Bayesian P-splines and advanced computing in R for a changepoint analysis on spatio-temporal point processes

ABSTRACT

This work presents advanced computational aspects of a new method for changepoint detection on spatio-temporal point process data. We summarize the methodology, based on building a Bayesian hierarchical model for the data and declaring prior conjectures on the number and positions of the changepoints, and show how to take decisions regarding the acceptance of potential changepoints. The focus of this work is about choosing an approach that detects the correct changepoint and delivers smooth reliable estimates in a feasible computational time; we propose Bayesian P-splines as a suitable tool for managing spatial variation, both under a computational and a model fitting performance perspective. The main computational challenges are outlined and a solution involving parallel computing in R is proposed and tested on a simulation study. An application is also presented on a data set of seismic events in Italy over the last 20 years.     

Maximum likelihood estimation of bivariate circular hidden Markov models from incomplete data

In this paper, we propose a hidden Markov model for the analysis of the time series of bivariate circular observations, by assuming that the data are sampled from bivariate circular densities, whose parameters are driven by the evolution of a latent Markov chain. The model segments the data by accounting for redundancies due to correlations along time and across variables. A computationally feasible expectation maximization (EM) algorithm is provided for the maximum likelihood estimation of the model from incomplete data, by treating the missing values and the states of the latent chain as two different sources of incomplete information. Importance-sampling methods facilitate the computation of bootstrap standard errors of the estimates. The methodology is illustrated on a bivariate time series of wind and wave directions and compared with popular segmentation models for bivariate circular data, which ignore correlations across variables and/or along time.     

THE IMPACT OF IMMIGRATION ON THE STRUCTURE OF WAGES: THEORY AND EVIDENCE FROM BRITAIN

Immigration to the UK, particularly among more educated workers, has risen appreciably over the past 30 years and as such has raised labor supply. However studies of the impact of immigration have failed to find any significant effect on the wages of native‐born workers in the UK. This is potentially puzzling since there is evidence that changes in the supply of educated natives have had significant effects on their wages. Using a pooled time series of British cross‐sectional micro data on male wages and employment from the mid‐1970s to the mid‐2000s, this paper offers one possible resolution to this puzzle, namely that in the UK natives and foreign born workers are imperfect substitutes. We show that immigration has primarily reduced the wages of immigrants—and in particular of university educated immigrants—with little discernable effect on the wages of the native‐born.     

Disciplining Democracy: How the Upper and Middle Class in Manila Envision Democratic Order

Qualitative Sociology - I describe how the upper and middle class in Metro Manila see the democratic state and how they imagine reforming it. I argue that they are not turning away from democracy...     

Cointegration testing under structural change: reducing size distortions and improving power of residual based tests

This paper investigates how standard residual based tests for cointegration—under structural change in the long run relationship—can be modified in order to reduce size distortions and improve power, by following the same ideas used in the unit root context. This is a natural strategy given that these tests are unit root statistics applied to estimated residuals from a cointegrating regression. In order to assess the finite sample performance of the alternative tests, a Monte Carlo experiment will be implemented to analyze size and power. Critical values for the tests constructed with GLS detrended data, proposed by Elliot et al. (Econometrica 64:813–836, 1996), are obtained by simulation.     

The bipolar Choquet integral representation

Cumulative Prospect Theory is the modern version of Prospect Theory and it is nowadays considered a valid alternative to the classical Expected Utility Theory. Cumulative Prospect theory implies Gain-Loss Separability, i.e., the separate evaluation of losses and gains within a mixed gamble. Recently, some authors have questioned this assumption of the theory, proposing new paradoxes where the Gain-Loss Separability is violated. We present a generalization of Cumulative Prospect Theory which does not imply Gain-Loss Separability and is able to explain the cited paradoxes. On the other hand, the new model, which we call the bipolar Cumulative Prospect Theory, genuinely generalizes the original Prospect Theory of Kahneman and Tversky, preserving the main features of the theory. We present also a characterization of the bipolar Choquet Integral with respect to a bi-capacity in a discrete setting.     

