Random Change Point Research Articles

On Testing for the Constancy of Regression Coefficients under Random Walk and Change-Point Alternatives

The locally best invariant statistic to test for the constancy of regression coefficients under a random walk alternative is shown to be the same as a Bayesian-type statistic derived under a change-point alternative. Asymptotic theory for this and more general statistics is discussed.

Hierarchical Bayes Models for the Progression of HIV Infection Using Longitudinal CD4 T-Cell Numbers

Abstract Taking the absolute number of CD4 T-cells as a marker of disease progression for persons infected with the human immunodeficiency virus (HIV), we model longitudinal series of such counts for a sample of 327 subjects in the San Francisco Men's Health Study (Waves 1–8, excluding zidovudine cases). We conduct a fully Bayesian analysis of these data. We employ individual level nonlinear models incorporating such critical features as incomplete and unbalanced data, population covariates (age at study entry and an indicator of self-reported herpes simplex virus infection), unobserved random change points, heterogeneous variances, and errors in variables. We construct prior distributions using results of previously published work from several different sources and data from HIV-negative men in this study. We also develop an approach to Bayesian model choice and individual prediction. Our analysis provides marginal posterior distributions for all population parameters in our model for this cohort. Using an inverse prediction approach, we also develop the posterior distributions of time for CD4 T-cell number to reach a specified level.

Probability maximizing approach to a secretary problem by random change-point of the distribution law of the observed process

Before some random moment θ, independent identically distributed random variables x1, · ··, xθ–1 with common distribution function μ (dx) appear consecutively. After the moment θ, independent random variables xθ, xθ+1, · ·· have another common distribution function f (x)μ (dx). Our information about θ can be constructed only by successively observed values of the x's.In this paper we find an optimal stopping policy by which we can maximize the probability that the quantity associated with the stopping time is the largest of all θ + m – 1 quantities for a given integer m.

Probability maximizing approach to a secretary problem by random change-point of the distribution law of the observed process

Before some random moment θ, independent identically distributed random variables x 1, · ··, xθ– 1 with common distribution function μ (dx) appear consecutively. After the moment θ, independent random variables xθ, xθ +1, · ·· have another common distribution function f (x)μ (dx). Our information about θ can be constructed only by successively observed values of the x's. In this paper we find an optimal stopping policy by which we can maximize the probability that the quantity associated with the stopping time is the largest of all θ + m – 1 quantities for a given integer m.