Statistics and Probability Commons^™

Incorporating Historical Models With Adaptive Bayesian Updates, Philip S. Boonstra, Ryan P. Barbaro

The University of Michigan Department of Biostatistics Working Paper Series

This paper considers Bayesian approaches for incorporating information from a historical model into a current analysis when the historical model includes only a subset of covariates currently of interest. The statistical challenge is two-fold. First, the parameters in the nested historical model are not generally equal to their counterparts in the larger current model, neither in value nor interpretation. Second, because the historical information will not be equally informative for all parameters in the current analysis, additional regularization may be required beyond that provided by the historical information. We propose several novel extensions of the so-called power prior that adaptively …

Essentials Of Structural Equation Modeling, Mustafa Emre Civelek

Zea E-Books Collection

Structural Equation Modeling is a statistical method increasingly used in scientific studies in the fields of Social Sciences. It is currently a preferred analysis method, especially in doctoral dissertations and academic researches. However, since many universities do not include this method in the curriculum of undergraduate and graduate courses, students and scholars try to solve the problems they encounter by using various books and internet resources.

This book aims to guide the researcher who wants to use this method in a way that is free from math expressions. It teaches the steps of a research program using structured equality modeling …

Building A Better Risk Prevention Model, Steven Hornyak

National Youth Advocacy & Resilience Conference

This presentation chronicles the work of Houston County Schools in developing a risk prevention model built on more than ten years of longitudinal student data. In its second year of implementation, Houston At-Risk Profiles (HARP), has proven effective in identifying those students most in need of support and linking them to interventions and supports that lead to improved outcomes and significantly reduces the risk of failure.

A Comparison Of Machine Learning Techniques For Taxonomic Classification Of Teeth From The Family Bovidae, Gregory J. Matthews, Juliet K. Brophy, Maxwell Luetkemeier, Hongie Gu, George K. Thiruvathukal

Mathematics and Statistics: Faculty Publications and Other Works

This study explores the performance of machine learning algorithms on the classification of fossil teeth in the Family Bovidae. Isolated bovid teeth are typically the most common fossils found in southern Africa and they often constitute the basis for paleoenvironmental reconstructions. Taxonomic identification of fossil bovid teeth, however, is often imprecise and subjective. Using modern teeth with known taxons, machine learning algorithms can be trained to classify fossils. Previous work by Brophy et al. [Quantitative morphological analysis of bovid teeth and implications for paleoenvironmental reconstruction of plovers lake, Gauteng Province, South Africa, J. Archaeol. Sci. 41 (2014), pp. …

They're Only Nuclear Weapons: An Exploratory Analysis Of Safety Climate Within The Nuclear Enterprise, Brandon M. Clements

Theses and Dissertations

By possessing nuclear weapons, the United States Air Force is inherently exposed to extreme safety concerns. With multiple setbacks in recent years (e.g., unauthorized transport of nuclear weapons, cheating scandals, and career dissatisfaction), some have begun to wonder how safe the nuclear enterprise truly is. Building upon the concept of safety climate, this study explores safety climate constructs and trends associated with current nuclear maintenance safety climate survey data.

Forecasting Country Conflict Within Modified Combatant Command Regions Using Statistical Learning Methods, Sarah Neumann

Theses and Dissertations

Conflict forecasts are crucial to Combatant Commanders’ understanding of the dynamic environment encompassing countries within their area of responsibility. The current structure of the Combatant Commands (COCOMs) is rooted in geography by grouping nations in geographic proximity to the same regional command. However, leaders today question the effectiveness of the current structure. A novel modified k-means clustering algorithm is developed and implemented that groups countries based on data similarities and geographic proximity resulting in new COCOM groupings that improve conflict forecasts. The data spans various political, military, economic, and social characteristics of countries, and is used to develop conditional logistic …

A Spline-Assisted Semiparametric Approach To Nonparametric Measurement Error Models, Fei Jiang, Yanyuan Ma

COBRA Preprint Series

Nonparametric estimation of the probability density function of a random variable measured with error is considered to be a difficult problem, in the sense that depending on the measurement error prop- erty, the estimation rate can be as slow as the logarithm of the sample size. Likewise, nonparametric estimation of the regression function with errors in the covariate suffers the same possibly slow rate. The traditional methods for both problems are based on deconvolution, where the slow convergence rate is caused by the quick convergence to zero of the Fourier transform of the measurement error density, which, unfortunately, appears in …

