Influence of short- and long-term persistence on identification of rainfall temporal trends using different versions of the Mann-Kendall test in Mizoram, Northeast India

Investigating the temporal dynamics of rainfall in a changing climate, especially in rainfed agriculture regions, is crucial for analyzing climate-induced changes and offering adaptation options. Since Mizoram experiences unfavorable impacts of rain nearly every year, the region rainfall has been altering over the years, and vital climatic activity is becoming uncontrollable. The current study is primarily concerned with the changing trend of rainfall over Mizoram, which includes both short-term persistence (STP) and long-term persistence (LTP) of rainfall in seasonal and annual time series of rainfall overseeing for the period of 25 years of daily average rainfall from 1996 to 2020 collected collectively from the seven stations over the study area of Mizoram. Four different Mann-Kendall method iterations were used to analyze rainfall trends: the original or conventional method (without autocorrelation) (MnKn1), removing lag-1 autocorrelation (trend-free pre-whitening), considering multiple lag autocorrelation (more than lag-1 autocorrelation) (MnKn3), and Hurst coefficient or LTP (MnKn4). In the analysis, the study found that during monsoon, station Lawngtlai (LT) observed the highest rainfall having a Z value of 1.986, increased by 0.466 cm/year, while station Serchhip (SC) observed the lowest rainfall having Z value of -2.282, decreased by -0.163 cm/year. After applying modified MnKn4, we observed LTP of rainfall in winter at station Lawngtlai (LT) with an increasing trend and other stations observing STP in almost all seasons either increasing or decreasing trend. Therefore, possible climate change adaptation measures should be made to optimize rainfall use for various applications for the states of Mizoram.

When and where does violence beget violence?

Gun violence is frequently described in the language of epidemics. Yet, few quantitative studies have generated convincing evidence on the most basic question underlying the epidemic model of violence: Does violence at time t beget violence at time t + 1? With a sample of 98 of the 100 largest U.S. cities from 2014 to 2020, we employ an instrumental variable approach developed in (Jacob et al., 2007) that uses weather conditions in a given week to instrument for shootings in the same week. We find that throughout the entire period under study, shootings at week t have a negative or null effect on shootings at week t + 1 within cities. However, in years when cities went through sharp increases in gun violence, the prevalence of shootings in a given week has a strong, positive, causal effect on shootings in the following week. These results suggest that the relationship between current and subsequent violence is not static, but varies across different places and time periods. The results have implications for understanding how violence builds on itself during periods of sharp change.

Effective degrees of freedom of the Pearson's correlation coefficient under autocorrelation

The dependence between pairs of time series is commonly quantified by Pearson's correlation. However, if the time series are themselves dependent (i.e. exhibit temporal autocorrelation), the effective degrees of freedom (EDF) are reduced, the standard error of the sample correlation coefficient is biased, and Fisher's transformation fails to stabilise the variance. Since fMRI time series are notoriously autocorrelated, the issue of biased standard errors - before or after Fisher's transformation - becomes vital in individual-level analysis of resting-state functional connectivity (rsFC) and must be addressed anytime a standardised Z-score is computed. We find that the severity of autocorrelation is highly dependent on spatial characteristics of brain regions, such as the size of regions of interest and the spatial location of those regions. We further show that the available EDF estimators make restrictive assumptions that are not supported by the data, resulting in biased rsFC inferences that lead to distorted topological descriptions of the connectome on the individual level. We propose a practical "xDF" method that accounts not only for distinct autocorrelation in each time series, but instantaneous and lagged cross-correlation. We find the xDF correction varies substantially over node pairs, indicating the limitations of global EDF corrections used previously. In addition to extensive synthetic and real data validations, we investigate the impact of this correction on rsFC measures in data from the Young Adult Human Connectome Project, showing that accounting for autocorrelation dramatically changes fundamental graph theoretical measures relative to no correction.

