This study performs a stress testing exercise on the Italian banking system in view of the 2007 financial crisis which was triggered by the crash of subprime mortgages. At the base of the global financial crisis was a failure of finan- cial regulators to quantify the accumulation of endogenous risks. Following the crisis, stress testing has acquired particular emphasis in the field of risk measurement under the Basel II supervisory framework. An econometric rela- tionship between the probability of default and the macroeconomic indicators is modeled according to the Merton approach for structural analysis using data on the Italian banking system. A latent factor model is employed to under- stand the dependence of the credit risk on the changes in the macroeconomic environment. The resulting relationship is exploited to compute the capital requirement under stressed conditions in order to draw inference about the resilience of the Italian banking system. JEL Classification G0, G01, G17, G10, C50, C22 Keywords Financial crisis, macroeconomic stress testing, credit risk, latent-factor model Author's e-mail jacomessi@yahoo.it Supervisor's e-mail petr.gapko@seznam.cz Abstrakt Klasifikace JEL G0, G01, G17, G10, C50, C22 Klíčová slova Financial crisis, macroeconomic stress test- ing, credit risk,...

The significance of credit risk models has increased with the introduction of new Basel accord known as Basel II. The aim of this study is default rate modeling. This thesis follows the two possible approaches of a macro credit risk modeling. First, empirical models are investigated. Second, a latent factor model based on Merton's idea is introduced. Both of these models are derived from individual default probability models. We employed data over the time period from 1988 to 2003 of the Finnish economy in the first part of this thesis. Time series of bankruptcy and firm's numbers were used. Aggregate data for whole economy as well as industry specific data were available. First, linear vector autoregressive models was used in case of dynamic empirical model. We examined how significant macroeconomic indicators determined the default rate in the whole economy and in the industry specific sector. However these models cannot provide microeconomic foundation as latent factor models. We employed a one- factor model in our estimation although, multi-factor models were also considered. A one-factor model was estimated using disaggregated industrial data. This estimation can help understand relation between credit risk and macroeconomic indicators. Obtained results were used in the second part of this...

A latent factor model for count data is popularly applied when deconvoluting mixed signals in biological data as exemplified by sequencing data for transcriptome or microbiome studies. Due to the availability of pure samples such as single-cell transcriptome data, the estimators can enjoy much better accuracy by utilizing the extra information. However, such an advantage quickly disappears in the presence of excessive zeros. To correctly account for such a phenomenon, we propose a zero-inflated non-negative matrix factorization that models excessive zeros in both mixed and pure samples and derive an effective multiplicative parameter updating rule. In simulation studies, our method yields smaller bias comparing to other deconvolution methods. We applied our approach to gene expression from brain tissue as well as fecal microbiome datasets, illustrating the superior performance of the approach. Our method is implemented as a publicly available R-package, iNMF. In zero-inflated non-negative matrix factorization (iNMF) for the deconvolution of mixed signals of biological data, pure-samples play a significant role by solving the identifiability issue as well as improving the accuracy of estimates. One of the main issues of using single-cell data is that the identities(labels) of the cells are not given. Thus, it is crucial to sort these cells into their correct types computationally. We propose a nonlinear latent variable model that can be used for sorting pure-samples as well as grouping mixed-samples via deep neural networks. The computational difficulty will be handled by adopting a method known as variational autoencoding. While doing so, we keep the NMF structure in a decoder neural network, which makes the output of the network interpretable.

Intrinsic connectivity networks (ICNs) refer to brain functional networks that are consistently found under various conditions, during tasks or at rest. Some studies demonstrated that while some stimuli do not impact intrinsic connectivity, other stimuli actually activate intrinsic connectivity through suppression, excitation, moderation or modi cation. Most analyses of functional magnetic resonance imaging (fMRI) data use ad-hoc methods to estimate the latent structure of ICNs. Modeling the effects on ICNs has also not been fully investigated. Bayesian Intrinsic Connectivity Network (BICNet) captures the ICN structure with We propose a BICNet model, an extended Bayesian dynamic sparse latent factor model, to identify the ICNs and quantify task-related effects on the ICNs. BICNet has the following advantages: (1) It simultaneously identifies the individual and group-level ICNs; (2) It robustly identifies ICNs by jointly modeling resting-state fMRI (rfMRI) and task-related fMRI (tfMRI); (3) Compared to independent component analysis (ICA)-based methods, it can quantify the difference of ICNs amplitudes across different states; (4) The sparsity of ICNs automatically performs feature selection, instead of ad-hoc thresholding. We apply BICNet to the rfMRI and language tfMRI data from the Human Connectome Project (HCP) and identify several ICNs related to distinct language processing functions.