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The dynamics governing the movement of the radon are complex and dependent on many factors. In the present study, we characterise the nature of temporal variations of 2-hourly and daily radon measurements in several monitoring sites of the Italian Radon mOnitoring Network (IRON) in Italy. By means of continuous wavelet transformation, a spectral analysis in time-frequency domain is performed. The results reveal that there are sub-daily, daily and yearly persistent periodicities that are common for all the stations. We observe structural seasonal breaks, that occur at the same frequency but at distinct time. Variations in radon concentration and local temperature are studied in terms of frequency contents and synchronicity. When analysing several long time series together, it is evident that the phase difference at low frequency movements (365-day period) between the radon and local temperature time series is depending on the sites’ location and therefore strongly controlled by local factors. This could at least partially explain the apparently contrasting results available in the literature obtained investigating smaller dataset about the relationships between temperature and radon variations. On the other hand, results show that all radon time series are characterised by marked cycles at 1 and 365-days and less evident cycles at 0.5-day and 180-days. They would be all ascribable to environmental-climatic factors: the short-period cycles to temperature and pressure variations, the long-period cycles also to seasonal rainfall variations.

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The detection of clustering structure in a point pattern is one of the main focuses of attention in spatiotemporal data mining. Indeed, statistical tools for clustering detection and identification of individual events belonging to clusters are welcome in epidemiology and seismology. Local second-order characteristics provide information on how an event relates to nearby events. In this work, we extend local indicators of spatial association (known as LISA functions) to the spatiotemporal context (which will be then called LISTA functions). These functions are then used to build local tests of clustering to analyse differences in local spatiotemporal structures. We present a simulation study to assess the performance of the testing procedure, and we apply this methodology to earthquake data

Radon (222Rn) is a radioactive gas, which originates everywhere in rocks of Earth's crust through a process of natural decay of other radioactive elements. The monitoring of soil radon can be useful to address a multitude of geological and environmental issues. However, some difficulties arise when trying to use radon as earthquake precursor because the earthquake‐related anomaly cannot be easily and univocally discriminated from other anomalies of different origin. To explore the relationship between soil radon emission and seismicity, a local network is operating in southeastern Sicily (Italy). Its peculiarities are the uniform geological condition of the monitoring sites and the long data record with simultaneous measures of radon and the main climate variables. In this paper, we applied continuous wavelet transformation to a ≈ 3.5 years long soil radon time series to detect periodic variations. Results indicate the occurrence of cycles at annual, semiannual, and monthly periodicity, which are ascribable to the effects of the climatic‐environmental parameters. The periodic components have been modeled and the signal conveniently filtered. We show as the characterization of the long‐term behavior of radon signals is essential to recognize anomalies in radon emission, which can be related to geological/environmental phenomena. The methodology proposed in this work provides a reliable characterization of the radon time series and can be applied at various spatial/temporal scales, depending on the scientific objectives to be achieved. This approach can also represent the base for further analysis like the investigation of the modulation between the periodic components and short‐term forecasts.

Diagnostics of goodness-of-fit in the theory of point processes are often considered through the transformation of data into residuals as a result of a thinning or a rescaling procedure. We alternatively consider here second-order statistics coming from weighted measures. Motivated by Adelfio and Schoenberg (2009) for the temporal and spatial cases, we consider an extension to the spatio-temporal context in addition to focussing on local characteristics. In particular, our proposed method assesses goodness-of-fit of spatio-temporal models by using local weighted secondorder statistics, computed after weighting the contribution of each observed point by the inverse of the conditional intensity function that identifies the process. Weighted second-order statistics directly apply to data without assuming homogeneity nor transforming the data into residuals, eliminating thus the sampling variability due to the use of a transforming procedure. We provide some characterisations and show a number of simulation studies. Keywords K-function • Local properties • Residual analysis • Second-order characteristics • Spatio-temporal point patterns

This paper focuses on inferential tools in the logistic regression model fitted by the Firth penalized likelihood. In this context, the Likelihood Ratio statistic is often reported to be the preferred choice as compared to the 'traditional' Wald statistic. In this work, we consider and discuss a wider range of test statistics, including the robust Wald, the Score, and the recently proposed Gradient statistic. We compare all these asymptotically equivalent statistics in terms of interval estimation and hypothesis testing via simulation experiments and analyses of two real datasets. We find out that the Likelihood Ratio statistic does not appear the best inferential device in the Firth penalized logistic regression.

In this paper, a version of hybrid of Gibbs point process models is proposed as method to characterise the multiscale interaction structure of several seismic sequences occurred in the Eastern Sicily in the last decade. Seismic sequences were identified by a clustering technique based on space-time distance criterion and hierarchical clustering. We focus our analysis on five small seismic sequences, showing that two of these are described by an inhomogeneous Poisson process (not significant interaction among events) while the other three clusters are described by a Hybrid-Geyer process (mutiscale interaction between events). The proposed method, although it still needs extensive testing on a larger catalogue, seems to be a promising tool for the characterization of seismogenic sources through the analysis of induced seismicity.