Ulf Grenander
Encyclopedia
Ulf Grenander is a statistician
and a professor of applied mathematics
at Brown University
.
His early research was in probability theory
, stochastic processes, time series
analysis, and statistical theory
(particularly the order-constrained estimation of cumulative distribution functions using his sieve estimator
). In recent decades, Grenander contributed to computational statistics
, image processing
, pattern recognition
, and artificial intelligence
.
. Grenander earned his Ph.D. at Stockholm University
in 1950 under the supervision of Harald Cramér
.
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
and a professor of applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
at Brown University
Brown University
Brown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
.
His early research was in probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, stochastic processes, time series
Time series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
analysis, and statistical theory
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
(particularly the order-constrained estimation of cumulative distribution functions using his sieve estimator
Sieve estimator
In statistics, sieve estimators are a class of nonparametric estimator which use progressively more complex models to estimate an unknown high-dimensional function as more data becomes available, with the aim of asymptotically reducing error towards zero as the amount of data increases. This method...
). In recent decades, Grenander contributed to computational statistics
Computational statistics
Computational statistics, or statistical computing, is the interface between statistics and computer science. It is the area of computational science specific to the mathematical science of statistics....
, image processing
Image processing
In electrical engineering and computer science, image processing is any form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or, a set of characteristics or parameters related to the image...
, pattern recognition
Pattern recognition
In machine learning, pattern recognition is the assignment of some sort of output value to a given input value , according to some specific algorithm. An example of pattern recognition is classification, which attempts to assign each input value to one of a given set of classes...
, and artificial intelligence
Artificial intelligence
Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...
.
Honors
In 1966 Grenander was elected to be a member of Royal Academy of Sciences of Sweden. He received an honorary doctorate in 2005 from the Royal Institute of Technology of Stockholm, Sweden.Schooling
Grenander earned his undergraduate degree at Uppsala UniversityUppsala University
Uppsala University is a research university in Uppsala, Sweden, and is the oldest university in Scandinavia, founded in 1477. It consistently ranks among the best universities in Northern Europe in international rankings and is generally considered one of the most prestigious institutions of...
. Grenander earned his Ph.D. at Stockholm University
Stockholm University
Stockholm University is a state university in Stockholm, Sweden. It has over 28,000 students at four faculties, making it one of the largest universities in Scandinavia. The institution is also frequently regarded as one of the top 100 universities in the world...
in 1950 under the supervision of Harald Cramér
Harald Cramér
Harald Cramér was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory. He was once described by John Kingman as "one of the giants of statistical theory".-Early life:Harald Cramér was born in Stockholm, Sweden on September...
.