Backward simulation of multivariate mixed Poisson processes

In multi-attribute process monitoring, when a control chart signals an out-of-control condition indicating the existence of a special cause, knowing when the process has really changed (the change point) accelerates the identification of the source of the special cause and makes the corrective measures to be employed sooner. This, of course, results in a considerable amount of savings in time and money. Since many real world multi-attribute processes are Poisson and most process changes are step-change, a new method is proposed, in this paper, to derive the maximum likelihood estimator of the time of a step-change in the mean vector of multivariate Poisson processes. In this method, two transformations are first employed to almost remove the inherent skewness involved in multi-attribute processes and make them almost multivariate normal, and also to almost diminish correlations between the attributes. Then, a T2 control chart is employed for out-of-control detection and a maximum likelihood estimator is used to estimate the change point. The performance of the proposed methodology is illustrated using some simulation experiments in which we show that the proposed procedure is relatively accurate and reliable in detecting and estimating the change point.

We consider a new class of processes, called LG processes, defined as linear combinations of independent gamma processes. Their distributional and path‐wise properties are explored by following their relation to polynomial and Dirichlet (B‐)splines. In particular, it is shown that the density of an LG process can be expressed in terms of Dirichlet (B‐)splines, introduced independently by Ignatov and Kaishev and Karlin, Micchelli, and Rinott. We further show that the well‐known variance gamma (VG) process, introduced by Madan and Seneta, and the bilateral gamma (BG) process, recently considered by Küchler and Tappe are special cases of an LG process. Following this LG interpretation, we derive new (alternative) expressions for the VG and BG densities and consider their numerical properties. The LG process has two sets of parameters, the B‐spline knots and their multiplicities, and offers further flexibility in controlling the shape of the Levy density, compared to the VG and the BG processes. Such flexibility is often desirable in practice, which makes LG processes interesting for financial and insurance applications. Multivariate LG processes are also introduced and their relation to multivariate Dirichlet and simplex splines is established. Expressions for their joint density, the underlying LG‐copula, the characteristic, moment and cumulant generating functions are given. A method for simulating LG sample paths is also proposed, based on the Dirichlet bridge sampling of gamma processes, due to Kaishev and Dimitriva. A method of moments for estimation of the LG parameters is also developed. Multivariate LG processes are shown to provide a competitive alternative in modeling dependence, compared to the various multivariate generalizations of the VG process, proposed in the literature. Application of multivariate LG processes in modeling the joint dynamics of multiple exchange rates is also considered.

Background: Radiologically dense area (DA) on a mammogram represents the stromal and epithelial tissue in the breast, while non-dense area (NDA) represents adipose tissue. Quantitative measurements of DA, NDA as well as the proportion of dense area in the breast (percent density, PD) adjusted for age and body mass index (BMI) have all been associated with breast cancer (BC) risk. Previous genome-wide association studies (GWAS) have identified genetic loci that show association with both mammographic density (MD) phenotypes and BC, but little is known about the genome-wide and local genetic correlation between MD phenotypes and BC. Methods: We estimated the genome-wide and local genetic correlation between MD phenotypes adjusted for age and BMI and BC, leveraging GWAS summary statistics for MD phenotypes based on 12,866 women (MODE consortium) and for BC based on 122,977 cases and 105,974 controls (BCAC consortium). We also conducted partitioned heritability analysis to identify specific functional annotations that contribute to MD heritability. Results: We observed a negative genetic correlation between DA and NDA (-0.62, p=0.002). Both DA and PD showed positive genetic correlations with overall BC (DA: rg=0.24, p=0.004; PD: rg=0.27, p=0.0001), estrogen receptor-positive (ER+) BC (DA: rg=0.23, p=0.005; PD: rg=0.23, p=0.001), and ER- BC (DA: rg=0.26, p=0.01; PD: rg=0.32, p=0.0006). In contrast, NDA showed a nonsignificant negative genetic correlation with BC (rg=-0.11, p=0.21). Local genetic correlation analyses between MD phenotypes and BC reflected known findings including positive correlation at 10q21 region between both PD and DA and BC (both p<5x10-7), negative correlation at 22q13.1 between DA and BC (p=4.6x10-6), and positive correlation at 8p11.23 between NDA and BC (p=2.8x10-6). Two known BC regions that have not previously been associated with MD showed suggestive genetic correlations between BC and DA: 1q21.2 (negative genetic correlation, p=1.3x10-4) and 12q21.31 (positive genetic correlation, p=6.7x10-4). In exploratory analyses estimating the genome-wide genetic correlation between MD and hormone-related phenotypes in UK Biobank (n=337,199), we observed nominally significant positive genetic correlations between PD and benign mammary dysplasia (rg=0.45, p=0.01), NDA and endometriosis (rg=0.45, p=0.02), and negative genetic correlation between NDA and menstrual cycle length (rg=-0.30, p=0.05). We identified multiple functional annotations that contribute to MD heritability including histone mark H3K27ac that marks active enhancers (~2,5-fold enrichment in heritability for both DA and NDA) and DNAsel Hypersensitive Sites (DHS, 9.1-fold enrichment in heritability for DA). Conclusion: Our results provide evidence of shared genetic basis between mammographic density and breast cancer. Citation Format: Hongjie Chen, Julie Douglas, William Gordon, Deborah Thompson, Fergus Couch, Peter Fasching, Per Hall, John Hopper, Gertraud Maskarenic, Marina Pollan, Jennifer Stone, Rulla Tamimi, Sara Lindstroem. Evidence for a shared genetic basis between breast cancer and mammographic density phenotypes [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 224.

