Accounting for Heterogeneity in Stop Frequency Models of Work Tours Using Latent Class Poisson Models

Stop frequency models, as one of the elements of activity based models, represent an important part of travel behavior. Unobserved heterogeneity across the travelers should be taken into consideration to prevent biasedness and inconsistency in the estimated parameters in the stop frequency models. Additionally, previous studies on the stop frequency have mostly been done in larger metropolitan areas and less attention has been paid to the areas with less population. This study addresses these gaps by using 2012 travel data from a medium sized U.S. urban area using the work tour for the case study. Stop in the work tour were classified into three groups of outbound leg, work based subtour, and inbound leg of the commutes. Latent Class Poisson Regression Models were used to analyze the data. The results indicate the presence of heterogeneity across the commuters. Using latent class models significantly improves the predictive power of the models compared to regular one class Poisson regression models. In contrast to one class Poisson models, gender becomes insignificant in predicting the number of tours when unobserved heterogeneity is accounted for. The commuters are associated with increased stops on their work based subtour when the employment density of service-related occupations increases in their work zone, but employment density of retail employment does not significantly contribute to the stop making likelihood of the commuters. Additionally, an increase in the number of work tours was associated with fewer stops on the inbound leg of the commute. The results of this study suggest the consideration of unobserved heterogeneity in the stop frequency models and help transportation agencies and policy makers make better inferences from such models.

Robust Estimators for Poisson Regression

The present paper proposes a new robust estimator for Poisson regression models. We used the weighted maximum likelihood estimators which are regarded as Mallows-type estimators. We perform a Monte Carlo simulation study to assess the performance of a suggested estimator compared to the maximum likelihood estimator and some robust methods. The result shows that, in general, all robust methods in this paper perform better than the classical maximum likelihood estimators when the model contains outliers. The proposed estimators showed the best performance compared to other robust estimators.

On two actuarial quantities for the compound Poisson risk model with tax and a threshold dividend strategy

In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability function for the total number of taxation periods over the lifetime of the surplus process is derived. Second, analytical expression of the expected accumulated discounted dividends paid between two consecutive taxation periods is provided. In addition, explicit expressions are also given for the exponential individual claims.

Analysis of Ozone Behaviour in the City of Puebla-Mexico Using Non-Homogeneous Poisson Models with Multiple Change-Points

In this work, some non-homogeneous Poisson models are considered to study the behaviour of ozone in the city of Puebla, Mexico. Several functions are used as the rate function for the non-homogeneous Poisson process. In addition to their dependence on time, these rate functions also depend on some parameters that need to be estimated. In order to estimate them, a Bayesian approach will be taken. The expressions for the distributions of the parameters involved in the models are very complex. Therefore, Markov chain Monte Carlo algorithms are used to estimate them. The methodology is applied to the ozone data from the city of Puebla, Mexico.

Comparing the Adequacy of Some Non-Homogeneous Poisson Models to Estimate Ozone Exceedances in Mexico City

We consider some non-homogeneous Poisson models to estimate the mean number of times that a given environmental threshold of interest is surpassed by a given pollutant. Seven different rate functions for the Poisson processes describing the models are taken into account. The rate functions considered are the Weibull, exponentiated-Weibull, and their generalisation the Beta-Weibull rate function. We also use the Musa-Okumoto, the Goel-Okumoto, a generalised Goel- Okumoto and the Weibull-geometric rate functions. Whenever thought justifiable, the model allowing the presence of change-points is also going to be considered. The different models are applied to the daily maximum ozone measurements data provided by the monitoring network of the Metropolitan Area of Mexico City. The aim is to compare the adjustment of different rate functions to the data. Even though, some of the rate functions have been considered before, now we are applying them to the same data set. In previous works they were used in different data sets and therefore a comparison of the adequacy of those models were not possible. The measurements considered here were obtained after a series of environmental measures were implemented in Mexico City. Hence, the data present a different behaviour from that of earlier studies.

Effect of Exposure to Trace Elements in the Soil on the Prevalence of Neural Tube Defects in a High-Risk Area of China

Objective Our objective is to build a model that explains the association between the exposure to trace elements in the soil and the risk of neural tube defects. Methods We built a function with different parameters to describe the effects of trace elements on neural tube defects. The association between neural tube defects and trace element levels was transformed into an optimization problem using the maximum likelihood method. Results Tin, lead, nickel, iron, copper, and aluminum had typical layered effects （dosage effects） on the prevalence of neural tube defects. Arsenic, selenium, zinc, strontium, and vanadium had no effect, and molybdenum had one threshold value that affected the prevalence of birth defects. Conclusion As an exploratory research work, our model can be used to determine the direction of the effect of the trace element content of cultivated soil on the risk of neural tube defects, which shows the clues by the dosage effect of their toxicological characteristics. Based on our findings, future biogeochemical research should focus on the direct effects of trace elements on human health.

