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Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…
In this paper we develop a tractable structural model with analytical default probabilities depending on some dynamics parameters, and we show how to calibrate the model using a chosen number of Credit Default Swap (CDS) market quotes. We…
Traditional economic models typically treat private information, or signals, as generated from some underlying state. Recent work has explicated alternative models, where signals correspond to interpretations of available information. We…
We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. We show how the parameters of…
Motivated by investigating spatio-temporal patterns of the distribution of continuous variables, we consider describing the conditional distribution function of the response variable incorporating spatio-temporal components given…
In structural credit risk models, default events and the ensuing losses are both derived from the asset values at maturity. Hence it is of utmost importance to choose a distribution for these asset values which is in accordance with…
We set up a structural model to study credit risk for a portfolio containing several or many credit contracts. The model is based on a jump--diffusion process for the risk factors, i.e. for the company assets. We also include correlations…
Simulation-based inference methods that feature correct conditional coverage of confidence sets based on observations that have been compressed to a scalar test statistic require accurate modeling of either the p-value function or the…
We study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning…
Data analyses typically rely upon assumptions about missingness mechanisms that lead to observed versus missing data. When the data are missing not at random, direct assumptions about the missingness mechanism, and indirect assumptions…
We introduce a new model for sums of exchangeable binary random variables. The proposed distribution is an approximation to the exact distributional form, and relies on the theory of completely monotone functions and the Laplace transform…
We model the term structure of the forward default intensity and the default density by using L\'evy random fields, which allow us to consider the credit derivatives with an after-default recovery payment. As applications, we study the…
Pair-copula constructions are flexible dependence models that use bivariate copulas as building blocks. In this paper, we use generalized additive models to extend them by allowing covariates effects. Borrowing ideas from a traditionally…
We consider a binary sequence generated by thresholding a hidden continuous sequence. The hidden variables are assumed to have a compound symmetry covariance structure with a single parameter characterizing the common correlation. We study…
We consider multiple diseases spreading in a static Configuration Model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a…
We study various properties of $f$-divergences and Csisz\'ar indices between two probability distributions in very general setups for the convex function $f$ and for the probability distributions. We establish general structural properties…
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…
Let X be a locally compact Abelian group. We consider linear forms of independent random variables with values in X. In doing so, one of the coefficients of the linear forms is a random variable with a Bernoulli distribution. For some…
We use the exponential random graph models to understand the network structure and its generative process for the Japanese bipartite network of banks and firms. One of the well known and simple model of exponential random graph is the…
Modeling the dependence between multiple risk types is a central challenge in contemporary insurance risk management. The standard approaches, L\'evy copulas and zero-mixed models, often face practical difficulties in simulation and…