Tag: statistics

At some point in your life, you’ve probably had somebody — a parent, a teacher, a mentor — tell you that “the more you practice, the better you become.” The expression is often attributed to Thomas Bayes, an 18^th century British minister who was interested in winning at games and formalized this simple observation into a now-famous mathematical expression.

Used to examine behaviors, properties and other mechanisms that constitute a concept or phenomenon, Bayesian analysis employs an array of varied, but similar, data to statistically inform an optimal model of that concept or phenomenon.

“Simply put, Bayesian statistics is a way of starting with our best current understanding and then updating that with new data from experiments or simulations to come up with a better-informed understanding,” said Noah Paulson, a computational materials scientist at the U.S. Department of Energy’s (DOE) Argonne National Laboratory.

The method met with some success over the 300 years since its inception, but it is an idea whose time has finally arrived.

In some fields, like cosmology, researchers have been successfully developing and sharing Bayesian techniques and codes for some time. In others, like materials science, implementation of Bayesian analysis methods is just beginning to pay dividends.

“Simply put, Bayesian statistics is a way of defining something we already understand and then updating that with new data from experiments or simulations to come up with a more accurate understanding.” — Noah Paulson, computational materials scientist, Argonne National Laboratory

Paulson and several Argonne colleagues are applying Bayesian methods to quantify uncertainties in the thermodynamic properties of materials. In other words, they want to determine how much confidence they can place in the data they collect about materials and the mathematical models used to represent those data.

While the statistical techniques are applicable to many fields, the researchers set out to create an optimal model of the thermodynamic properties of hafnium (Hf), a metal emerging as a key component in computer electronics. Results derived from this approach will be published published in the September 2019 issue of the International Journal of Engineering Science.

“We found that we didn’t know all that we could about this material because there were so many datasets and so much conflicting information. So we performed this Bayesian analysis to propose a model that the community can embrace and use in research and application,” said Marius Stan, who leads intelligent materials design in Argonne’s Applied Materials division (AMD) and is a senior fellow at both the University of Chicago’s Consortium for Advanced Science and Engineering and the Northwestern-Argonne Institute for Science and Engineering.

To derive an optimal model of a material’s thermodynamic properties, researchers use some prior knowledge or data related to the subject matter as a starting point.

In this case, the team was looking to define the best models for the enthalpy (the amount of energy in a material) and the specific heat (the heat necessary to increase the temperature of the unit mass of the material by one degree Celsius) of hafnium. Represented as equations and mathematical expressions, the models have different parameters that control them. The goal is to find the optimal parameters.

“We had to start with a guess of what those parameters should be,” said Paulson of AMD’s Thermal and Structural Materials group. “Looking through the literature we found some ranges and values that made sense, so we used those for our prior distribution.”

One of the parameters the researchers explored is the temperature of a crystal’s highest normal mode of vibration. Referred to as the Einstein or Debye temperature, this parameter affects a material’s specific heat.

The prior — or initial — guess is based on existing models, preliminary data or the intuition of experts in the field. Using calibration data from experiments or simulation, Bayesian statistics update that prior knowledge and determine the posterior — the updated understanding of the model. The Bayesian framework can then determine whether new data are in better or worse agreement with the model being tested.

“Like cosmology, materials science must find the optimal model and parameter values that best explain the data and then determine the uncertainties related to these parameters. There’s not much point in having a best-fit parameter value without an error bar,” said team member Elise Jennings, a computational scientist in statistics with the Argonne Leadership Computing Facility (ALCF), a DOEOffice of Science User Facility, and an associate of the Kavli Institute for Cosmological Physics at the University of Chicago.

And that, she said, is the biggest challenge for materials science: a lack of error bars or uncertainties noted in available datasets. The hafnium research, for example, relied on datasets selected from previously published papers, but error ranges were either absent or excluded.

So, in addition to presenting models for the specific thermodynamic properties of hafnium, the article also explores techniques by which materials science and other fields of study can make allowances for datasets that don’t have uncertainties.