Jimma zone is one of the most potential coffee producing areas in Ethiopia. The livelihood of the farmers is mainly depend on coffee production. However,majority of them are smalholders characterized by traditional farm management system and limited use of coffee production technology. The aim of this study was to assess the adoption status of different coffee technologies in Jimma zone and to identify the determining factors of coffee technology adoption in the area. In the study, 393 respondents were involved and the adoption status of six selected coffee technologies, namely: the adoption of improved coffee variety, stumping, pruning, fertilizer, shade and mulching was investigated. Accordingly 67.4 % of the sample respondents did not use improved coffee variety. Similarly 45.8%, 31%, 53.4%, 4.1% and 25.7% of the farmers have not yet started to use stumping, pruning, fertilizer, shade tree and mulching, respectively. The factors influencing the adoption of each of these technologies were analyzed by using binomial regression model. As a result, age was found to be significant and negatively correlated with adoption of improved coffee variety. Sex of the farmer was the second variable which was found to be significant and had a negative correlation with mulching practice. Educational status was the other important factor which was found to be significant and had a positive correlation with adoption of the improved coffee variety, stumping technology and using shade tree. Family size was also found to be significant and had a positive correlation with using of stumping technologies, pruning, fertilizer application, mulching and shade trees. Dependency ratio, which was significant and showed a negative correlation with stumping and fertilizer application, was found to have a positive correlation with pruning. Likewise coffee farm size was found to be significant and had a negative correlation with improved coffee variety, fertilizer and mulching but it had a positive significant correlation with stumping. The coffee growing experience of the farmers was also significant and had a negative correlation with stumping, pruning and fertilizer. Moreover development agent support had a significant positive correlation with adoption of improved coffee variety, stumping, pruning, fertilizer application and mulching.Market distance was a factor that had a negative correlation with adoption of improved coffee variety, stumping, shade and mulching. Cooperative membership also showed a significant and negative corelation with improved coffee variety and pruning. Credit on the other hand was found to have a positive correlation with fertilizer application and was negatively correlated with the adoption of pruning practice and mulching. The total income of the household was found to be significant and had a positive correlation with adoption of improved coffee variety, pruning, using fertilizer and using of shade tree and training was also found to have a positive relationship with adoption of improved coffee variety, stumping technology, pruning practice, using shade tree and mulching.

Drought analysis framework based on copula and Poisson process with nonstationarity

We prove large deviation results for the random sum , , where are non-negative integer-valued random variables and are i.i.d. non-negative random variables with common distribution function F, independent of . Special attention is paid to the compound Poisson process and its ramifications. The right tail of the distribution function F is supposed to be of Pareto type (regularly or extended regularly varying). The large deviation results are applied to certain problems in insurance and finance which are related to large claims.

The Hawkes process, which is generally defined for the continuous-time setting, can be described as a self-exciting simple point process with a clustering effect, whose jump rate depends on its entire history. Due to past events determining future developments of self-exciting point processes, the Hawkes model is generally not Markovian. In certain special circumstances, it can be Markovian with a generator of the model if the exciting function is an exponential function or the sum of exponential functions. In the case of non-Markovian processes, difficulties arise when the exciting function is not an exponential function or a sum of exponential functions. The intensity of the Hawkes process is given by the sum of a baseline intensity and other terms that depend on the entire history of the point process, as compared to a standard Poisson process. It is one of the main methods used for studying the dynamical properties of general point processes, and is highly important for credit risk studies. The baseline intensity, which is instrumental in the Hawkes model, is usually defined for deterministic cases. In this paper, we consider a linear Hawkes model where the baseline intensity is randomly defined, and investigate the asymptotic results of the large deviations principle for the newly defined model. The Hawkes processes with randomized baseline intensity, dealt with in this paper, have wide applications in insurance, finance, queue theory, and statistics.

