### Approximate simulation free multiple changepoint analysis with Gaussian Markov random field segment models

, 2010

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### ii TABLE OF CONTENTS

, 2010

"... 2010 c ○ 2010 Jonathan HutchinsThe dissertation of Jonathan Hutchins ..."

### ROBUSTNESS OF TWO-PHASE REGRESSION TESTS Authors:

"... This article studies the robustness of different likelihood ratio tests proposed by Quandt ([1]) and ([2]), (Q-Test), Kim and Siegmund ([3]), (KS-Test), and Kim ([4]), (K-Test), to detect a change in simple linear regression models. These tests are evaluated and compared with respect to their perfor ..."

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This article studies the robustness of different likelihood ratio tests proposed by Quandt ([1]) and ([2]), (Q-Test), Kim and Siegmund ([3]), (KS-Test), and Kim ([4]), (K-Test), to detect a change in simple linear regression models. These tests are evaluated and compared with respect to their performance taking into account different scenarios, such as, different error distributions, different sample sizes, different locations of the change point and departure from the homoscedasticity. Two different alternatives are considered: i) with a change in the intercept from one model to the other with the same slope and ii) with a change in both the intercept and slope. The simulation results reveal that the KS-Test is superior to the Q-Test for both models considered while the K-Test is more powerful than the other two tests for nonhomogeneous models with a known variance. Key-Words: segmented regression models; likelihood ratio tests; robustness. AMS Subject Classification: • 62J02, 62F03. 2 Diniz and BrochiRobustness of two-phase regression tests 3 1.

### Universidade de São Paulo,

"... Markov Chain Monte Carlo (MCMC) methods are used to perform a Bayesian analysis for interfailure data with constant hazard function in the presence of one or more change-points. We also present some Bayesian criteria to discriminate different models. The methodology is illustrated with a data set or ..."

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Markov Chain Monte Carlo (MCMC) methods are used to perform a Bayesian analysis for interfailure data with constant hazard function in the presence of one or more change-points. We also present some Bayesian criteria to discriminate different models. The methodology is illustrated with a data set originally reported in Maguire, Pearson and Wynn [8]. Key-Words:

### Direct Simulation Methods for Multiple Changepoints Problems

, 2007

"... The multiple changepoint model has been considered in a wide range of statistical modelling, as it increases the flexibility to simple statistical applications. The main purpose of the thesis enables the Bayesian inference from such models by using the idea of particle filters. Compared to the exist ..."

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The multiple changepoint model has been considered in a wide range of statistical modelling, as it increases the flexibility to simple statistical applications. The main purpose of the thesis enables the Bayesian inference from such models by using the idea of particle filters. Compared to the existed methodology such as RJMCMC of Green (1995), the attraction of our particle filter is its simplicity and efficiency. We propose an on-line algorithm for exact filtering for a class of multiple changepoint problems. This class of models satisfy an important conditional independence property. This algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models. The computational cost of this exact algorithm is quadratic in the number of observations. We further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations, at the expense of introducing small errors; and propose two new, optimum resampling algorithms for this problem. In practice, large computational

### Bayesian Inference from Continuously Arriving Informant Reports, with Application to Crisis Response ∗

, 2004

"... Note: This is a draft document. Please do not cite without permission. Effective decision-making for crisis response depends upon the rapid integration of limited information from (possibly unreliable) human sources. Here, a Bayesian modeling framework is developed for inference from informant repor ..."

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Note: This is a draft document. Please do not cite without permission. Effective decision-making for crisis response depends upon the rapid integration of limited information from (possibly unreliable) human sources. Here, a Bayesian modeling framework is developed for inference from informant reports. Reports are assumed to arrive via a Poisson-like process, whose rates are dependent upon the (unknown) state of the world in addition to assorted covariates. A hierarchical modeling structure is used to represent error processes which vary based on informants ’ group memberships, with the possibility of multiple, overlapping memberships for each informant. Procedures are shown for sampling from the joint posterior distribution of the parameters, and for obtaining posterior predictive quantities.

### An Objective Bayesian Analysis of theChangePointProblem

, 2004

"... The Bayesian literature on the change point problem deals with the inference of a change in the distribution of a set of timeordered data based on a sample of fixed size. This is the so-called “retrospective or off-line ” analysis of the change point problem. A related but different problem is that ..."

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The Bayesian literature on the change point problem deals with the inference of a change in the distribution of a set of timeordered data based on a sample of fixed size. This is the so-called “retrospective or off-line ” analysis of the change point problem. A related but different problem is that of the “sequential ” change point detection, mainly analyzed from a frequentist viewpoint. While the former typically focuses on the estimation of the position in which the change point occurs, the latter is a testing problem which has a natural formulation as a Bayesian model selection problem. In this paper we provide such a Bayesian formulation, which generalizes previous formulations such as the well-known CUSUM stopping rule. We show that the conventional improper priors (also called non-informative, objective or default), cannot be used either for sequential detection of the change or for retrospective estimation. Then, we propose objective intrinsic prior distributions for the unknown model parameters. The normal and Poisson cases are studied in detail and examples with simulated and real data are provided.

### Analysis ofa Simple Debugging Model

, 1986

"... A system has an unknown number of faults. Each fault causes a failure of the system, and is then located and removed. The failure times are independent exponential random variables with common mean. A Bayesian analysis of this model is presented, with emphasis on the situation where vague prior know ..."

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A system has an unknown number of faults. Each fault causes a failure of the system, and is then located and removed. The failure times are independent exponential random variables with common mean. A Bayesian analysis of this model is presented, with emphasis on the situation where vague prior knowledge is represented by limiting, improper, prior forms. This provides a test for reliability growth, estimates of the number of faults, an evaluation of current system reliability, and a prediction of the time to full debugging. Three examples are given.

### Old Jungle Saying Contents

, 2011

"... In the real world, lots of things are uncertain; including the proper way to handle uncertainty. ..."

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In the real world, lots of things are uncertain; including the proper way to handle uncertainty.