Telotristat Ethyl In Carcinoid Syndrome: Safety And Efficacy In The Telecast Phase 3 Trial, Marianne Pavel, David J. Gross, Marta Benavent, Petros Perros, Raj Srirajaskanthan, Richard R. P. Warner, Matthew H. Kulke, Lowell B. Anthony, Pamela L. Kunz, Dieter Hörsch, Martin O Weickert, Pablo Lapuerta, Wenjun Jiang, Kenneth Kassler-Taub, Suman Wason, Rosanna Fleming, Douglas Fleming, Rocio Garcia-Carbonero

Internal Medicine Faculty Publications

Telotristat ethyl, a tryptophan hydroxylase inhibitor, was efficacious and well tolerated in the phase 3 TELESTAR study in patients with carcinoid syndrome (CS) experiencing ≥ 4 bowel movements per day (BMs/day) while on somatostatin analogs (SSAs). TELECAST, a phase 3 companion study, assessed the safety and efficacy of telotristat ethyl in patients with CS (diarrhea, flushing, abdominal pain, nausea or elevated urinary 5-hydroxyindoleacetic acid (u5-HIAA)) with < 4 BMs/day on SSAs (or ≥ 1 symptom or ≥ 4 BMs/day if not on SSAs) during a 12-week double-blind treatment period followed by a 36-week open-label extension (OLE). The primary safety and efficacy endpoints were incidence of treatment-emergent adverse events (TEAEs) and percent change from baseline in 24-h u5-HIAA at week 12. Patients (N = 76) were randomly assigned (1:1:1) to receive placebo or telotristat ethyl 250 mg or 500 mg 3 times per day (tid); 67 continued receiving telotristat ethyl 500 mg tid during the OLE. …

Density Estimation Of Spatio-Temporal Point Patterns Using Moran’S Statistics, Jennifer L. Lorio, Norou Diawara, Lance A. Waller

Mathematics & Statistics Faculty Publications

Moran’s Index is a statistic that measures spatial autocorrelation, quantifying the degree of dispersion (or spread) of objects in space. When investigating data in an area, a single Moran statistic may not give a sufficient summary of the autocorrelation spread. However, by partitioning the area and taking the Moran statistic of each subarea, we discover patterns of the local neighbors not otherwise apparent. In this paper, we consider the model of the spread of an infectious disease, incorporate time factor, and simulate a multilevel Poisson process where the dependence among the levels is captured by the rate of increase of …

Partitioning The Effects Of Eco-Evolutionary Feedbacks On Community Stability, Swati Patel, Michael H. Cortez, Sebastian J. Schreiber

Mathematics and Statistics Faculty Publications

A fundamental challenge in ecology continues to be identifying mechanisms that stabilize community dynamics. By altering the interactions within a community, eco-evolutionary feedbacks may play a role in community stability. Indeed, recent empirical and theoretical studies demonstrate that these feedbacks can stabilize or destabilize communities and, moreover, that this sometimes depends on the relative rate of ecological to evolutionary processes. So far, theory on how eco-evolutionary feedbacks impact stability exists only for a few special cases. In our work, we develop a general theory for determining the effects of eco-evolutionary feedbacks on stability in communities with an arbitrary number of …

Angiostrongylus Cantonensis: Epidemiologic Review, Location-Specific Habitat Modelling, And Surveillance In Hillsborough County, Florida, U.S.A., Brad Christian Perich

USF Tampa Graduate Theses and Dissertations

Angiostrongylus cantonensis is a parasitic nematode endemic to tropical and subtropical regions and is the leading cause of human eosinophilic meningitis. The parasite is commonly known as rat lungworm because the primary host in its lifecycle is the rat. A clinical overview of rat lungworm infection is presented, followed by a literature review of rat lungworm epidemiology, risk factors, and surveillance projects. Data collected from previous snail surveys in Florida was considered alongside elevation, population per square kilometer, median household income by zip code territory, and normalized difference vegetation index specific to the geographic coordinates from which the snail samples …

Antenatal Care Provider And Cesarean Section In Urban Areas In Indonesia, Terry Yuliana Rahadian Pristya, Milla Herdayati, Besral Besral, Dheni Fidyah Fika

