Lecture 7: Bayesian inference for model calibration in UQ
Lecture 7: Bayesian inference for model calibration in UQ
Lecture 7: Bayesian inference for model calibration in UQ
In this issue:
2018-2019 Programs Open – page 1
PMED Workshop Opens 2018-19 Academic Year
MUMS Opening Workshop Brings Together Leading Minds in Uncertainty Quantification – page 2
SAMSI Closes 2017-18 Programs – page 3
CLIM Program Transitions After Positive Year
QMC Leaders Priase Research Advances at Transition Workshop – page 4
Grad Students Enjoy 2018 IMSM – page 5
SAMSI Welcomes NEW Directorate and Members and NEW Postdocs – page 6
SAMSI Introduces 2019-2020 Academic Programs – page 7
SAMSI Seeking Postdoctoral Researchers for 2019-2020 Academic Programs – Page 8
SAMSI Upcoming Events
Each year SAMSI welcomes a new crop of postdoctoral researchers that support their annual academic programs. This year, SAMSI welcomes five new researchers who are focused on supporting the 2018-19 PMED and MUMS Programs.
Supporting the Program on Statistical, Mathematical and Computational Methods for Precision Medicine (PMED)
Xinyi Li received her Ph.D. in Statistics from Iowa State University in 2018, under the supervision of Dr. Lily Wang. Her research interests are in developing statistical methods as well as designing computational algorithms in sparse learning, functional data analysis, and high-dimensional nonparametric regression. Her application areas include neuroimaging, genomics, and public health. In her spare time she enjoys sports (badminton, hiking, skiing, etc), reading and watching sports (tennis, football, badminton, etc).
John Nardini received his Ph.D. from the University of Colorado, Boulder, where his dissertation was on mathematical models of epidermal wound healing. He is interested in the derivation and analysis of partial differential equation models of biological phenomena, as well as inverse problems to fit these models to experimental data. While at SAMSI, he will be working with Professors Kevin Flores from NC State and Greg Forest from UNC Chapel Hill.
Supporting the Program on Model Uncertainty: Mathematical and Statistical (MUMS)
Pulong Ma received his Ph.D. in Statistics from University of Cincinnati. He has worked on spatial and spatio-temporal statistics with applications in remote-sensing science and climate science in his dissertation. In particular, he developed flexible (e.g., nonstationary and non-separable) covariance function models for massive spatial and spatio-temporal datasets. He also proposed a statistical downscaling framework to simulate high-resolution geophysical fields in global observing system simulation experiments (OSSEs). While at SAMSI, he will be working with Professor Jim Berger, from Duke University, in the area of uncertainty quantification (UQ). He is currently exploring interesting applications with focus on building statistical emulators for expensive computer models.
Wenjia Wang received his Ph.D. in Operations Research from Industrial and Systems Engineering, Georgia Tech. His research interests are focused on statistical modeling, statistical design and theoretical analysis of Gaussian process as well as Kriging. He is also interested in their applications in computer experiments, machine learning and uncertainty quantification.
Lei Yang earned her Ph.D. in Statistics from Colorado State University in 2018. During her Ph.D. study, she developed theoretical framework and computational methods for stochastic inverse problem, which turns out to be related to generalized fiducial inference. She is also interested in bayesian projected normal time series model applied to protein sequence data as well. At her spare time, she enjoys swimming and getting hands dirty on predictive modeling projects.
More than 100 researchers from across the country attended the opening workshop for the Program on Model Uncertainty: Mathematical and Statistical (MUMS) on the campus of Duke University in late August.
The MUMS program brings together statisticians and applied mathematicians with disciplinary scientists from a wide-range of fields to understand the effects of modeling and uncertainty on predictions. The focus of the workshop was to layout the foundations for the MUMS program by examining the theoretical basis for statistical uncertainty, the strengths and weaknesses of models of real world processes and the uncertainty of those processes.
The workshop featured statisticians, mathematicians and data science researchers who presented their talks on how model uncertainty and uncertainty quantification methodologies can be used across a broad spectrum of subjects.
“The kickoff meeting brought together the world leaders in uncertainty quantification, many of
whom continue to work and interact at SAMSI as long-term visitors,” said David Banks, Director of SAMSI and the program’s directorate liaison. “Additionally, the participants are teaching a graduate course in model uncertainty,
which has drawn in students from all over the Triangle.”
In addition to the working groups, a fall course is being presented for graduate students that introduces statistical and mathematical sensitivity analysis and uncertainty quantification techniques for large-scale models arising in current applications. The course is ongoing through December.