“For a scientist or an engineer, this is an important problem,” said Stan. “We’re presenting a better way of evaluating how valuable our information is. We want to know how much trust we can put in the models and the data. And this work reveals a methodology, a better way of evaluating that.”

A paper based on the study, “Bayesian strategies for uncertainty quantification of the thermodynamic properties of materials,” is available online (June 13) and will appear in the September 2019 edition of the International Journal of Engineering Science. Noah Paulson, Elise Jennings and Marius Stan collaborated on the research.

This study is supported through the CHiMaD Program, funded by the National Institute for Standards and Technology (NIST).

“In this study, we worked with patients with epilepsy whose brain activity was being recorded with electrodes to find where their seizures started. While the electrodes were in place, we showed the patients pictures and asked them to name them while we recorded their brain activity,” said co-corresponding author Dr. Xaq Pitkow, assistant professor of neuroscience and McNair Scholar at Baylor College of Medicine and assistant professor of electrical and computer engineering at Rice University.

“We then analyzed the data we recorded and derived a new level of understanding of how the brain network comes up with the right word and enables us to say that word,” said Dr. Nitin Tandon, professor in the Vivian L. Smith Department of Neurosurgery at McGovern Medical School at The University of Texas Health Science Center at Houston.

The researchers’ findings support the view that when a person names a picture, the different behavioral stages — looking at the image, thinking of the name and saying it — consistently correspond to dynamic interactions within neural networks.

“Before our findings, the typical view was that separate brain areas would be activated in sequence,” Pitkow said. “But we used more complex statistical methods and fast measurement methods, and found more interesting brain dynamics.”

“This methodological advance provides a template by which to assess other complex neural processes, as well as to explain disorders of language production,” Tandon said.

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Essential functions of the cell are carried out by protein molecules, which interact with each other in varying complexity. When a virus enters the body, it disrupts their interactions and manipulates them for its own replication. This is the foundation of genetic diseases, and it is of great interest to understand how viruses operate.

Adversaries like viruses inspired Paul Bogdan, associate professor in the Ming Hsieh Department of Electrical and Computer Engineering, and recent Ph.D. graduate, Yuankun Xue, from USC’s Cyber Physical Systems Group, to determine how exactly they interact with proteins in the human body. “We tried to reproduce this problem using a mathematical model,” said Bogdan. Their groundbreaking statistical machine learning research on “Reconstructing missing complex networks against adversarial interventions,” was published in Nature Communications journal earlier this April.

Xue, who earned his Ph.D. in electrical and computer engineering last year with the 2018 Best Dissertation Award, said: “Understanding the invisible networks of critical proteins and genes is challenging, and extremely important to design new medicines or gene therapies against viruses and even diseases like cancer.”

The ‘protein interaction network’ models each protein as a ‘node.’ If two proteins interact, there is an ‘edge’ connecting them. Xue explained, “An attack by a virus is analogous to removing certain nodes and links in this network.” Consequently, the original network is no longer observable.

“Some networks are highly dynamic. The speed at which they change may be extremely fast or slow,” Bogdan said. “We may not have sensors to get accurate measurements. Part of the network cannot be observed and hence becomes invisible.”

To trace the effect of a viral attack, Bogdan and Xue needed to reconstruct the original network by finding a reliable estimate of the invisible part, which was no easy task. Said Bogdan: “The challenge is that you don’t see the links, you don’t see the nodes, and you don’t know the behavior of the virus.” To solve this problem, Xue added, “The trick is to rely on a statistical machine learning framework to trace all possibilities and find the most probable estimate.”

In sharp contrast to prior research, the lab’s novel contribution is that they actively incorporate the influence and causality of the attack, or ‘adversarial intervention’, into their learning algorithm rather than treat it as a random sampling process. Bogdan explained, “Its real power lies in its generality — it can work with any type of attack and network model.”

