Haiyan Cai

Critical sensor density for partial connectivity in large area wireless sensor networks

Assume sensor deployment follows the Poisson distribution. For a given partial connectivity requirement &#961;, 0.5 < &#961; < 1, we prove, for a hexagon model, that there exists a critical sensor density &#955;0, around which the probability that at least 100&#961;% of sensors are connected in the network increases sharply from &#949; to 1-&#949; within a short interval of sensor density &#961;. The location of &#961;0 is at the sensor density where the above probability is about 1/2. We also extend the results to the disk model. Simulations are conducted to confirm the theoretical results.

Critical Sensor Density for Partial Connectivity in Large Area Wireless Sensor Networks

Assume sensor deployment follows the Poisson distribution. For a given partial connectivity requirement ρ, 0.5 < ρ < 1, we prove, for a hexagon model, that there exists a critical sensor density λ0, around which the probability that at least 100ρ% of sensors are connected in the network increases sharply from ε to 1-ε within a short interval of sensor density ρ. The location of ρ0 is at the sensor density where the above probability is about 1/2. We also extend the results to the disk model. Simulations are conducted to confirm the theoretical results.

Regression for censored survival data with lag effects

We consider regression modeling of survival data subject to right censoring when the full effect of some covariates (e.g. treatment) may be delayed. Several models are proposed, and methods for computing the maximum likelihood estimates of the parameters are described. Consistency and asymptotic normality properties of the estimators are derived. Some numerical examples are used to illustrate the implementation of the modeling and estimation procedures. Finally we apply the theory to interim data from a large scale randomized clinical trial for the prevention of skin cancer.

Wavelet Change-Point Estimation for Long Memory Non-Parametric Random Design Models

For a random design regression model with long memory design and long memory errors, we consider the problem of detecting a change point for sharp cusp or jump discontinuity in the regression function. Using the wavelet methods, we obtain estimators for the change point, the jump size and the regression function. The strong consistencies of these estimators are given in terms of convergence rates.

Exact bound for the convergence of metropolis chains

In this note, we present a calculation which gives us the exact bound for the convergence of Metropolis chains in a finite state space and therefore improves the existing results which are only for the upper bounds of such convergence (see the references below). Our result is based on an interesting observation on the transition probability of Metropolis chains

Cluster Algorithms for Spatial Point Processes with Symmetric and Shift Invariant Interactions

Abstract In this article, Swendsen–Wang–Wolff algorithms are extended to simulate spatial point processes with symmetric and stationary interactions. Convergence of these algorithms is considered. Some further generalizations of the algorithms are discussed. The ideas presented in this article can also be useful in handling some large and complicated systems.

A normal approximation theorem in comparing two binomial distributions

Let p0 and be the parameters of two independent binomial distributions. Suppose p0 is known and has a prior distribution with a density function which is positive and continuous at p0. We introduce a normal approximation theorem for approximating the posterior distribution of the scaled difference , given that the difference of the corresponding binomial random variables increases slowly ([less-than-or-equals, slant]n[gamma], ). The theorem is proved based on a local limit theorem which links the probability of the difference of two independent and nearly identical binomial random variables to the density function of a normal distribution.

Piecewise deterministic Markov processes

In this paper we construct and study a class of Markov processes whose sample paths are piecewise deterministic and whose random jumps can have limiting points in finite time intervals. A characterization of the infinitesimal generators of such processes will be given

Coexistence in a competition model

For a d-dimensional multi-state competition model we identify a critical dimension dc such that the coexistence of the states can occur with a positive probability if and only if d>dc. We will also give a description of the limiting distributions of the model.

A law of iterated logarithm for the wavelet transforms of i.i.d. random variables

We apply a general result on the law of iterated logarithm to the wavelet transforms of i.i.d. random variables and show that a version of this law holds under some regularity conditions on the wavelet. This result provides asymptotic estimates of the rate of decay of the wavelet coefficients at intermediate scaling levels.