“The MUMS program is a classic melding of applied mathematics and statistics,” said Banks.
“Uncertainty quantification is an exciting new field, with important applications in weather forecasting, modeling of pyroclastic flows, and materials science,
The opening workshop produced six working groups:
The working groups will meet throughout the academic year and discuss ways to use these uncertainty principles in a diverse variety of disciplines, such as: engineering, probability, operations research and machine learning, just to name a few.
“One of the grand challenges scientists face is how to make probability statements when the model is so complex and intractable that it cannot be studied with standard tools from mathematical statistics,” said Banks. “The MUMS program provides a general solution strategy, by approximating the complex model with Gaussian processes. Bayesian methods enable the scientist to not only fit the most accurate Gaussian process, but also to estimate a discrepancy function, which indicates where the approximation is poor.”
For more information about the MUMS program, visit: https://www.samsi.info/mums.
Almost 150 mathematicians, statisticians, data and biomedical scientists participated in the opening workshop for the Program on Statistical, Mathematical, and Computational Methods for Precision Medicine (PMED) on the campus of N.C. State University (NCSU) in mid-August.
The goal of the PMED program is to bring together mathematical, statistical, computational, and biomedical scientists in order to develop innovative advances in data-driven, quantitative methodology for precision medicine.
“Personalized medicine is a recently developed hot area in bio medicine and medicine that is about custom-tailoring treatments, medicines and interventions for the individual person,” said Elvan Ceyhan, Deputy Director of SAMSI and a directorate liaison for the PMED Program. “There are a lot of methodological, statistical and mathematical and practical challenges, so there is a dire need to address these issues.”
Researchers from all over the United States attended the week-long event that opened SAMSI’s 2018-19 academic programs. There were numerous talks from some of the most influential minds in biomedicine, applied mathematics and statistics. The researchers highlighted a wide-range of methodologies and approaches used in precision medicine
“I have been interested in this general area for quite some time…I am a biostatistician, so I work with problems in the health sciences,” said Marie Davidian, professor of statistics in the Department of Statistics at NCSU and a local scientific contributor to the PMED program. “This is the big challenge in how science research can personalize treatment to the patient. My research area involves statistical methodologies directed toward that goal.”
PMED produced eight working groups and one subgroup for this academic program year. The working groups will focus primarily on medical issues that require more refined and accurate data derived by biostatisticians, applied mathematicians and other researchers.
“In general, in regular medicine, statistics is applied for the average person, but an average person is not really a person as much as it is median data point, there is no ‘average person,’ said Ceyhan. “In personalized medicine, each person is an individual and different. In this field, the treatment would be customized to the individual, which causes a lot of uncertainty from person to person and unexpected outcomes. Statistics is very useful in predicting bounds or quantifying those uncertainties.”
This SAMSI workshop is helping to bring together a diverse group of professionals who do not ordinarily collaborate. Programs like this one in precision medicine are forging a path towards using more dynamic and broad-based methods to ensure that more effective and efficient medicines and treatments can be used to improve an individual’s healthcare needs.
“What strikes me, just from the talks I’ve seen, is the diversity of the approaches that different disciplines are taking to address these problems,” said Davidian.
Davidian is hopeful that the internal collaborations on the working groups lead to some innovative approaches as to how statisticians can make an impact into improving precision medicine.
The issues being discussed are not only beneficial to the more senior researchers, but also to the next generation of statisticians – Master of Science and Ph.D. students.
“The thought of personalized medicine and tailoring treatments to individual characteristics is exciting to me,” said Yeng Saanchi, a statistics student enrolled in the graduate program at NCSU. “I don’t think giving generic treatments to everybody, irrespective of their individuality is the way to go, especially if we want healthcare to be efficient and effective.”
Saanchi appreciated the opportunity to have access to a large number of experts in her field and in medicine. In many ways it has helped her to realize where her talents in statistics can be valuable.
“Aside from the great exposure to the work that is being done in the field in precision medicine and meeting all of these knowledgeable people and talking to them about their work, I hope to be able to see how my research could possibly tie into the personalized medicine field,” she said.
“SAMSI workshops are great in order to get a conversation started about a particular subject and building networks to address various problem definitions in those subjects,” said Ceyhan. “SAMSI is very experienced in this…We have received positive feedback already from participants that they have met new people from new areas of study and they look forward to further collaborations.”
In addition to the opening workshop and working group research, the PMED program will also host a spring course for graduate students in 2019. It will be interesting to see what new and innovative ideas come out of this experience.
