scholarly journals Density Estimation of Spatio-temporal Point Patterns Using Moran's Statistic

2018 ◽  
Vol 7 (2) ◽  
pp. 80
Author(s):  
Jennifer L. Lorio ◽  
Norou Diawara ◽  
Lance A. Waller
Keyword(s):  
Infectious Disease ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Poisson Process ◽  
Common Factor ◽  
Disease Spread ◽  
Point Patterns ◽  
Rate Of Increase ◽  
Spatio Temporal ◽  
Over Time

Moran's Index is a statistic that measures spatial autocorrelation, quantifying the degree of dispersion (or spread) of objects in space. When investigating data in an area, a single Moran statistic may not give a sufficient summary of the autocorrelation spread. However, by partitioning the area and taking the Moran statistic of each subarea, we discover patterns of the local neighbors not otherwise apparent. In this paper, we consider the model of the spread of an infectious disease, incorporate time factor, and simulate a multilevel Poisson process where the dependence among the levels is captured by the rate of increase of the disease spread over time, steered by a common factor in the scale. The main consequence of our results is that our Moran statistic is calculated from an explicit algorithm in a Monte Carlo simulation setting. Results are compared to Geary's statistic and estimates of parameters under Poisson process are given.

scholarly journals The effect of social distancing on the reach of an epidemic in social networks

2021 ◽  
Author(s):  
Gregory Gutin ◽  
Tomohiro Hirano ◽  
Sung-Ha Hwang ◽  
Philip R. Neary ◽  
Alexis Akira Toda
Keyword(s):  
Public Health ◽  
Infectious Disease ◽  
Social Networks ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Disease Transmission ◽  
Global Level ◽  
Social Distancing ◽  
The Public ◽  
Simulation Results

AbstractHow does social distancing affect the reach of an epidemic in social networks? We present Monte Carlo simulation results of a susceptible–infected–removed with social distancing model. The key feature of the model is that individuals are limited in the number of acquaintances that they can interact with, thereby constraining disease transmission to an infectious subnetwork of the original social network. While increased social distancing typically reduces the spread of an infectious disease, the magnitude varies greatly depending on the topology of the network, indicating the need for policies that are network dependent. Our results also reveal the importance of coordinating policies at the ‘global’ level. In particular, the public health benefits from social distancing to a group (e.g. a country) may be completely undone if that group maintains connections with outside groups that are not following suit.

scholarly journals Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility

Risks ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 35
Author(s):  
Moawia Alghalith ◽  
Christos Floros ◽  
Konstantinos Gkillas
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Volatility ◽  
Discrete Time ◽  
Simulation Analysis ◽  
Stochastic Volatility Models ◽  
Nonparametric Estimators ◽  
Volatility Models ◽  
Equity Index ◽  
Over Time

We propose novel nonparametric estimators for stochastic volatility and the volatility of volatility. In doing so, we relax the assumption of a constant volatility of volatility and therefore, we allow the volatility of volatility to vary over time. Our methods are exceedingly simple and far simpler than the existing ones. Using intraday prices for the Standard & Poor’s 500 equity index, the estimates revealed strong evidence that both volatility and the volatility of volatility are stochastic. We also proceeded in a Monte Carlo simulation analysis and found that the estimates were reasonably accurate. Such evidence implies that the stochastic volatility models proposed in the literature with constant volatility of volatility may fail to approximate the discrete-time short rate dynamics.

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