Latent Variable Poisson Models for Assessing the Regularity of Circadian Patterns over Time

Many researchers in biology and medicine have focused on trying to understand biological rhythms and their potential impact on disease. A common biological rhythm is circadian, where the cycle repeats itself every 24 hours. However, a disturbance of the circadian pattern may be indicative of future disease. In this article, we develop new statistical methodology for assessing the degree of disturbance or irregularity in a circadian pattern for count sequences that are observed over time in a population of individuals. We develop a latent variable Poisson modeling approach with both circadian and stochastic short-term trend (autoregressive latent process) components that allow for individual variation in the degree of each component. A parameterization is proposed for modeling covariate dependence on the proportion of these two model components across individuals. In addition, we incorporate covariate dependence in the overall mean, the magnitude of the trend, and the phase-shift of the circadian pattern. Innovative Markov chain Monte Carlo sampling is used to carry out Bayesian posterior computation. Several variations of the proposed models are considered and compared using the deviance information criterion. We illustrate this methodology with longitudinal physical activity count data measured in a longitudinal cohort of adolescents.

Multi-scale detection of rate changes in spike trains with weak dependencies

The statistical analysis of neuronal spike trains by models of point processes often relies on the assumption of constant process parameters. However, it is a well-known problem that the parameters of empirical spike trains can be highly variable, such as for example the firing rate. In order to test the null hypothesis of a constant rate and to estimate the change points, a Multiple Filter Test (MFT) and a corresponding algorithm (MFA) have been proposed that can be applied under the assumption of independent inter spike intervals (ISIs). As empirical spike trains often show weak dependencies in the correlation structure of ISIs, we extend the MFT here to point processes associated with short range dependencies. By specifically estimating serial dependencies in the test statistic, we show that the new MFT can be applied to a variety of empirical firing patterns, including positive and negative serial correlations as well as tonic and bursty firing. The new MFT is applied to a data set of empirical spike trains with serial correlations, and simulations show improved performance against methods that assume independence. In case of positive correlations, our new MFT is necessary to reduce the number of false positives, which can be highly enhanced when falsely assuming independence. For the frequent case of negative correlations, the new MFT shows an improved detection probability of change points and thus, also a higher potential of signal extraction from noisy spike trains.

A moving blocks empirical likelihood method for longitudinal data

In the analysis of longitudinal or panel data, neglecting the serial correlations among the repeated measurements within subjects may lead to inefficient inference. In particular, when the number of repeated measurements is large, it may be desirable to model the serial correlations more generally. An appealing approach is to accommodate the serial correlations nonparametrically. In this article, we propose a moving blocks empirical likelihood method for general estimating equations. Asymptotic results are derived under sequential limits. Simulation studies are conducted to investigate the finite sample performances of the proposed methods and compare them with the elementwise and subject-wise empirical likelihood methods of Wang et al. (2010, Biometrika 97, 79-93) and the block empirical likelihood method of You et al. (2006, Can. J. Statist. 34, 79-96). An application to an AIDS longitudinal study is presented.

Bayesian Hierarchical Poisson Regression Models: An Application to a Driving Study with Kinematic Events

Although there is evidence that teenagers are at a high risk of crashes in the early months after licensure, the driving behavior of these teenagers is not well understood. The Naturalistic Teenage Driving Study (NTDS) is the first U.S. study to document continuous driving performance of newly-licensed teenagers during their first 18 months of licensure. Counts of kinematic events such as the number of rapid accelerations are available for each trip, and their incidence rates represent different aspects of driving behavior. We propose a hierarchical Poisson regression model incorporating over-dispersion, heterogeneity, and serial correlation as well as a semiparametric mean structure. Analysis of the NTDS data is carried out with a hierarchical Bayesian framework using reversible jump Markov chain Monte Carlo algorithms to accommodate the flexible mean structure. We show that driving with a passenger and night driving decrease kinematic events, while having risky friends increases these events. Further the within-subject variation in these events is comparable to the between-subject variation. This methodology will be useful for other intensively collected longitudinal count data, where event rates are low and interest focuses on estimating the mean and variance structure of the process. This article has online supplementary materials.