To see more information about the PMED program, visit: https://www.samsi.info/pmed.
It was another productive year for SAMSI’s 24th annual Industrial Math and Statistics Modeling (IMSM) Workshop for Graduate Students, presented in July, on the campus of N.C. State University in Raleigh, NC.
Almost 40 students from more than 30 universities nationwide attended the annual workshop that began in 1993. The workshop offered students something they don’t ordinarily get in a classroom and gave them a snapshot of life as a data science researcher.
“Students worked in groups of six or seven on problems that came from industry or national labs,” said Mansoor Haider, who is an Associate Director at SAMSI, a professor in the math department at N.C. State University and also Chair of the IMSM workshop. “It’s often their first experience working on problem solving, using mathematics and statistics that come from folks outside of academia.”
From day one of the workshop, the students in attendance relied, not just on their personal knowledge of mathematics, but also on developing relationships with their peers so that they could work together as a team to present their findings. The collaborative environment is intentionally setup each year in order to mirror current industry trends.
“The thing that I think is really unique about IMSM is that it’s a short period of time where you really have to work collaboratively to get something done,” said Grant Weller, a Vice President for Research at Savvysherpa, a division of the United Healthcare Group. “The projects we [Savvysherpa] tend to work on are very large and require collaborative work and people of different backgrounds and disciplines working with each other. It’s been impressive to see how this group has come together.”
Weller is very familiar with SAMSI. He supported the 2011-2012 Uncertainty Quantification Program as a graduate student visitor. Like Weller, many former SAMSI undergraduate and graduate students and postdocs come back to attend SAMSI programs and workshops later in their professional and academic careers. They share their knowledge and their experience with the next crop of talented applied mathematicians, statisticians and computer scientists.
This year’s supporting organizations included:
“This was the first workshop I have been to of this kind and I wanted to get a feel what a job in industry would be like and this workshop was a really good experience for me in terms of that,” said Michael Byrne, an attending graduate student enrolled in the applied math Ph.D. program at Arizona State University. “It was a great opportunity for me to work with other people that are industry-minded and to get an idea of what people do in industry on a daily basis.”
In addition, to their group research, students also participated in a short career fair where they got an opportunity to connect and network with this year’s partner organizations. Companies and organizations often comment that there is a shortage of math and statistical science students to fill the critical roles they need to address their current research. IMSM helps to potentially fill that void.
“We really viewed this as an opportunity to connect and develop relationships with SAMSI, which is a great research institution in statistics and applied mathematical sciences, and is the primary focus of what we [Savvysherpa] do,” said Weller.
At the end of week-long event, each group presented their findings to their peers and faculty and industry mentors. The students walked away from the experience with a new perspective on how research is conducted and they also walked away with new contacts and friendships from the experience.
To see what the groups presented and to find out more about IMSM, visit: https://www.samsi.info/imsm-18.
There is a proverb that states, “March comes in like a lion and out like a lamb.” It is a proverb that truly explains the extreme swings of the weather effects on our environment.
Much like this proverb, the Program on Mathematical and Statistical Methods for Climate and the Earth System (CLIM ) also came in like a lion and then transitioned quietly this May to complete another successful SAMSI year-long program.
The CLIM Program began in spectacular fashion with a solar eclipse, followed by the first of three devastating hurricanes to hit the United States in the summer of 2017 – and that was just the opening workshop!
During the academic year, the CLIM program hosted a distinguished atmospheric scientist from MIT, Kerry Emanuel. Widely regarded as the world’s leading hurricane expert, Emanuel gave a fascinating talk the future of hurricanes and how changes in our environment are causing these storms to become more and more intense.
In all, the program produced 13 working groups that addressed issues such as: remote sensing, data assimilation, analytics, climate prediction, environmental health and climate extremes, just to name a few.
A research course for graduate students was also hosted in the fall semester, called “Statistics for Climate Research.” The course was taught by seven different instructors who were part of the nearly 15 academic visitors for the CLIM program. Over 20 students registered for the course (plus several auditors in regular attendance) with students from departments such as Marine Sciences at UNC and Economics at NCSU, in addition to the local mathematics and statistics departments. The fall course was followed up by a spring course that covered statistical and computational methods for the analysis of data arising from climate research.
The program was a huge success and it attracted some of the most talented minds in environmental research today. The Transition Workshop met in May and each working group presented their findings to their peers that addressed their particular research topic.
