scholarly journals Location, Location, Location: An MCMC Approach to Modeling the Spatial Context of War and Peace

2002 ◽  
Vol 10 (3) ◽  
pp. 244-260 ◽  
Author(s):  
Michael D. Ward ◽  
Kristian Skrede Gleditsch
Keyword(s):  
Likelihood Function ◽  
War And Peace ◽  
Likelihood Methods ◽  
Autologistic Model ◽  
Unconditional Model ◽  
Out Of Sample ◽  
Maximum Likelihood Methods ◽  
Alternative Techniques ◽  
Categorical Response ◽  
Better Than

This article demonstrates how spatially dependent data with a categorical response variable can be addressed in a statistical model. We introduce the idea of an autologistic model where the response for one observation is dependent on the value of the response among adjacent observations. The autologistic model has likelihood function that is mathematically intractable, since the observations are conditionally dependent upon one another. We review alternative techniques for estimating this model, with special emphasis on recent advances using Markov chain Monte Carlo (MCMC) techniques. We evaluate a highly simplified autologistic model of conflict where the likelihood of war involvement for each nation is conditional on the war involvement of proximate states. We estimate this autologistic model for a single year (1988) via maximum pseudolikelihood and MCMC maximum likelihood methods. Our results indicate that the autologistic model fits the data much better than an unconditional model and that the MCMC estimates generally dominate the pseudolikelihood estimates. The autologistic model generates predicted probabilities greater than 0.5 and has relatively good predictive abilities in an out-of-sample forecast for the subsequent decade (1989 to 1998), correctly identifying not only ongoing conflicts, but also new ones.

scholarly journals HARK the SHARK: Realized Volatility Modeling with Measurement Errors and Nonlinear Dependencies*

2019 ◽  
Author(s):  
Giuseppe Buccheri ◽  
Fulvio Corsi
Keyword(s):  
Long Memory ◽  
Measurement Errors ◽  
Asymptotic Theory ◽  
Linear Models ◽  
Real Data ◽  
Realized Variance ◽  
Likelihood Methods ◽  
Out Of Sample ◽  
Maximum Likelihood Methods ◽  
Integrated Variance

Abstract Despite their effectiveness, linear models for realized variance neglect measurement errors on integrated variance and exhibit several forms of misspecification due to the inherent nonlinear dynamics of volatility. We propose new extensions of the popular approximate long-memory heterogeneous autoregressive (HAR) model apt to disentangle these effects and quantify their separate impact on volatility forecasts. By combining the asymptotic theory of the realized variance estimator with the Kalman filter and by introducing time-varying HAR parameters, we build new models that account for: (i) measurement errors (HARK), (ii) nonlinear dependencies (SHAR) and (iii) both measurement errors and nonlinearities (SHARK). The proposed models are simply estimated through standard maximum likelihood methods and are shown, both on simulated and real data, to provide better out-of-sample forecasts compared to standard HAR specifications and other competing approaches.

Real-space molecular-dynamics structure refinement

1999 ◽  
Vol 55 (2) ◽  
pp. 464-468 ◽  
Author(s):  
Zhi Chen ◽  
Eric Blanc ◽  
Michael S. Chapman
Keyword(s):  
Molecular Dynamics ◽  
Structure Refinement ◽  
Target Function ◽  
Optimization Method ◽  
Real Space ◽  
Likelihood Methods ◽  
Local Refinement ◽  
Isomorphous Replacement ◽  
Maximum Likelihood Methods ◽  
Better Than

Real-space targets and molecular-dynamics search protocols have been combined to improve the convergence of macromolecular atomic refinement. This was accomplished by providing a local real-space target function for the molecular-dynamics program X-PLOR. With poor isomorphous replacement experimental phases, molecular dynamics does not improve real-space refinement. However, with high-quality anomalous diffraction phases convergence is improved at the start of refinement, and torsion-angle real-space molecular dynamics performs better than other available least-squares or maximum-likelihood methods in real or reciprocal space. It is shown that the improvements result from an optimization method that can escape local minima and from a reduction of overfitting through the implicit use of phases and through use of a local refinement in which errors in remote parts of the structure cannot be mutually compensating.

scholarly journals The observed velocity distribution of young pulsars – II. Analysis of complete PSRπ