Linear quantile mixed models

Dependent data arise in many studies. Frequently adopted sampling designs, such as cluster, multilevel, spatial, and repeated measures, may induce this dependence, which the analysis of the data needs to take into due account. In a previous publication (Geraci and Bottai in Biostatistics 8:140–154, 2007), we proposed a conditional quantile regression model for continuous responses where subject-specific random intercepts were included to account for within-subject dependence in the context of longitudinal data analysis. The approach hinged upon the link existing between the minimization of weighted absolute deviations, typically used in quantile regression, and the maximization of a Laplace likelihood. Here, we consider an extension of those models to more complex dependence structures in the data, which are modeled by including multiple random effects in the linear conditional quantile functions. We also discuss estimation strategies to reduce the computational burden and inefficiency associated with the Monte Carlo EM algorithm we have proposed previously. In particular, the estimation of the fixed regression coefficients and of the random effects’ covariance matrix is based on a combination of Gaussian quadrature approximations and non-smooth optimization algorithms. Finally, a simulation study and a number of applications of our models are presented.     

Inverse Sampling with Unequal Selection Probabilities

In some real situations the population of interest is divided into two groups, of which one contains only a few units. In other cases, the population may be considered as subdivided into two group', for example, if only a few units display a value of the variable of interest which is highly different from zero, while all the other units show a value equal to or near zero. In both cases, inverse sampling is more efficient than classical fixed sample-size designs to obtain the parameter estimators for the whole population as well as for its groups (e.g., Salehi and Seber, 2004 Salehi , M. M. , Seber , G. A. F. ( 2004 ). A general inverse sampling scheme and its application to adaptive cluster sampling . Austral. NZ J. Statist. 46 : 483 – 494 .[Crossref], [Web of Science ®] , [Google Scholar]). In fact, in this design the procedure selection continues until a prefixed number of units with the characteristic of interest is sampled. Since it is not known a priori to which group the population units belong, the sample size is a random variable. Christman and Lan (2001 Christman , M. C. , Lan , F. ( 2001 ). Inverse adaptive cluster sampling . Biometrics 57 : 1096 – 1105 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and Salehi and Seber (2001 Salehi , M. M. , Seber , G. A. F. ( 2001 ). A new proof of Murthy's estimator which applies to sequential sampling . Austral. NZ J. Statist. 43 : 281 – 286 . [Google Scholar] 2004 Salehi , M. M. , Seber , G. A. F. ( 2004 ). A general inverse sampling scheme and its application to adaptive cluster sampling . Austral. NZ J. Statist. 46 : 483 – 494 .[Crossref], [Web of Science ®] , [Google Scholar]) considered inverse sampling designs when all the population units have equal selection probabilities. In this article, we consider the general case in which the units may have unequal probabilities of being included in the sample. In fact, in many real situations different units may have different selection probabilities because of some inherent features of the sampling procedure, or in order to obtain better estimates. We derive unbiased estimators of the totals of the two groups, their variance and the corresponding unbiased variance estimators in inverse sampling with replacement. Finally, we derive similar results for more complex designs, where the selection procedure stops before observing the prefixed number of units from the rare group.     

A progressive shift alternative to evaluate nonparametric tests for skewed data

ABSTRACT

When the power of different nonparametric tests is evaluated by simulation, the alternative hypothesis should be carefully designed to ensure validity of the results in the specific research field. In the article, we propose a probit-based progressive shift alternative that is more realistic than the simple shift alternative for skewed non-negative data that occur in many research areas. Our motivation comes from parasitology. The progressive shift alternative is used to compare the power of six location-scale tests and seven commonly used location tests for several skewed theoretical and empirical parasite distributions. It is shown that location-scale tests are more powerful than location tests. Programs for applying the methods studied in the article are freely available for download.