Variance Change Point Detection Under a Smoothly-Changing Mean Trend with Application to Liver Procurement

Abstract

Literature on change point analysis mostly requires a sudden change in the data distribution, either in a few parameters or the distribution as a whole. We are interested in the scenario that the variance of data may make a significant jump while the mean of data changes in a smooth fashion. It is motivated by a liver procurement experiment with organ surface temperature monitoring. Blindly applying the existing change point analysis methods to the example can yield erratic change point estimates since the smoothly-changing mean violates the sudden-change assumption. In my dissertation, we propose a penalized weighted least squares approach with an iterative estimation procedure that naturally integrates variance change point detection and smooth mean function estimation. Given the variance components, the mean function is estimated by smoothing splines as the minimizer of the penalized weighted least squares. Given the mean function, we propose a likelihood ratio test statistic for identifying the variance change point. The null distribution of the test statistic is derived together with the rates of convergence of all the parameter estimates. Simulations show excellent performance of the proposed method. Application analysis offers numerical support to the non-invasive organ viability assessment by surface temperature monitoring.The method above can only yield the variance change point of temperature at a single point on the surface of the organ at a time. In practice, an organ is often transplanted as a whole or in part. Therefore, it is generally of more interest to study the variance change point for a chunk of organ. With this motivation, we extend our method to study variance change point for a chunk of the organ surface. Now the variances become functions on a 2D space of locations (longitude and latitude) and the mean is a function on a 3D space of location and time. We model the variance functions by thin-plate splines and the mean function by the tensor product of thin-plate splines and cubic splines. However, the additional dimensions in these functions incur serious computational problems since the sample size, as a product of the number of locations and the number of sampling time points, becomes too large to run the standard multi-dimensional spline models. To overcome the computational hurdle, we introduce a multi-stages subsampling strategy into our modified iterative algorithm.The strategy involves several down-sampling or subsampling steps educated by preliminary statistical measures. We carry out extensive simulations to show that the new method can efficiently cut down the computational cost and make a practically unsolvable problem solvable with reasonable time and satisfactory parameter estimates. Application of the new method to the liver surface temperature monitoring data shows its effectiveness in providing accurate status change information for a portion of or the whole organ.The viability evaluation is the key issue in the organ transplant operation. The donated organ must be viable a...

Preliminary Simulation for Obtaining Accurate Heart Rate Data Using Imputation Methods

“…We used variance change point detection using the R package “changepoint” to determine significant change points in our time series data. We chose to use variance as opposed to mean to better identify significant jumps in heart rate changes as opposed to using the mean that addresses distribution changes in a smoother fashion (Gao et al, 2018). To test imputation performances, we randomly deleted intervals from one recorded heart rate data column.…”

Optimal Difference-based Variance Estimators in Time Series: A General Framework

“…• To test for a variance change point in the presence of a non-constant mean, a possible test statistic can be constructed by using Q (m) = i D 2 i /n with parameters chosen to minimize the long-run variance of log Q (m) , where D i is our proposed mth order difference statistics. This test could be used as an alternative to the recent work by Gao et al (2019).…”

Detecting Multiple Change Points: The PULSE Criterion

“…Frick et al (2014) suggested a simultaneous multiscale change-point estimator (SMUCE) by solving an optimization problem, Yao and Au (1989) proposed a penalized least squares-based approach for mean changes. A weighted least squares function-based method was suggested by Gao et al (2018). Harchaoui and Levy-Leduc (2010) proposed a LASSO-based approach.…”