study of the minimum Hellinger distance estimator of multivariate, gaussian, stationary, isotropic long-memory random fields The variables are observed on a finite set of points in space. We establish under certain assumptions, the almost sure convergence and the asymptotic distribution of this estimator.

Parametric Estimation of Long Memory Multivariate Gaussian random fields

The aim of this paper is to make a theoretically study of the minimum Hellinger distance estimator of multivariate, gaussian, stationary, isotropic long-memory random fields The variables are observed on a finite set of points in space. We establish under certain assumptions, the almost sure convergence and the asymptotic distribution of this estimator.

Multivariate postprocessing using Cholesky-based multivariate Gaussian regression

<p>To obtain reliable joint probability forecasts, multivariate postprocessing of numerical weather predictions (NWPs) must take into account dependencies among the univariate forecast errors—across different forecast horizons, locations or atmospheric quantities. We develop a framework for multivariate Gaussian regression (MGR), a flexible multivariate postprocessing technique with advantages over state-of-the-art methods.</p><p>In MGR both mean forecasts and parameters describing their error covariance matrix may be modeled simultaneously on NWP-derived predictor variables. The bivariate case is straightforward and has been used to postprocess horizontal wind vector forecasts, but higher dimensions present two major difficulties: ensuring the estimated error covariance matrix is positive definite and regularizing the high model complexity.</p><p>We tackle these problems by parameterizing the covariance through the entries of its basic and modified Cholesky decompositions. This ensures its positive definiteness and is the crucial fact making it possible to link parameters with predictors in a regression.  When there is a natural order to the variables, we can also sensibly reduce complexity through a priori restrictions of the parameter space.</p><p>MGR forecasts take the form of full joint parametric distributions—in contrast to ensemble copula coupling (ECC) that obtains samples from the joint distribution. This has the advantage that joint probabilities or quantiles can be easily derived.</p><p>Our novel method is applied to postprocess NWPs of surface temperature at an Alpine valley station for ten distinct lead times more than one week in the future.  All the mean forecasts and their full error covariance matrix are modelled on NWP-derived variables in one step. MGR outperforms ECC in combination with nonhomogeneous Gaussian regression.</p>