Different researchers have reported positive, null, and negative relationships between confidence and accuracy in reports from memory. One possible reason for this paradox is the variety of materials used across experiments, but the two experiments reported in this article show that positive and negative confidence-accuracy correlations can be observed using a single procedure and the same materials. Subjects studied words from semantic categories and then took a recognition test while making confidence ratings. For previously studied items, positive correlations between confidence and accuracy were obtained using three different measures. Yet when confidence-accuracy correlations were assessed for unstudied items from studied categories, the correlations were zero or negative. The critical factors in determining when negative correlations will be found are the similarity of lures to presented items and the type of analysis used. These results indicate that one should be cautious about relying on confidence of recognition when rememberers must decide among highly similar events.

ABSTRACTIn this paper, we consider a generalisation of the backward simulation method of Duch et al. [New approaches to operational risk modeling. IBM J Res Develop. 2014;58:1–9] to build bivariate Poisson processes with flexible time correlation structures, and to simulate the arrival times of the processes. The proposed backward construction approach uses the Marshall–Olkin bivariate binomial distribution for the conditional law and some well-known families of bivariate copulas for the joint success probability in lieu of the typical conditional independence assumption. The resulting bivariate Poisson process can exhibit various time correlation structures which are commonly observed in real data.

A note on Marked Point Processes and multivariate subordination

We prove that arbitrary Hunt processes on a general state space can be approximated by multivariate Poisson processes starting from each point of the state space. The key point is that no additional regularity assumption on the state space and on the underlying transition semigroup is used.

We propose a novel tie-oriented model for longitudinal event network data. The generating mechanism is assumed to be a multivariate Poisson process that governs theonsetandrepetitionof yearly observed events with two separate intensity functions. We apply the model to a network obtained from the yearly dyadic number of international deliveries of combat aircraft trades between 1950 and 2017. Based on the trade gravity approach, we identify economic and political factors impeding or promoting the number of transfers. Extensive dynamics as well as country heterogeneities require the specification of semiparametric time-varying effects as well as random effects. Our findings reveal strong heterogeneous as well as time-varying effects of endogenous and exogenous covariates on theonsetandrepetitionof aircraft trade events.

Spike-time correlations capture the short timescale covariance between the activity of neurons on a single trial. These correlations can significantly vary in magnitude and sign from trial to trial, and have been proposed to contribute to information encoding in visual cortex. While monkeys performed a motion-pulse detection task, we examined the behavioral impact of both the magnitude and sign of single-trial spike-time correlations between two nonoverlapping pools of middle temporal (MT) neurons. We applied three single-trial measures of spike-time correlation between our multiunit MT spike trains (Pearson's, absolute value of Pearson's, and mutual information), and examined the degree to which they predicted a subject's performance on a trial-by-trial basis. We found that on each trial, positive and negative spike-time correlations were almost equally likely, and, once the correlational sign was accounted for, all three measures were similarly predictive of behavior. Importantly, just before the behaviorally relevant motion pulse occurred, single-trial spike-time correlations were as predictive of the performance of the animal as single-trial firing rates. While firing rates were positively associated with behavioral outcomes, the presence of either strong positive or negative correlations had a detrimental effect on behavior. These correlations occurred on short timescales, and the strongest positive and negative correlations modulated behavioral performance by ∼9%, compared with trials with no correlations. We suggest a model where spike-time correlations are associated with a common noise source for the two MT pools, which in turn decreases the signal-to-noise ratio of the integrated signals that drive motion detection.SIGNIFICANCE STATEMENT Previous work has shown that spike-time correlations occurring on short timescales can affect the encoding of visual inputs. Although spike-time correlations significantly vary in both magnitude and sign across trials, their impact on trial-by-trial behavior is not fully understood. Using neural recordings from area MT (middle temporal) in monkeys performing a motion-detection task using a brief stimulus, we found that both positive and negative spike-time correlations predicted behavioral responses as well as firing rate on a trial-by-trial basis. We propose that strong positive and negative spike-time correlations decreased behavioral performance by reducing the signal-to-noise ratio of integrated MT neural signals.

Anxiolytic-like effect of pregabalin on unconditioned fear in the rat: An autoradiographic brain perfusion mapping and functional connectivity study

On the stochastic equation [formula omitted] and properties of Mittag–Leffler distributions