2020 ◽  
Vol 494 (3) ◽  
pp. 3663-3674 ◽  
Author(s):  
Andrei P Igoshev
Keyword(s):  
Large Data ◽  
Maxwellian Distribution ◽  
Proper Motions ◽  
Likelihood Methods ◽  
Complete Sample ◽  
Low Velocity ◽  
Data Set ◽  
Maximum Likelihood Methods ◽  
Distribution Parameters ◽  
Better Than

ABSTRACT Understanding the natal kicks, or birth velocities, of neutron stars is essential for understanding the evolution of massive binaries and double neutron star formation. We use maximum likelihood methods as published in Verbunt et al. to analyse a new large data set of parallaxes and proper motions measured by Deller et al. This sample is roughly three times larger than number of measurements available before. For both the complete sample and its younger part (spin-down ages τ < 3 Myr), we find that a bimodal Maxwellian distribution describes the measured parallaxes and proper motions better than a single Maxwellian with probability of 99.3 and 95.0 per cent, respectively. The bimodal Maxwellian distribution has three parameters: fraction of low-velocity pulsars and distribution parameters σ1 and σ2 for low- and high-velocity modes. For a complete sample, these parameters are as follows: $42_{-15}^{+17}$ per cent, $\sigma _1=128_{-18}^{+22}$ km s−1, and σ2 = 298 ± 28 km s−1. For younger pulsars, which are assumed to represent the natal kick, these parameters are as follows: $20_{-10}^{+11}$ per cent, $\sigma _1=56_{-15}^{+25}$ km s−1, and σ2 = 336 ± 45 km s−1. In the young population, 5 ± 3 per cent of pulsars have velocities less than 60 km s−1. We perform multiple Monte Carlo tests for the method taking into account realistic observational selection. We find that the method reliably estimates all parameters of the natal kick distribution. Results of the velocity analysis are weakly sensitive to the exact values of scale lengths of the Galactic pulsar distribution.

On Approximation of Transition Density for One-Dimensional Diffusion Processes

2016 ◽  
Vol 63 (2) ◽  
pp. 173-190
Author(s):  
Piotr Szczepocki
Keyword(s):  
Diffusion Processes ◽  
Likelihood Function ◽  
Transition Density ◽  
Estimation Methods ◽  
Likelihood Methods ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Maximum Likelihood Methods ◽  
General Method Of Moments ◽  
General Method

Estimation methods for stochastic differentia equations driver by discretely sampled continuous diffusion processes may be split into two categories: maximum likelihood methods and methods based on the general method of moments. Usually, one does not know neither likelihood function nor the-oretical moments of diffusion process and cannot construct estimators. Therefore many methods was developed to approximating unknown transition density. The aim of article is to compare properties of selected approaches, indicate their merits and limitations.

scholarly journals Selecting between causal and noncausal models with quantile autoregressions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alain Hecq ◽  
Li Sun
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Latin American ◽  
Financial Time Series ◽  
Selection Criterion ◽  
Likelihood Methods ◽  
Approximate Maximum Likelihood ◽  
Financial Time ◽  
Maximum Likelihood Methods ◽  
Latin American Countries

AbstractWe propose a model selection criterion to detect purely causal from purely noncausal models in the framework of quantile autoregressions (QAR). We also present asymptotics for the i.i.d. case with regularly varying distributed innovations in QAR. This new modelling perspective is appealing for investigating the presence of bubbles in economic and financial time series, and is an alternative to approximate maximum likelihood methods. We illustrate our analysis using hyperinflation episodes of Latin American countries.

scholarly journals A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1226
Author(s):  
Inmaculada Barranco-Chamorro ◽  
Yuri A. Iriarte ◽  
Yolanda M. Gómez ◽  
Juan M. Astorga ◽  
Héctor W. Gómez
Keyword(s):  
Heavy Tails ◽  
Real Data ◽  
Rate Function ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Stochastic Representation ◽  
Likelihood Methods ◽  
Chi Square ◽  
Maximum Likelihood Methods ◽  
Family Of Distributions

Specifying a proper statistical model to represent asymmetric lifetime data with high kurtosis is an open problem. In this paper, the three-parameter, modified, slashed, generalized Rayleigh family of distributions is proposed. Its structural properties are studied: stochastic representation, probability density function, hazard rate function, moments and estimation of parameters via maximum likelihood methods. As merits of our proposal, we highlight as particular cases a plethora of lifetime models, such as Rayleigh, Maxwell, half-normal and chi-square, among others, which are able to accommodate heavy tails. A simulation study and applications to real data sets are included to illustrate the use of our results.

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