Kesmas

Tren persalinan sesar di Indonesia (2007-2012) mengalami peningkatan dua kali lipat berisiko pada munculnya masalah kesehatan jangka panjang maupun pendek. Penelitian ini bertujuan mengetahui hubungan tenaga kesehatan pemeriksa kehamilan dengan persalinan sesar. Penelitian kuantitatif ini menggunakan desain potong lintang dengan sampel penelitian 5143 wanita usia subur berusia 15-49 tahun yang melahirkan anak terakhirnya, baik melahirkan sesar maupun tidak di wilayah perkotaan yang terpilih dalam sampel Survei Demografi Kesehatan Indonesia tahun 2012. Analisis multivariat regresi logistik digunakan untuk mengetahui hubungan tenaga pemeriksa kehamilan dengan persalinan sesar, dikontrol oleh usia ibu, tempat periksa kehamilan, paritas, dan tempat melahirkan. Hasil penelitian menunjukkan bahwa …

Early Inititation Of Breastfeeding And Vitamin A Supplementation With Nutritional Status Of Children Aged 6-59 Months, Betty Yosephin Simanjuntak, Miratul Haya, Desri Suryani, Che An Ahmad

Kesmas

Masa balita, khususnya dua tahun pertama kehidupan merupakan usia emas bagi anak karena pertumbuhan dan perkembangannya yang cepat. Oleh karena itu, terjadinya gangguan nutrisi pada masa itu bisa bersifat permanen dan tidak dapat diubah. Penelitian ini mengkaji hubungan antara inisiasi dini pemberian air susu ibu dan vitamin A dengan status gizi. Total sampel yang dianalisis dalam penelitian ini adalah 1.592 anak di bawah lima tahun (balita) berusia 6-59 bulan yang diambil dari Pemantauan Status Gizi Indonesia 2015 di Bengkulu. Data termasuk usia, jenis kelamin, inisiasi menyusui dini, panjang kelahiran, berat lahir, suplementasi vitamin Adikumpulkan dengan menggunakan kuesioner. Berat dan tinggi …

Family Support As A Factor Influencing The Provision Of Exclusive Breastfeeding Among Adolescent Mothers In Bantul, Yogyakarta, Maulida Lailatussu’Da, Niken Meilani, Nanik Setiyawati, Sammy Onyapidi Barasa

Kesmas

Kehamilan remaja di Indonesia cukup tinggi. Kecamatan Sewon memiliki angka persalinan remaja tertinggi di Kabupaten Bantul pada tahun 2015-2016. Penelitian ini bertujuan untuk mengetahui faktor-faktor yang memengaruhi pemberian ASI eksklusif pada ibu usia remaja di Kecamatan Sewon, Kabupaten Bantul. Penelitian ini menggunakan desain potong lintang dan sampel penelitian berjumlah 45 orang ibu usia remaja yang mempunyai bayi usia 6-24 bulan. Pengumpulan data menggunakan kuesioner terstruktur. Analisis bivariat menggunakan kai kuadrat dan fisher’s exact test, sedangkan analisis multivariat menggunakan regresi logistik. Hasil penelitian menunjukkan bahwa 53.3% ibu usia remaja tidak memberikan ASI eksklusif. Analisis bivariat menunjukkan faktor status kehamilan (nilai p …

Effect Of Nutrition Counseling Knowledge And Attitude Toward Mother Breastfeeding And Baby Growth In Sub Lubuk Pakam, Herta Masthalina, Zein Agustina

Kesmas

Untuk dapat menjalankan program ASI eksklusif, ibu menyusui harus memiliki pengetahuan yang baik. Salah satu cara dalam menambah pengetahuan yaitu dengan memberikan konseling gizi. Penelitian ini bertujuan untuk mengetahui pengaruh konseling gizi tentang ASI eksklusif dan status gizi terhadap pengetahuan dan sikap ibu menyusui di wilayah Puskesmas Kecamatan Lubuk Pakam. Jenis penelitian ini adalah quasi experimental non-equivalent control group design. Sampel sejumlah 60 ibu dibagi ke dalam dua kelompok, yaitu 30 ibu yang diberikan konseling gizi intensif pada kelompok intervensi di wilayah kerja Puskesmas Lubuk Pakam dan 30 ibu pada kelompok kontrol di wilayah kerja Puskesmas Tanjung Morawa. Kelompok perlakuan …