The stress release model and results from modelling features of some seismic regions in China

The stress release model is a stochastic point process model developed from the theory of elastic rebound. It can be used to analyse, simulate or predict the seismicity in a certain seismic region. This paper first gives a brief representation of the theory of the stress release model and the method of how to use it to analyse earthquake data, then this model is to fit the earthquake data in North China, Southwest China and Taiwan. The results show that the stress release model fits to the data better than the Poisson model. The different features of stress accumulation and release in these regions imply that the seismic activity is essentially different among these regions.

DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.

Existence and Uniqueness of Positive Solutions for a System of Multi-order Fractional Differential Equations

In this paper, we study a class of ruin problems, in which premiums and claims are dependent. Under the assumption that premium income is a stochastic process, we raise the model that premiums and claims are dependent, give its numerical characteristics and the ruin probability of the individual risk model in the surplus process. In addition, we promote the number of insurance policies to a Poisson process with parameter λ, using martingale methods to obtain the upper bound of the ultimate ruin probability.

X-ray pulsar signal detection using photon interarrival time

The distribution probability of the photon interarrival time （PIT） without signal initial phases is derived based on the Poisson model of X-ray pulsar signals, and a pulsar signal detection algorithm employing the PIT sequence is put forward. The joint probability of the PIT sequence is regarded as a function of the distribution probability and used to compare a constant radiation intensity model with the nonhomogeneous Poisson model for the signal detection. The relationship between the number of detected photons and the probabilities of false negative and positive is studied, and the success rate and mean detection time are estimated based on the number of the given photons. For the spacecraft velocity data detection, the changes of time of photon arrival （TOPA） and PIT caused by spacecraft motion are presented first, then the influences on detection are analyzed respectively. By using the analytical pulse profile of PSR B0531＋21, the simulation of the Xray pulsar signal detection is implemented. The simulation results verify the effectiveness of the proposed method, and the contrast tests show that the proposed method is suitable for the spacecraft velocity data detection.

Improved stress release model: Application to the study of earthquake prediction in Taiwan Region

Stress release model used to be applied to seismicity study of large historical earthquakes in a space of large scale. In this paper, we improve the stress release model, and discuss whether the stress release model is still applicable or not in the case of smaller spatio-temporal scale and weaker earthquakes. As an example of testing the model, we have analyzed the M greater than or equal 6 earthquakes in recent about 100 years. The result shows that the stress release model is still applicable. The earthquake conditional probability intensity in Taiwan Region is calculated with the improved stress release model. We see that accuracy of earthquake occurrence time predicted by the improved stress release model is higher than that by Poisson model in the test of retrospect earthquake prediction.

On the Markov-dependent risk model with tax

In this paper we consider the Markov-dependent risk model with tax payments in which the claim occurrence, the claim amount as well as the tax rate are controlled by an irreducible discrete-time Markov chain. Systems of integro-differential equations satisfied by the expected discounted tax payments and the non-ruin probability in terms of the ruin probabilities under the Markov-dependent risk model without tax are established. The analytical solutions of the systems of integro-differential equations are also obtained by the iteration method.

The estimation of yearly probability gain for seismic statistical model

Based on the calculation method of information gain in the stochastic process presented by Vere-Jones, the rela tion between information gain and probability gain is studied, which is very common in earthquake prediction, and the yearly probability gain for seismic statistical model is proposed. The method is applied to the non stationary Poisson model with whole-process exponential increase and stress release model. In addition, the prediction method of stress release model is obtained based on the inverse function simulation method of stochastic variable.

Numerical Investigation into the Effect of Air Voids on the Anisotropy of Asphalt Mixtures

The aim of this study is to investigate the asphalt mixture anisotropy of both the modulus and Poisson＇s ratio due to air voids using a discrete element modeling simulation method. Three three-dimensional cubic digital samples of asphalt mixture with different shapes of single air void were built using discrete element software PFC^（3D）. The aggregate gradation, air voids and mastic included in the digital samples were modeled using different contact models, with due consideration of the volumetric fractions of the different phases. Laboratory uniaxial complex modulus test and indirect tensile strength test were conducted to obtain material input parameters for numerical modeling. Simulation of the uniaxial cyclic compressive tests was performed on the three cubic samples loaded in three different directions. Dynamic modulus in three directions and Poisson＇s ratio in six directions were calculated from the compression stress-strain responses. Results show that both the modulus and Poisson＇s ratio are dependent on the preferential orientation of air voids. The anisotropy of the modulus and Poisson＇s ratio increases as the pressure loading on the asphalt mixture increases. Compared to the modulus, Poisson＇s ratio due to air voids has been shown to be more anisotropic. The maximum of Poisson＇s ratio and modulus is shown to be up to 80% and 11% higher than the minimum, respectively.

