How do you sift through hundreds of billions of bits of information and make accurate inferences from such gargantuan sets of data? Brown University mathematician Charles “Chip” Lawrence and graduate student Luis Carvalho have arrived at a fresh answer with broad applications in science, technology and business.

In new work published in the Proceedings of the National Academy of Sciences, Lawrence and Carvalho describe a new class of statistical estimators and prove four theorems concerning their properties. Their work shows that these “centroid” estimators allow for better statistical predictions – and, as a result, better ways to extract information from the immense data sets used in computational biology, information technology, banking and finance, medicine and engineering.

“What’s exciting about this work – what makes it every scientist’s dream – is that it’s so fundamental,” Lawrence said. “These new estimators have applications in biology and beyond and they advance a statistical method that’s been around for decades.”

For more than 80 years, one of the most common methods of statistical prediction has been maximum likelihood estimation (MLE). This method is used to find the single most probable solution, or estimate, from a set of data.

But new technologies that capture enormous amounts of data – human genome sequencing, Internet transaction tracking, instruments that beam high-resolution images from outer space – have opened opportunities to predict discrete “high dimensional” or “high-D” unknowns. The huge number of combinations of these “high-D” unknowns produces enormous statistical uncertainty. Data has outgrown data analysis.

This discrepancy creates a paradox. Instead of producing more precise predictions about gene activity, shopping habits or the presence of faraway stars, these large data sets are producing more unreliable predictions, given current procedures. That’s because maximum likelihood estimators use data to identify the single most probable solution. But because any one data point swims in an increasingly immense sea, it’s not likely to be representative.

Lawrence, a professor of applied mathematics and a faculty member in the Center for Computational Molecular Biology at Brown, first came upon this paradox and a potential way around it while working on predicting the structure of RNA molecules. If you want to predict the structure of these molecules – how the molecule will look when it folds onto itself – you’d have billions and billions of possible shapes to choose from.

“Using maximum likelihood estimation, the most likely outcome would be very, very, very unlikely,” Lawrence said, “so we knew we needed a better estimation method.”

Lawrence and Carvahlo used statistical decision theory to understand the limitations of the old procedure when faced with new “high-D” problems. They also used statistical decision-making theory to find an estimation procedure that applies to a broad range of statistical problems. These “centroid” estimators identify not the single most probable solution, but the solution that is most representative of all the data in a set.

Lawrence and Carvahlo went on to prove four theorems that illustrate the favorable properties of these estimators and show that they can be easily computed in many important applications.

“This new procedure should benefit any field that needs to reliably make predictions of large-scale, high-D unknowns,” Lawrence said. Medical News Today News Article

The randomized clinical trial, widely considered the most reliable biomedical research method, can have significant drawbacks, a new study suggests, because patients included may not be representative of the broader population.

The scientists, writing in the December issue of The Annals of Surgical Oncology, reviewed 29 clinical trials of surgical procedures in prostate, colon, breast and lung cancer involving 13,991 patients. Although 62 percent of those cancers occur in people over 65, just 27 percent of the participants in the trials were that old. Although patients younger than 55 account for 16 percent of cancer cases, they made up 44 percent of the participants. More than 86 percent of the participants were white, and fewer than 8 percent African-American.

Thirty percent of the cases were breast cancers, but nearly 75 percent of the participants had that disease. Although prostate cancer accounted for 27 percent of the cancers, fewer than 2 percent of the patients were in prostate cancer studies.

In colon and lung cancer trials, women were less likely to be enrolled than men, and at all study sites, the rates of participation in trials was extremely low, from 0.04 to 1.7 percent.

Dr. John H. Stewart IV, the lead author and an assistant professor of surgery at Wake Forest University, said the disparities could call the results into question. “Our ability to generalize the findings of surgical trials,” he said, “is directly dependent on having equitable participation in trials by underrepresented groups.”

Eye trackers necessarily measure the rotation of the eye with
respect to the measuring system. If the measuring system is head
mounted, as with EOG, then eye-in-head angles are measured. If the
measuring system is table mounted, as with scleral search coils or
table mounted camera (“remote”) systems, then gaze angles are measured.

In many applications, the head position is fixed using a bite bar, a
forehead support or something similar, so that eye position and gaze
are the same. In other cases, the head is free to move, and head
movements are measured with systems such as magnetic or video based
head trackers.

For head-mounted trackers, head position and direction are added to
eye-in-head direction to determine gaze direction. For table-mounted
systems, such as search coils, head direction is subtracted from gaze
direction to determine eye-in-head position.