The Effect Of Health Insurance On Institutional Delivery In Indonesia, Mazda Novi Mukhlisa, Pujiyanto Pujiyanto

Kesmas

Pemanfaatan pelayanan persalinan di fasilitas kesehatan berdampak pada menurunnya angka kematian ibu (AKI). Di Indonesia, persalinan di fasilitas kesehatan mengalami peningkatan setiap tahunnya, tetapi masih terdapat sekitar 30% ibu yang bersalin di rumah. Sayangnya, peningkatan pemanfaatan pelayanan persalinan di fasilitas kesehatan tersebut tidak diimbangi dengan penurunan AKI, sehingga Indonesia tidak berhasil mencapai target MDGs. Untuk mencapai Universal Health Coverage, Indonesia mengimplementasikan program Jaminan Kesehatan Nasional (JKN) yang mengintegrasikan empat jaminan kesehatan, yaitu Askes/ASABRI, Jamsostek, Jamkesmas, dan Jamkesda. Jaminan kesehatan dapat mengatasi kendala biaya pada persalinan di fasilitas kesehatan. Dengan menggunakan data Riset Kesehatan Dasar 2013 dan data Potensi Desa 2011 …

Risk Of Adolescent Pregnancy Toward Maternal And Infant Health, Analisis Of Idhs 2012, Anni Fithriyatul Mas'udah, Besral Besral, Bimandra Adiputra Djaafara

Kesmas

Dampak kehamilan pada remaja erat kaitannya dengan risiko kesehatan ibu dan bayi. Penelitian ini bertujuan untuk mengembangkan komposit indeks kesehatan ibu, indeks kesehatan bayi dan untuk menelaah pengaruh kehamilan remaja terhadap kesehatan ibu dan bayi. Penelitian ini menggunakan data Survei Demografi Kesehatan Indonesia tahun 2012, dengan sampel 2.167 responden yang memenuhi syarat inklusi (wanita usia subur yang pernah melahirkan anak pertama sejak Januari 2007 sampai survei dilaksanakan). Analisis menggunakan Polychoric Principal Component Analysis untuk menentukan komposit indeks kesehatan ibu dan bayi, serta regresi logistik untuk mengetahui besar hubungan kehamilan remaja terhadap kesehatan ibu dan bayi. Kesehatan ibu dapat ditentukan melalui …

Exclusive Breastfeeding Intention Among Pregnant Women, Tria Astika Endah Permatasari, Ratu Ayu Dewi Sartika, Endang Laksminingsih Achadi, Urip Purwono, Anies Irawati, Dwiana Ocviyanti, Evi Martha

Kesmas

Intensi pemberian ASI eksklusif adalah intensi ibu untuk memberikan hanya ASI pada bayinya sejak dilahirkan hingga berusia enam bulan. Intensi pada periode prenatal merupakan penentu langsung pemberian ASI eksklusif. Penelitian ini bertujuan mengetahui faktor paling dominan berhubungan dengan intensi pemberian ASI eksklusif pada ibu hamil di sebuah rumah sakit ibu dan anak di Kota Tangerang Selatan. Penelitian dengan desain studi potong lintang dilakukan secara primer. Sampel berjumlah 143 ibu hamil trimester ketiga dipilih secara purposive sampling. Intensi pemberian ASI eksklusif diukur menggunakan kuesioner the Infant Feeding Intentions scale. Sedangkan sikap, norma subjektif dan persepsi kontrol perilaku dinilai menggunakan modifikasi kuesioner …

Technical Considerations In The Use Of The E-Value, Tyler J. Vanderweele, Peng Ding, Maya Mathur

Harvard University Biostatistics Working Paper Series

The E-value is defined as the minimum strength of association on the risk ratio scale that an unmeasured confounder would have to have with both the exposure and the outcome, conditional on the measured covariates, to explain away the observed exposure-outcome association. We have elsewhere proposed that the reporting of E-values for estimates and for the limit of the confidence interval closest to the null become routine whenever causal effects are of interest. A number of questions have arisen about the use of E-value including questions concerning the interpretation of the relevant confounding association parameters, the nature of the transformation …