Due to the generality of their proposed framework, their research has far-reaching applications to any network reconstruction problem involving adversarial attack, in diverse fields such as ecology, social science, neuroscience, and network security. Their paper has also demonstrated its capability to determine the influence of trolls and bots on social media users.

Bogdan plans to extend their work by experimenting with a range of attack models, more complex and varied datasets, and larger network sizes to understand their effect on the reconstructed network.

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As described in the journal PLOS Computational Biology, their five-year project resulted in a model that shows how subtle changes in the stream of reported cases of a disease may be predictive of both an approaching epidemic and of the final success of a disease eradication campaign.

“We hope that in the near future, we will be available to monitor and track warning signals for emerging diseases identified by this model,” said John Drake, Distinguished Research Professor of Ecology and director for the Center for the Ecology of Infectious Diseases who researches the dynamics of biological epidemics. His current projects include studies of Ebola virus in West Africa and Middle East respiratory syndrome-related coronavirus in the horn of Africa.

In recent years, the reemergence of measles, mumps, polio, whooping cough and other vaccine-preventable diseases has sparked a refocus on emergency preparedness.

“Research has been done in ecology and climate science about tipping points in climate change,” he said. “We realized this is mathematically similar to disease dynamics.”

Drake and colleagues focused on “critical slowing down,” or the loss of stability that occurs in a system as a tipping point is reached. This slowing down can result from pathogen evolution, changes in contact rates of infected individuals, and declines in vaccination. All these changes may affect the spread of a disease, but they often take place gradually and without much consequence until a tipping point is crossed.

Most data analysis methods are designed to characterize disease spread after the tipping point has already been crossed.

“We saw a need to improve the ways of measuring how well-controlled a disease is, which can be difficult to do in a very complex system, especially when we observe a small fraction of the true number of cases that occur,” said Eamon O’Dea, a postdoctoral researcher in Drake’s laboratory who focuses on disease ecology.

The research team found that their predictions were consistent with well-known findings of British epidemiologists Roy Anderson and Robert May, who compared the duration of epidemic cycles in measles, rubella, mumps, smallpox, chickenpox, scarlet fever, diphtheria and pertussis from the 1880s to 1980s. For instance, Anderson and May found that measles in England and Wales slowed down after extensive immunization in 1968. Similarly, the model shows that infectious diseases slow as an immunization threshold is approached. Slight variations in infection levels could be useful early warning signals for disease reemergence that results from a decline in vaccine uptake, they wrote.

“Our goal is to validate this on smaller scales so states and cities can potentially predict disease, which is practical in terms of how to make decisions about vaccines,” O’Dea said. “This could be particularly useful in countries where measles is still a high cause of mortality.”

To illustrate how the infectious disease model behaves, the team created a visualization that looks like a series of bowls with balls rolling in them. In the model, vaccine coverage affects the shallowness of the bowl and the speed of the ball rolling in it.

“Very often, the conceptual side of science is not emphasized as much as it should be, and we were pleased to find the right visuals to help others understand the science,” said Eric Marty, an ecology researcher who specializes in data visualization.

As part of Project AERO, which stands for Anticipating Emerging and Re-emerging Outbreaks, Drake and colleagues are creating interactive tools based on critical slowing down for researchers and policymakers to use in the field and guide decisions. For instance, the team is developing an interactive dashboard that will help non-scientists plot and analyze data to understand the current trends for a certain infectious disease. They’re presenting a prototype to fellow researchers now and anticipating a public release within the next year.

“If a computer model of a particular disease was sufficiently detailed and accurate, it would be possible to predict the course of an outbreak using simulation,” Marty said. “But if you don’t have a good model, as is often the case, then the statistics of critical slowing down might still give us early warning of an outbreak.”

In the study published Monday, April 15 in Proceedings of the National Academy of Sciences (PNAS), the researchers found natural variation in regional baseline SRBs that differ from the previously held standard baseline male-to-female ratio of 1.05 for most regions.

