We study the Latent Dirichlet Allocation model, a popular Bayesian algorithm for text analysis. We show that the model's parameters are not identified, which suggests that the choice of prior matters. We characterize the range of values that the posterior mean of a given functional of the...

A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent factorizations are established, leading to semi-closed-form...

Matrix algebra was covered in the linear regression, multiple regression section and simultaneous equations models. I use simple EViews 6 and matrix algebra examples to facilitate your learning experience and increase your enjoyment. Econometrics is basically related to economic measurement. It...

Topological relation between geographical objects is one of the key components of the Geographical Information System (GIS). Considering the objects to be exact with sharp boundaries, four intersection, and nine intersection matrices initiated the study of calculating the topological relations....

In the context of some multi-criteria decision-making methods, such as the Analytic Hierarchy Process, an expert is required to compare entities, e.g. alternatives and criteria. However, often, for various reasons, the expert cannot provide judgments on all pairs of entities. For these cases,...

Vorwort -- Mathematische Zeichen und Symbole -- Logik -- Arithmetik -- Algebra -- Lineare Algebra -- Kombinatorik -- Finanzmathematik -- Optimierung linearer Modelle -- Funktionen -- Differentialrechnung -- Integralrechnung -- Elastizitäten -- Ökonomische Funktionen -- Peren-Theorem --...

We develop estimation methods for Bayesian models where the covariance matrix has a block structure. A block covariance matrix partitions the data into groups or blocks; variances and covariances are equal within blocks while covariances are equal across blocks. We derive the posterior and...

We investigate the performance of non-linear return prediction models in the high complexity regime, i.e., when the number of model parameters exceeds the number of observations. We document a "virtue of complexity" in all asset classes that we study (US equities, international equities, bonds,...

There is considerable literature on matrix-variate gamma distributions, also known as Wishart distributions, which are driven by a shape parameter with values in the (Gindikin) set {i/2, i = 1, . . . , k−1}∪((k−1)/2, ∞). We provide an extension of this class to the case where the shape...

The generalized asymmetric Laplace (GAL) distribution, also known as the variance/mean-gamma model, is a popular flexible class of distributions that can account for peakedness, skewness, and heavier than normal tails, often observed in financial or other empirical data. We consider extensions...

In this work we present a new method for Quickest Change Detection (QCD) and Quickest Hub Discovery (QHD) in correlation structures that geometrically represents solutions from asymptotic Random Matrix theory (RMT) consistently, and allows to incorporate new distance metrics for both tests. We...