Though the CLIM Program has transitioned, the research captured during the program is still ongoing and the environmental and applied math and statistical scientists will continue to collaborate for further study. To see an overview of the CLIM program, visit: https://www.samsi.info/clim.
SAMSI completed their Undergraduate Modeling Workshop in May. The week-long workshop brought more than 30 undergraduate students from across the country together to understand how applied mathematics, statistics and computer science technologies can be used to interpret and predict ongoing changes in our environment.
“In this workshop, we wanted undergraduates from mostly quantitative fields to experience the mathematical/statistical applications in climate research,” said Elvan Ceyhan, SAMSI’s Deputy Director. Ceyhan was also an organizer of the workshop.
The workshop gave students valuable experience in how modern research is conducted, while also encouraging them to enter careers in the math sciences. Because of this workshop, many students became aware of how much applied mathematical, computer science-based and statistical concepts are used environmental research.
Students listened to researchers in the fields of applied mathematics, statistics and environmental research. The researchers lectured on how applied math and statistics work in concert with scientific data to help build models for study of the factors that affect various elements of our environment, such as ocean temperature, air quality and seasonal variations in vegetation in a given region.
Students also learned some basics about R Software, which is widely used to crunch data for the purpose of building simulations, plotting variances and finding trends to predict change in a given subject.
“The ‘SAMSI 2018 May UG Workshop’ was very helpful in broadening my knowledge about not just Statistical Modeling but Machine Learning as well – I learned new things which I would not have otherwise,” said Chandini Malhorta, a statistics major at NC State University (NCSU). “The multiple R-sessions, especially the ones on Spatial Statistics by Doug [Nychka] and Andrew [Finley] were quite helpful, this was something which I would have never learned in my entire Undergraduate had I not attended their session.”
Students worked in various groups and were guided and mentored by SAMSI postdoctoral fellows and workshop leaders. The student groups presented their findings on the following topics:
The students wrapped up the week by presenting their findings to their peers and fellow mentors.
“The lecturers and post-docs really have broadened my horizon and expanded my network,” said Rice University Junior, Hongyu Mao. “This workshop connected us to many friends of the same interests and we learned from each other.”
“In a week’s time, the students showed impressive progress and had some tangible results to present at the end,” said Ceyhan.
The subjects presented challenged the students, in a group setting, to give them practical experience working together to solve problems. SAMSI hosts multiple education and outreach opportunities like this annually as a way to raise awareness for the importance of applied math and statistics. To see more of what was presented and discussed at this workshop, visit the web page: https://www.samsi.info/18-ugrad-modeling.
At the end of May, SAMSI hosted a transition workshop, bringing a close to their Program on Quasi-Monte Carlo and High-Dimensional Sampling Methods for Applied Mathematics (QMC).
The workshop was the culminating event of the year-long QMC program and brought together more than 100 researchers from around the world to discuss a multitude of ways in which QMC methodologies could be used to improve such things as data sampling; process efficiency and troubleshooting systems; and how these concepts can be integrated into machine learning or computer-based technologies.
“The SAMSI QMC program, small but highly productive, set a perfect example of SAMSI’s mission: Mathematicians and statisticians working together to create new foundations and computational methods, with a future view towards solving challenging technological problems: making power grids more reliable by preventing break downs, and making nuclear reactors safer by tightly monitoring the nuclear reactions (criticality),” said Ilse Ipsen, program organizer and former SAMSI associate director. Ipsen is also a mathematics professor at NC State University
The QMC year began with an opening working last August, followed by mid-term workshops at Duke University and the Alan Turing Institute in the UK, and officially ending with this transition workshop.
Program participants from all over the world (Austria, Australia, Canada, Germany, the UK, and the US) reviewed the impressive accomplishments of ten productive working groups over the past year, which included:
“QMC has a rich and deep theory that has found a handful of extremely suitable use cases, but I am convinced that there are more to discover,” said Art Owen, a QMC program leader and a statistics professor at Stanford University. “The SAMSI program built bridges to US based researchers, especially in engineering related applications.”
The transition workshop was an opportunity for the program researchers to reconvene and to discuss their findings from the past year in their research. It also gave the program participants a way to reconnect with colleagues and discuss future collaborations about their research.
“During the lively discussion sessions it was often hard to tell who was a mathematician and who a statistician — an indication of the close collaborations and the growing synthesis of mathematics and statistics,” said Ipsen. “The workshop participants are now looking beyond the SAMSI program, by organizing future workshops and continuing their virtual webex meetings — whatever it takes to ensure the thriving of the research community formed during the SAMSI QMC year.
