Using simulation studies to evaluate statistical methods

Simulation studies are computer experiments that involve creating data by pseudorandom sampling. The key strength of simulation studies is the ability to understand the behaviour of statistical methods because some 'truth' (usually some parameter/s of interest) is known from the process of generating the data. This allows us to consider properties of methods, such as bias. While widely used, simulation studies are often poorly designed, analysed and reported. This tutorial outlines the rationale for using simulation studies and offers guidance for design, execution, analysis, reporting and presentation. In particular, this tutorial provides: a structured approach for planning and reporting simulation studies, which involves defining aims, data-generating mechanisms, estimands, methods and performance measures ('ADEMP'); coherent terminology for simulation studies; guidance on coding simulation studies; a critical discussion of key performance measures and their estimation; guidance on structuring tabular and graphical presentation of results; and new graphical presentations. With a view to describing recent practice, we review 100 articles taken from Volume 34 of Statistics in Medicine that included at least one simulation study and identify areas for improvement.Comment: 31 pages, 9 figures (2 in appendix), 8 tables (1 in appendix

Graphs with specified degree distributions, simple epidemics and local vaccination strategies

Consider a random graph, having a pre-specified degree distribution F but other than that being uniformly distributed, describing the social structure (friendship) in a large community. Suppose one individual in the community is externally infected by an infectious disease and that the disease has its course by assuming that infected individuals infect their not yet infected friends independently with probability p. For this situation the paper determines R_0 and tau_0, the basic reproduction number and the asymptotic final size in case of a major outbreak. Further, the paper looks at some different local vaccination strategies where individuals are chosen randomly and vaccinated, or friends of the selected individuals are vaccinated, prior to the introduction of the disease. For the studied vaccination strategies the paper determines R_v: the reproduction number, and tau_v: the asymptotic final proportion infected in case of a major outbreak, after vaccinating a fraction v.Comment: 31 pages, 3 figure

EZ-AG: Structure-free data aggregation in MANETs using push-assisted self-repelling random walks

This paper describes EZ-AG, a structure-free protocol for duplicate insensitive data aggregation in MANETs. The key idea in EZ-AG is to introduce a token that performs a self-repelling random walk in the network and aggregates information from nodes when they are visited for the first time. A self-repelling random walk of a token on a graph is one in which at each step, the token moves to a neighbor that has been visited least often. While self-repelling random walks visit all nodes in the network much faster than plain random walks, they tend to slow down when most of the nodes are already visited. In this paper, we show that a single step push phase at each node can significantly speed up the aggregation and eliminate this slow down. By doing so, EZ-AG achieves aggregation in only O(N) time and messages. In terms of overhead, EZ-AG outperforms existing structure-free data aggregation by a factor of at least log(N) and achieves the lower bound for aggregation message overhead. We demonstrate the scalability and robustness of EZ-AG using ns-3 simulations in networks ranging from 100 to 4000 nodes under different mobility models and node speeds. We also describe a hierarchical extension for EZ-AG that can produce multi-resolution aggregates at each node using only O(NlogN) messages, which is a poly-logarithmic factor improvement over existing techniques