Bayesian Segmentation of Piecewise Linear Regression Models Using Reversible Jump MCMC Algorithm

Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation ofpiecewise linear regression models. The method used to estimate the parameters ofpicewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC （Marcov Chain Monte Carlo） algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters ofpicewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.

Knowledge Discovery in Learning Management System Using Piecewise Linear Regression

Recent developments in database technology have seen a wide variety of data being stored in huge collections. The wide variety makes the analysis tasks of a generic database a strenuous task in knowledge discovery. One approach is to summarize large datasets in such a way that the resulting summary dataset is of manageable size. Histogram has received significant attention as summarization/representative object for large database. But, it suffers from computational and space complexity. In this paper, we propose an idea to transform the histogram object into a Piecewise Linear Regression (PLR) line object and suggest that PLR objects can be less computational and storage intensive while compared to those of histograms. On the other hand to carry out a cluster analysis, we propose a distance measure for computing the distance between the PLR lines. Case study is presented based on the real data of online education system LMS. This demonstrates that PLR is a powerful knowledge representative for very large database.

An easy,convenient statistical method to analyze bark beetle populations

A non-invasive method to estimate the number of Trypodendron lineatum holes on dead standing pines(Pinus sylvestris L.)was developed using linear and nonlinear estimations.A clas sical linear regres sion model was first used to analyze the relationship between the number of holes caused by T.lineatum on selected stem units and the total number of holes on an entire dead stem of P.sylvestris.Then,to obtain a better fit of the regression function to the data for the stem unit selected in the first step,piecewise linear regression(PLR)was used.Last,in an area used to evaluate wood decomposition(method validation),the total and mean numbers of T.lineatum holes were estimated for single dead trees and for a sample(n=8 dead trees).Data were collected in 2009(data set D1),in 2010-2014(data set D2)and in 2020(data set D3)in forests containing P.sylvestris located within Suchedniow-Oblegorek Landscape Park,Poland.A model was constructed with three linear equations.An evaluation of model accuracy showed that it was highly effective regardless of the density of T.lineatum holes and sample size.The method enables the evaluation of the biological role of this species in the decomposition of dead standing wood of P.sylvestris in strictly protected areas.

Optimal Antibody Puri cation Strategies Using Data-Driven Models

This work addresses the multiscale optimization of the puri cation processes of antibody fragments. Chromatography decisions in the manufacturing processes are optimized, including the number of chromatography columns and their sizes, the number of cycles per batch, and the operational ow velocities. Data-driven models of chromatography throughput are developed considering loaded mass, ow velocity, and column bed height as the inputs, using manufacturing-scale simulated datasets based on microscale experimental data. The piecewise linear regression modeling method is adapted due to its simplicity and better prediction accuracy in comparison with other methods. Two alternative mixed-integer nonlinear programming (MINLP) models are proposed to minimize the total cost of goods per gram of the antibody puri cation process, incorporating the data-driven models. These MINLP models are then reformulated as mixed-integer linear programming (MILP) models using linearization techniques and multiparametric disaggregation. Two industrially relevant cases with different chromatography column size alternatives are investigated to demonstrate the applicability of the proposed models.

Evolution and Effects of the Social-ecological System in Karst Mountainous Regions:A Case Study of Guangxi,China

Karst regions are the typical areas of interaction between human society and natural ecosystems.Understanding the historical mechanisms of the evolution of social-ecological systems(SES)is crucial for the future sustainable management of karst regions.This study selected Guangxi,a typical karst mountainous region in Southwest China,as the study area,and used population,cropland area,and forest coverage as the SES elements.Based on the framework of SES research in the karst region,it adopted segmented linear regression to identify the stages of the interactions among these elements,to reveal the evolutionary stages of social development from the long-term perspective.In addition,the driving factor indicators were constructed from the aspects of natural environment,social development,government policy,and climate change,and then the feedback changes brought about by the evolution were investigated.The results show that the evolution of SES in Guangxi from 1363-2020 can be divided into seven stages.In the first,second,and early period of the third stages,the government of Guangxi mainly focused on agricultural activities,although the only way to meet the growing demand for food was by expanding the area of cropland,and the timber trade’s pursuit of economic development,resulting in an increase in rocky desertification.In the fourth stage,the ecological environment improved under the implementation of measures such as the control of rocky desertification and the compensation of forest ecological benefits.After the fifth stage,the effect of rocky desertification control has been remarkable.Although the implementation of relevant policies has alleviated the environmental problems to some extent,the continual changes in the structure and function of SES can challenge further progress towards sustainability in karst regions.This study aims to provide a reference for the long-term national spatial planning and the development of environmental policies in karst regions.