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This contribution deals with effect measures for covariates in ordinal data models to address the interpretation of the results on the extreme categories of the scales, evaluate possible response styles, and motivate collapsing of extreme categories. It provides a simpler interpretation of the influence of the covariates on the probability of the response categories both in standard cumulative link models under the proportional odds assumption and in the recent extension of the Combination of Uncertainty and Preference of the respondents models, the mixture models introduced to account for uncertainty in rating systems. The article shows by means of marginal effect measures that the effects of the covariates are underestimated when the uncertainty component is neglected. Visualization tools for the effect of covariates are proposed, and measures of relative size and partial effect based on rates of change are evaluated by the use of real data sets.

Proper evaluation of the risk associated to a cyber attack is a crucial aspect for many companies. There is an increasing need to plan for and implement effective ways to address cyber security, data security, and privacy protection. Estimating the risk of a successful cyber attack is an important issue, since this type of threat is proliferating and thus poses increasing danger to companies and the customers who use their services. While quantitative loss data are rarely available, it is possible to obtain a qualitative evaluation on an ordinal scale of severity of cyber attacks from experts of the sector. Hence, it is natural to apply order response models for the analysis of cyber risk. In particular, we rely on cumulative link models. We explain the experts' assessment of the severity of a cyber attack as a function of a set of explanatory variables describing the characteristics of the attack under consideration. A measure of diffusion of the effects of the attacks obtained via the use of a network structure is also incorporated into the set of explanatory variables of the model. Along with the description of the methodology, we present a detailed analysis of a real data set that includes information on serious cyber attacks occurred worldwide in the period 2017–2018. [ABSTRACT FROM AUTHOR]

We introduce a novel Bayesian approach for quantitative learning for graphical log-linear marginal models. These models belong to curved exponential families that are difficult to handle from a Bayesian perspective. The likelihood cannot be analytically expressed as a function of the marginal log-linear interactions, but only in terms of cell counts or probabilities. Posterior distributions cannot be directly obtained, and Markov Chain Monte Carlo (MCMC) methods are needed. Finally, a well-defined model requires parameter values that lead to compatible marginal probabilities. Hence, any MCMC should account for this important restriction. We construct a fully automatic and efficient MCMC strategy for quantitative learning for such models that handles these problems. While the prior is expressed in terms of the marginal log-linear interactions, we build an MCMC algorithm that employs a proposal on the probability parameter space. The corresponding proposal on the marginal log-linear interactions is obtained via parameter transformation. We exploit a conditional conjugate setup to build an efficient proposal on probability parameters. The proposed methodology is illustrated by a simulation study and a real dataset. [ABSTRACT FROM AUTHOR]

We survey effect measures for models for ordinal categorical data that can be simpler to interpret than the model parameters. For describing the effect of an explanatory variable while adjusting for other explanatory variables, we present probability‐based measures, including a measure of relative size and partial effect measures based on instantaneous rates of change. We also discuss summary measures of predictive power that are analogs of R‐squared and multiple correlation for quantitative response variables. We illustrate the measures for an example and provide R code for implementing them. [ABSTRACT FROM AUTHOR]

This paper extends the ordinary quasi-symmetry ( QS) model for square contingency tables with commensurable classification variables. The proposed generalised QS model is defined in terms of odds ratios that apply to ordinal variables. In particular, we present QS models based on global, cumulative and continuation odds ratios and discuss their properties. Finally, the conditional generalised QS model is introduced for local and global odds ratios. These models are illustrated through the analysis of two data sets. [ABSTRACT FROM AUTHOR]

In this paper we propose a novel Bayesian methodology for Value-at-Risk computation based on parametric Product Partition Models. Value-at-Risk is a standard tool for measuring and controlling the market risk of an asset or portfolio, and is also required for regulatory purposes. Its popularity is partly due to the fact that it is an easily understood measure of risk. The use of Product Partition Models allows us to remain in a Normal setting even in the presence of outlying points, and to obtain a closed-form expression for Value-at-Risk computation. We present and compare two different scenarios: a product partition structure on the vector of means and a product partition structure on the vector of variances. We apply our methodology to an Italian stock market data set from Mib30. The numerical results clearly show that Product Partition Models can be successfully exploited in order to quantify market risk exposure. The obtained Value-at-Risk estimates are in full agreement with Maximum Likelihood approaches, but our methodology provides richer information about the clustering structure of the data and the presence of outlying points. [ABSTRACT FROM AUTHOR]

We propose a novel Bayesian optimization procedure for outlier detection in the Capital Asset Pricing Model. We use a parametric product partition model to robustly estimate the systematic risk of an asset. We assume that the returns follow independent normal distributions and we impose a partition structure on the parameters of interest. The partition structure imposed on the parameters induces a corresponding clustering of the returns. We identify via an optimization procedure the partition that best separates standard observations from the atypical ones. The methodology is illustrated with reference to a real dataset, for which we also provide a microeconomic interpretation of the detected outliers. [ABSTRACT FROM AUTHOR]

Compares two alternative Markov Chain Monte Carlo (MCMC) samplers for the Bayesian analysis of discrete graphical models. Presentation of a hierarchical and nonhierarchical version of MCMC model; Evaluation of logistic models for large contingency tables.