Influence Of The Event Rate On Discrimination Abilities Of Bankruptcy Prediction Models, Lili Zhang, Jennifer Priestley, Xuelei Ni

Published and Grey Literature from PhD Candidates

In bankruptcy prediction, the proportion of events is very low, which is often oversampled to eliminate this bias. In this paper, we study the influence of the event rate on discrimination abilities of bankruptcy prediction models. First the statistical association and significance of public records and firmographics indicators with the bankruptcy were explored. Then the event rate was oversampled from 0.12% to 10%, 20%, 30%, 40%, and 50%, respectively. Seven models were developed, including Logistic Regression, Decision Tree, Random Forest, Gradient Boosting, Support Vector Machine, Bayesian Network, and Neural Network. Under different event rates, models were comprehensively evaluated and compared …

An Old Tool With Enduring Value: Using Excel To Prepare Data For Analysis, Gregory A. Smith

Faculty Publications and Presentations

Microsoft Excel was first released on the Windows platform 30 years ago and has since become widely used. Although new tools for manipulating, analyzing, and visualizing data are constantly emerging, Excel remains a potent tool—and not just because of newer features. Simple functions such as TRIM, MID, SUBSTITUTE, FIND, ROUNDDOWN, and VLOOKUP can be used to manipulate data sets in powerful ways.

This workshop applies selected functions to realistic library data sets. Demonstrations include:

• deriving time-series categories from date and time stamps
• pre-coding survey comments based on keywords
• dealing with messy data points such as …

Strategies To Adjust For Response Bias In Clinical Trials: A Simulation Study, Victoria R. Swaidan

USF Tampa Graduate Theses and Dissertations

Background: Response bias can distort treatment effect estimates and inferences in clinical trials. Although prevention, quantification, and adjustments have been developed, current methods are not applicable when subject-level reliability is used as the measure of response bias. Thus, the objective of the current study is to develop, test, and recommend a series of bias correction strategies for use in these cases. Methods: Monte Carlo simulation and logistic regression modeling were used to develop the strategies, examining the collective impact of sample size (N), effect size (ES), reliability distribution, and response style on estimating the treatment effect size in a series …

Effect Of Anthropometric Variability On Middle-Market Aircraft Seating, Tara C. Sriram

International Journal of Aviation, Aeronautics, and Aerospace

A middle-of-market aircraft, or MoMA, is defined as an aircraft capable of flying 180-250 passengers without refueling for 2,300-5,800 miles(~2,000-5,000 nautical miles). As the name suggests, middle-of-market aircraft are positioned in between the market segments served by narrow body (single-aisle) and wide body (twin-aisle) aircraft. This paper presents the findings of a study on the effect of anthropomorphic variability on economy class seating on middle-market aircraft currently in service. The study found that among 130 middle-market LOPAs, the mean seat pitch was greater for US airlines than for Asian airlines. Furthermore, the sampled Asian airlines had a higher preference …

The Association Of Long-Term Exposure To Particulate Matter Air Pollution With Brain Mri Findings: The Aric Study., Melinda C Power, Archana P Lamichhane, Duanping Liao, Xiaohui Xu, Clifford R Jack, Rebecca F Gottesman, Thomas Mosley, James D Stewart, Jeff D Yanosky, Eric A Whitsel

Epidemiology Faculty Publications

BACKGROUND: Increasing evidence links higher particulate matter (PM) air pollution exposure to late-life cognitive impairment. However, few studies have considered associations between direct estimates of long-term past exposures and brain MRI findings indicative of neurodegeneration or cerebrovascular disease.

OBJECTIVE: Our objective was to quantify the association between brain MRI findings and PM exposures approximately 5 to 20 y prior to MRI in the Atherosclerosis Risk in Communities (ARIC) study.

