Voter model with non-Poissonian interevent intervals

Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a non-Poissonian nature of human behavior on dynamics of opinion formation. We use a variant of the voter model and numerically compare the time to consensus of all the voters with different distributions of interevent intervals and different networks. Compared with the exponential distribution of interevent intervals (i.e., the standard voter model), the power-law distribution of interevent intervals slows down consensus on the ring. This is because of the memory effect; in the power-law case, the expected time until the next update event on a link is large if the link has not had an update event for a long time. On the complete graph, the consensus time in the power-law case is close to that in the exponential case. Regular graphs bridge these two results such that the slowing down of the consensus in the power-law case as compared to the exponential case is less pronounced as the degree increases.Comment: 18 pages, 8 figure

Fletcher-Turek Model Averaged Profile Likelihood Confidence Intervals

We evaluate the model averaged profile likelihood confidence intervals proposed by Fletcher and Turek (2011) in a simple situation in which there are two linear regression models over which we average. We obtain exact expressions for the coverage and the scaled expected length of the intervals and use these to compute these quantities in particular situations. We show that the Fletcher-Turek confidence intervals can have coverage well below the nominal coverage and expected length greater than that of the standard confidence interval with coverage equal to the same minimum coverage. In these situations, the Fletcher-Turek confidence intervals are unfortunately not better than the standard confidence interval used after model selection but ignoring the model selection process

Nonparametric confidence intervals for monotone functions

We study nonparametric isotonic confidence intervals for monotone functions. In Banerjee and Wellner (2001) pointwise confidence intervals, based on likelihood ratio tests for the restricted and unrestricted MLE in the current status model, are introduced. We extend the method to the treatment of other models with monotone functions, and demonstrate our method by a new proof of the results in Banerjee and Wellner (2001) and also by constructing confidence intervals for monotone densities, for which still theory had to be developed. For the latter model we prove that the limit distribution of the LR test under the null hypothesis is the same as in the current status model. We compare the confidence intervals, so obtained, with confidence intervals using the smoothed maximum likelihood estimator (SMLE), using bootstrap methods. The `Lagrange-modified' cusum diagrams, developed here, are an essential tool both for the computation of the restricted MLEs and for the development of the theory for the confidence intervals, based on the LR tests.Comment: 31 pages, 13 figure

Predictive physiological anticipatory activity preceding seemingly unpredictable stimuli: An update of Mossbridge et al\u2019s meta-analysis

Background: This is an update of the Mossbridge et al\u2019s meta-analysis related to the physiological anticipation preceding seemingly unpredictable stimuli which overall effect size was 0.21; 95% Confidence Intervals: 0.13 - 0.29 Methods: Nineteen new peer and non-peer reviewed studies completed from January 2008 to June 2018 were retrieved describing a total of 27 experiments and 36 associated effect sizes. Results: The overall weighted effect size, estimated with a frequentist multilevel random model, was: 0.28; 95% Confidence Intervals: 0.18-0.38; the overall weighted effect size, estimated with a multilevel Bayesian model, was: 0.28; 95% Credible Intervals: 0.18-0.38. The weighted mean estimate of the effect size of peer reviewed studies was higher than that of non-peer reviewed studies, but with overlapped confidence intervals: Peer reviewed: 0.36; 95% Confidence Intervals: 0.26-0.47; Non-Peer reviewed: 0.22; 95% Confidence Intervals: 0.05-0.39. Similarly, the weighted mean estimate of the effect size of Preregistered studies was higher than that of Non-Preregistered studies: Preregistered: 0.31; 95% Confidence Intervals: 0.18-0.45; No-Preregistered: 0.24; 95% Confidence Intervals: 0.08-0.41. The statistical estimation of the publication bias by using the Copas selection model suggest that the main findings are not contaminated by publication bias. Conclusions: In summary, with this update, the main findings reported in Mossbridge et al\u2019s meta-analysis, are confirmed

Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters

Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level Model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series

The relationship between ARIMA-GARCH and unobserved component models with GARCH disturbances

The objective of this paper is to analyze the consequences of fitting ARIMA-GARCH models to series generated by conditionally heteroscedastic unobserved component models. Focusing on the local level model, we show that the heteroscedasticity is weaker in the ARIMA than in the local level disturbances. In certain cases, the IMA(1,1) model could even be wrongly seen as homoscedastic. Next, with regard to forecasting performance, we show that the prediction intervals based on the ARIMA model can be inappropriate as they incorporate the unit root while the intervals of the local level model can converge to the homoscedastic intervals when the heteroscedasticity appears only in the transitory noise. All the analytical results are illustrated with simulated and real time series