“The QMC Program has fulfilled its main objective: Strengthening the community of researchers who work on Quasi-Monte Carlo methods and the related area of Probabilistic Numerics; and raising the visibility of these vital research areas in the US,” said Ipsen.
To see all of the workshops and what were presented during this program, visit the QMC web page at: https://www.samsi.info/qmc.
SAMSI welcomes three new members to their Directorate, effective July 1, 2018.
The new directorate members are:
“I am personally grateful to all three of these professionals for having taken on these jobs,” said SAMSI Director, David Banks. “It is especially critical during a NSF renewal cycle, and I look forward to working with them as we advance the SAMSI mission.”
Dasmohaptra joined Duke in September 2017, where she has served as the Director of the Masters in Statistical Science Program. She had previously served at NCSU as an Associate Professor in Marketing Analytics at the Institute in Advanced Analytics. She has a well-established background in working with industry partners, government and non-profit organizations, as well as academia.
“I am very excited to join SAMSI to build and maintain a climate that fosters diversity and inclusiveness on an ongoing basis through collaborative relationships with a broad and diverse constituency,” said Dasmohaptra about beginning her new role at SAMSI.
Her research interests include: customer and marketing analytics, focused primarily on quantitative data analysis; data management; predictive modeling; and web and digital analytics, just to name a few. Sudipta hopes to continue the work in SAMSI’s diversity program that McClure began last year. Her focus as diversity director will be to further develop SAMSI’s diversity initiatives, identifying opportunities for under-represented groups to participate in SAMSI programs, workshops and special events.
Greg Forest will assume the role of Associate Director vacated by former Associate Director and Director, Richard Smith. Smith, who was the Director of SAMSI since 2010, stepped down after David Banks took over as Director in January 2018. Smith then moved to an associate director position to help facilitate the transition before going back to academic research.
Forest has been at UNC-CH since 1996 and is currently serving as the Grant Dahlstrom Distinguished University Professor of Mathematics and Biomedical Engineering and also as Director of the Carolina Center for Interdisciplinary Applied Mathematics.
Forest’s research is focused primarily on biomedical technologies and how those enhancements can improve modern medicine. He is also heavily involved in nanoparticle drug strategies for human cancer; studying the correlations between mathematics and multiple applied science challenges; gaining understanding virology and immunology and much more.
Forest’s experience in this research will no doubt be vital in SAMSI’s 2018-2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine (PMED) starting in August 2018.
Lastly, Mansoor Haider fills out the new list of recent appointees in the directorate at SAMSI.
Haider will be replacing long-time Associate Director, Ilse Ipsen. Ipsen and Haider are both mathematics professors at NCSU. Ipsen has been an Associate Director at SAMSI since 2011.
“I am excited to join the SAMSI directorate and work with leading scientists from the triangle universities in order to advance SAMSI’s mission,” said Haider of his new appointment.
Haider is an applied mathematician who has been a member of the faculty at NCSU since 1999. His focus is on interdisciplinary research, primarily the application of mathematical and computational models to problems in the life sciences. In addition, Haider also served as Director of Graduate Programs for the Department of Mathematics from 2012-2016.
Haider, who is no stranger to SAMSI, has served as an organizer of numerous SAMSI programs and workshops. “I am looking forward to developing creative strategies for integrating SAMSI’s research programs with mathematical sciences training at all levels [postdoc, grad, undergrad],” Haider said.
Haider also serves as the current Chair of the Industrial Math/Statistical Modeling Workshop (IMSM) for Graduate Students (he has previously served as this committee’s chair in 2017 and 2004 and 2005). IMSM is a joint venture between SAMSI and NCSU that serves as an education and outreach opportunity for graduate students.
“I am particularly grateful to Ilse Ipsen and Richard Smith for their leadership in advancing the mission of our Institute,” said Banks of the outgoing directorate members.
“Ilse ensured the prominence of applied mathematics in the SAMSI portfolio through the creation and facilitation of several spectacularly successful programs, and through the recruitment and mentoring of outstanding postdoctoral fellows. Richard contributed hugely to SAMSI as well —he was the former director, and kindly agreed to stay on for an additional six months to facilitate the transition of new directorate members. Richard’s vision and stewardship ensured the survival of SAMSI, and did much to shape its current form. Both Ilse and Richard will be missed,” said Banks.
This new group of leaders will help to bring a fresh perspective on how best to advance SAMSI’s role in applied mathematics, statistics and the computational sciences. SAMSI staff welcomes these new members and looks forward to working together with them well into the future.