METHODS: ARIC is based in four U.S. sites: Washington County, Maryland; Minneapolis suburbs, Minnesota; Forsyth County, North Carolina; and Jackson, Mississippi. A subset of ARIC participants underwent 3T brain MRI in …

Dietary Inflammatory Index And Cardiovascular Risk And Mortality—A Meta-Analysis, Nitin Shivappa, Justyna Godos, James R. Hébert, Michael Wirth, Gabriele Piuri, Attilio Speciani, Giuseppe Grosso

Faculty Publications

Diet and chronic inflammation have been suggested to be risk factors in the development of cardiovascular disease (CVD) and related mortality. The possible link between the inflammatory potential of diet measured through the Dietary Inflammatory Index (DII^®) and CVD has been investigated in several populations across the world. The aim of this study was to conduct a meta-analysis on studies exploring this association. Data from 14 studies were eligible, of which two were case-control, eleven were cohort, and one was cross-sectional. Results from the random-effects meta-analysis showed a positive association between increasing DII, indicating a pro-inflammatory diet, and …

Lower Dietary Inflammatory Index Scores Are Associated With Lower Glycemic Index Scores Among College Students, Yeonsoo Kim, Jie Chen, Michael Wirth, Nitin Shivappa, James R. Hébert

Faculty Publications

The association between the Dietary Inflammatory Index (DII^®), the glycemic index (GI), and the glycemic load (GL) is not known, although it is known that carbohydrates are pro-inflammatory. We aimed to measure the association between the DII and both GI and GL among college students. In this cross-sectional study, 110 college students completed a 3-day food diary, which was used to calculate the DII, the GI, the GL, and the healthy eating index (HEI)-2010. Least square means and 95% confidence intervals of the GI, the GL, and the HEI-2010 were presented per DII tertile using generalized linear mixed …

Monte Carlo Simulations Of Three-Dimensional Electromagnetic Gaussian Schell-Model Sources, Milo W. Hyde Iv, Santasri Bose-Pillai, Olga Korotkova

Faculty Publications

This article presents a method to simulate a three-dimensional (3D) electromagnetic Gaussian-Schell model (EGSM) source with desired characteristics. Using the complex screen method, originally developed for the synthesis of two-dimensional stochastic electromagnetic fields, a set of equations is derived which relate the desired 3D source characteristics to those of the statistics of the random complex screen. From these equations and the 3D EGSM source realizability conditions, a single criterion is derived, which when satisfied guarantees both the realizability and simulatability of the desired 3D EGSM source. Lastly, a 3D EGSM source, with specified properties, is simulated; the Monte Carlo simulation …

Supporting Accurate Interpretation Of Self-Administered Medical Test Results For Mobile Health: Assessment Of Design, Demographics, And Health Condition, Jess C. Hohenstein, Eric P.S. Baumer, Lindsay Reynolds, Elizabeth L. Murnane, Dakota O'Dell, Seoho Lee, Shion Guha, Yu Qi, Erin Rieger, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Technological advances in personal informatics allow people to track their own health in a variety of ways, representing a dramatic change in individuals’ control of their own wellness. However, research regarding patient interpretation of traditional medical tests highlights the risks in making complex medical data available to a general audience.

Objective: This study aimed to explore how people interpret medical test results, examined in the context of a mobile blood testing system developed to enable self-care and health management.

Methods: In a preliminary investigation and main study, we presented 27 and 303 adults, respectively, with hypothetical results from several …

Motivators For Alzheimer's Disease Clinical Trial Participation, Shoshana H. Bardach, Sarah D. Holmes, Gregory A. Jicha

Graduate Center for Gerontology Faculty Publications

Background

Alzheimer’s disease (AD) research progress is impeded due to participant recruitment challenges. This study seeks to better understand, from the perspective of individuals engaged in clinical trials (CTs), research motivations.

Methods

Participants, or their caregivers, from AD treatment and prevention CTs were surveyed about research motivators.

Results

The 87 respondents had a mean age of 72.2, were predominantly Caucasian, 55.2% were male, and 56.3% had cognitive impairment. An overwhelming majority rated the potential to help themselves or a loved one and the potential to help others in the future as important motivators. Relatively few respondents were motivated by free …

Approximation Degree Of Durrmeyer-Bézier Type Operators, Purshottam N. Agrawal, Serkan Araci, Martin Bohner, Kumari Lipi

Mathematics and Statistics Faculty Research & Creative Works

Recently, a mixed hybrid operator, generalizing the well-known Phillips operators and Baskakov-Szász type operators, was introduced. In this paper, we study Bézier variant of these new operators. We investigate the degree of approximation of these operators by means of the Lipschitz class function, the modulus of continuity, and a weighted space. We study a direct approximation theorem by means of the unified Ditzian-Totik modulus of smoothness. Furthermore, the rate of convergence for functions having derivatives of bounded variation is discussed.