Bayesian modelling of skewness and kurtosis with two-piece scale and shape distributions

We formalise and generalise the definition of the family of univariate double two--piece distributions, obtained by using a density--based transformation of unimodal symmetric continuous distributions with a shape parameter. The resulting distributions contain five interpretable parameters that control the mode, as well as the scale and shape in each direction. Four-parameter subfamilies of this class of distributions that capture different types of asymmetry are discussed. We propose interpretable scale and location-invariant benchmark priors and derive conditions for the propriety of the corresponding posterior distribution. The prior structures used allow for meaningful comparisons through Bayes factors within flexible families of distributions. These distributions are applied to data from finance, internet traffic and medicine, comparing them with appropriate competitors

On the Independence Jeffreys prior for skew--symmetric models with applications

We study the Jeffreys prior of the skewness parameter of a general class of scalar skew--symmetric models. It is shown that this prior is symmetric about 0, proper, and with tails $O(\lambda^{-3/2})$ under mild regularity conditions. We also calculate the independence Jeffreys prior for the case with unknown location and scale parameters. Sufficient conditions for the existence of the corresponding posterior distribution are investigated for the case when the sampling model belongs to the family of skew--symmetric scale mixtures of normal distributions. The usefulness of these results is illustrated using the skew--logistic model and two applications with real data

Redistribution and fiscal policy

This paper studies the optimal behavior of a democratic government in its use of fiscal policies to redistribute income. I present a stochastic dynamic general equilibrium model with heterogeneous agents to analyze (1) the differences between the effects on the optimal tax rate of permanent and nonpermanent perturbations and (2) the relationship between initial inequality and both steady-state levy and income distribution. In addition, the optimal fiscal policy for the transition is calculated. The analysis leads me to three main conclusions. First, there are no important differences between how taxes respond to a permanent or nonpermanent perturbation. Second, the initial inequality has a huge effect on both actual levy and actual income distribution. And finally, the Chari, Christiano, and Kehoe (1992) result, i.e., taxes on labor are roughly constant over the business cycle, holds only if the productivity ratio is constant. In addition, the model implies a positive correlation between inequality and tax rate, just as in the basic literature.Taxation ; Income distribution

Computing spectral sequences

In this paper, a set of programs enhancing the Kenzo system is presented. Kenzo is a Common Lisp program designed for computing in Algebraic Topology, in particular it allows the user to calculate homology and homotopy groups of complicated spaces. The new programs presented here entirely compute Serre and Eilenberg-Moore spectral sequences, in particular the groups and differential maps for arbitrary r. They also determine when the spectral sequence has converged and describe the filtration of the target homology groups induced by the spectral sequence

A Simple Approach to Maximum Intractable Likelihood Estimation

Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits maximum-likelihood (or maximum-a-posteriori) inference to be conducted, approximately, using essentially the same techniques. An elementary approach to this problem which simply obtains a nonparametric approximation of the likelihood surface which is then used as a smooth proxy for the likelihood in a subsequent maximisation step is developed here and the convergence of this class of algorithms is characterised theoretically. The use of non-sufficient summary statistics in this context is considered. Applying the proposed method to four problems demonstrates good performance. The proposed approach provides an alternative for approximating the maximum likelihood estimator (MLE) in complex scenarios

Time-Dependent Magnons from First Principles

We propose an efficient and non-perturbative scheme to compute magnetic excitations for extended systems employing the framework of time-dependent density functional theory. Within our approach, we drive the system out of equilibrium using an ultrashort magnetic kick perpendicular to the ground-state magnetization of the material. The dynamical properties of the system are obtained by propagating the time-dependent Kohn–Sham equations in real time, and the analysis of the time-dependent magnetization reveals the transverse magnetic excitation spectrum of the magnet. We illustrate the performance of the method by computing the magnetization dynamics, obtained from a real-time propagation, for iron, cobalt, and nickel and compare them to known results obtained using the linear-response formulation of time-dependent density functional theory. Moreover, we point out that our time-dependent approach is not limited to the linear-response regime, and we present the first results for nonlinear magnetic excitations from first principles in iron