Spatial Heterogeneity Association of HIV Incidence with Socio-economic Factors in Zimbabwe

This study examined the spatial heterogeneity association of HIV incidence and socio-economic factors including poverty severity index,permanently employed females and males,unemployed females,percentage of poor households i.e.,poverty prevalence,night lights index,literacy rate,household food security,and Gini index at district level in Zimbabwe.A mix of spatial analysis methods including Poisson model based on original log likelihood ratios(LLR),global Moran’s I,local indicator of spatial association-LISA were employed to determine the HIV hotspots.Geographically Weighted Poisson Regression(GWPR)and semi-parametric GWPR(s-GWPR)were used to determine the spatial association between HIV incidence and socio-economic factors.HIV incidence(number of cases per 1000)ranged from 0.6(Buhera district)to 13.30(Mangwe district).Spatial clustering of HIV incidence was observed(Global Moran’s I=-0.150;Z score 3.038;p-value 0.002).Significant clusters of HIV were observed at district level.HIV incidence and its association with socio-economic factors varied across the districts except percentage of females unemployed.Intervention programmes to reduce HIV incidence should address the identified socio-economic factors at district level.

Statistical inference for zero-and-one-inflated poisson models

In this paper, a zero-and-one-inflated Poisson (ZOIP) model is studied. The maximum likelihoodestimation and the Bayesian estimation of the model parameters are obtained based on dataaugmentation method. A simulation study based on proposed sampling algorithm is conductedto assess the performance of the proposed estimation for various sample sizes. Finally, two realdata-sets are analysed to illustrate the practicability of the proposed method.

A censored-Poisson model based approach to the analysis of RNA-seq data

Background:With the recent advance of sequencing technology,the collction of RNA expression(RNA-seq)data has been growing rapidly.RNA-seq data are statistically count-type measurements.Poisson distribution is a basic probability distribution for modeling count-type data.With Poisson regression models,various experimental factors,GC content as well as alternative splicing isoforms can be flexibly considered in RNA-seq data analysis.Due to the biochemical and technical limitations of sequencing technology,the biases among RNA-seq data have been recognized.Methods:In this study,an artificial censoring approach has been proposed to an isoform-specific Poisson regression model for analy zing RNA-seq data.Low expression values can be grouped(censored)into one probability category,and high expression values can also be grouped(censored)into another probability category.We have implemented the related Newton-Raphson numeric computing procedure to achieve the maximum likelihood estimation for our censored-Poisson regression model.The related mathematical simplifications have been derived for the consideration of stable and convenient numerical computing.Results:The advantages of our artificial censoring approach have been demonstrated in both simulation studies and application analysis of experimental data.Conclusions:Our proposed artificial censoring approach allows us to focus on the majority of data.As the extreme values(tails)of data are artificially censored,more efficient analysis results can be obtained,even from relatively simple Poisson regression models.Our proposed artificial censoring approach can certainly be considered for other well-developed models or methods for RNA-seq data analysis.

Analytical modeling and simulation of germanium single gate silicon on insulator TFET

This paper proposes a new two dimensional（2D） analytical model for a germanium（Ge） single gate silicon-on-insulator tunnel field effect transistor（SG SOI TFET）. The parabolic approximation technique is used to solve the 2D Poisson equation with suitable boundary conditions and analytical expressions are derived for the surfacepotential,theelectricfieldalongthechannelandtheverticalelectricfield.Thedeviceoutputtunnellingcurrent is derived further by using the electric fields. The results show that Ge based TFETs have significant improvements inon-currentcharacteristics.Theeffectivenessoftheproposedmodelhasbeenverifiedbycomparingtheanalytical model results with the technology computer aided design（TCAD） simulation results and also comparing them with results from a silicon based TFET.

Asymptotically Optimal Dividend Policy for Regime-Switching Compound Poisson Models

This work develops asymptotically optimal dividend policies to maximize the expected present value of dividends until ruin.Compound Poisson processes with regime switching are used to model the surplus and the switching（a continuous-time controlled Markov chain） represents random environment and other economic conditions.Assuming the switching to be fast varying together with suitable conditions,it is shown that the system has a limit that is an average with respect to the invariant measure of a related Markov chain.Under simple conditions,the optimal policy of the limit dividend strategy is a threshold policy.Using the optimal policy of the limit system as a guide,feedback control for the original surplus is then developed.It is demonstrated that the constructed dividend policy is asymptotically optimal.

Locally R-optimal designs for a class of nonlinear multiple regression models

This paper concerns with optimal designs for a wide class of nonlinear models with informa-tion driven by the linear predictor.The aim of this study is to generate an R-optimal design which minimizes the product of the main diagonal entries of the inverse of the Fisher informa tion matrix at certain values of the parameters.An equivalence theorem for the locally R optimal designs is provided in terms of the intensity function.Analytic solutions for the locally saturated R-optimal designs are derived for the models having linear predictors with and without intercept,respectively.The particle swarm optimization method has been employed to generate locally non-saturated R-optimal designs.Numerical examples are presented for ilustration of the locally R-optimal designs for Poisson regression models and proportional hazards regression models.