They also identified 12 countries with strong evidence of sex ratio at birth imbalances, or sex ratio inflation, due to sex-selective abortions and a preference for sons.

“Given that sex ratios at birth are still inflated in some countries and could increase in the future in other countries, the monitoring of the sex ratio at birth and how it compares with expected baseline levels is incredibly important to inform policy and programs when sex ratio inflations are detected,” says Alkema, associate professor in the School of Public Health and Health Sciences.

Alkema adds, “While prior studies have shown differences in the sex ratio at birth, for example based on ethnicity in population subgroups, there is no prior study that we know of that has assessed regional baseline levels of the SRB. When we did the estimation exercise, after excluding data that may have been affected by masculinization of the sex ratio at birth, we found that regional levels differed from the commonly assumed 1.05 in several regions.”

Estimated regional reference levels ranged from 1.031 in sub-Saharan Africa to 1.063 in southeastern Asia and eastern Asia, and 1.067 in Oceania.

Alkema regularly collaborates with United Nations agencies to develop statistical models to assess and interpret demographic and population-level health trends globally. For this study, along with Alkema at UMass Amherst, researchers at the National University of Singapore and the United Nations Population Division compiled a database from vital registries, censuses and surveys with 10,835 observations — 16,602 country-years of information from 202 countries. They developed Bayesian statistical methods to estimate the sex ratio at birth for all countries from 1950 to 2017.

“We found that the SRB imbalance in 12 countries since 1970 is associated with 23.1 million fewer female births than expected,” Alkema says.

The majority of the missing female births were in China, with 11.9 million, and India, with 10.6 million. The other countries identified with SRB imbalance were Albania, Armenia, Azerbaijan, Georgia, Hong Kong, Republic of Korea, Montenegro, Taiwan, Tunisia and Vietnam.

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These questions are not limited to the digital machines constructed by us. The human brain can be seen as a computer — one that gobbles an estimated 10 to 20 percent of all the calories a person consumes. Living cells, too, can be viewed as computers, but computers that “are many orders of magnitude more efficient” than any laptop or smartphone humans have constructed, says David Wolpert of the Santa Fe Institute.

Wolpert, a mathematician, physicist, and computer scientist, has been on the frontlines of a rapid resurgence of interest in a deep understanding of the energy cost of computing. That research is now hitting its stride, thanks to advances in using some revolutionary tools recently developed in statistical physics, in order to understand the thermodynamic behavior of nonequilibrium systems. The reason these tools are so important is that computers are decidedly nonequilibrium systems. (Unplug your laptop and wait for it to reach equilibrium, and then see if it still works.) Although Wolpert primarily approaches these issues using tools from computer science and physics, there is also sharp interest from researchers in other areas, including those who study chemical reactions, cellular biology, and neurobiology.

However, research in nonequilibrium statistical physics largely happens in silos, says Wolpert. In a review published today in the Journal of Physics A, Wolpert collects recent advances in understanding the thermodynamics of computation that are grounded in computer science and physics. The review functions as a sort of state-of-the-science report for a burgeoning interdisciplinary investigation.

“It is basically a snapshot of the current state of the fields, where these ideas are starting to explode, in all directions,” says Wolpert.

In the paper, Wolpert first summarizes the relevant theoretical ideas from physics and computer science. He then discusses what’s known about the entropic cost of a range of computations, from erasing a single bit to running a Turing machine. He goes on to show how breakthroughs in nonequilibrium statistical physics have enabled researchers to more formally probe those cases — moving far beyond simple bit erasure.

Wolpert also touches on the questions raised in this recent research which suggest real-world challenges, like how to design algorithms with energy conservation in mind. Can biological systems, for example, serve as inspiration for designing computers with minimal thermodynamic cost?

“We are being surprised and astonished in many ways,” Wolpert says. In putting together the review, and coediting a book on the topic due out later this year, “we’ve uncovered phenomena that no one has analyzed before that were very natural to us, as we pursue this modern version of the thermodynamics of computation.”

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