Empirical research

empiricalempirical evidenceempirical studies
Accurate analysis of data using standardized statistical methods in scientific studies is critical to determining the validity of empirical research. Statistical formulas such as regression, uncertainty coefficient, t-test, chi square, and various types of ANOVA (analyses of variance) are fundamental to forming logical, valid conclusions. If empirical data reach significance under the appropriate statistical formula, the research hypothesis is supported. If not, the null hypothesis is supported (or, more accurately, not rejected), meaning no effect of the independent variable(s) was observed on the dependent variable(s).


policingpolice forcepolice department
Michel Foucault claims that the contemporary concept of police as a paid and funded functionary of the state was developed by German and French legal scholars and practitioners in Public administration and Statistics in the 17th and early 18th centuries, most notably with Nicolas Delamare's Traité de la Police ("Treatise on the Police"), first published in 1705. The German Polizeiwissenschaft (Science of Police) first theorized by Philipp von Hörnigk a 17th-century Austrian Political economist and civil servant and much more famously by Johann Heinrich Gottlob Justi who produced an important theoretical work known as Cameral science on the formulation of police.


current eventscurrent affairscurrent event
Economically oriented newspapers published new types of data enabled the advent of statistics, especially economic statistics which could inform sophisticated investment decisions. These newspapers, too, became available for larger sections of society, not just elites, keen on investing some of their savings in the stock markets. Yet, as in the case other newspapers, the incorporation of advertising into the newspaper led to justified reservations about accepting newspaper information at face value. Economic newspapers also became promoters of economic ideologies, such as Keynesianism in the mid-1900s. Newspapers came to sub-Saharan Africa via colonization.

Feedforward neural network

feedforwardfeedforward neural networksfeedforward networks
The danger is that the network overfits the training data and fails to capture the true statistical process generating the data. Computational learning theory is concerned with training classifiers on a limited amount of data. In the context of neural networks a simple heuristic, called early stopping, often ensures that the network will generalize well to examples not in the training set. Other typical problems of the back-propagation algorithm are the speed of convergence and the possibility of ending up in a local minimum of the error function. Today there are practical methods that make back-propagation in multi-layer perceptrons the tool of choice for many machine learning tasks.

Least squares

least-squaresmethod of least squaresleast squares method
Best linear unbiased estimator (BLUE). Best linear unbiased prediction (BLUP). Gauss–Markov theorem. L 2 norm. Least absolute deviation. Measurement uncertainty. Orthogonal projection. Proximal gradient methods for learning. Quadratic loss function. Root mean square. Squared deviations.

Financial market

financial marketsmarketmarkets
In recent years the rise of algorithmic and high-frequency program trading has seen the adoption of momentum, ultra-short term moving average and other similar strategies which are based on technical as opposed to fundamental or theoretical concepts of market Behaviour. The scale of changes in price over some unit of time is called the volatility. It was discovered by Benoît Mandelbrot that changes in prices do not follow a Gaussian distribution, but are rather modeled better by Lévy stable distributions. The scale of change, or volatility, depends on the length of the time unit to a power a bit more than 1/2.

Fisher information

information matrixinformationsingular statistical model
If the Fisher information matrix is positive definite for all, then the corresponding statistical model is said to be regular; otherwise, the statistical model is said to be singular. Examples of singular statistical models include the following: normal mixtures, binomial mixtures, multinomial mixtures, Bayesian networks, neural networks, radial basis functions, hidden Markov models, stochastic context-free grammars, reduced rank regressions, Boltzmann machines. In machine learning, if a statistical model is devised so that it extracts hidden structure from a random phenomenon, then it naturally becomes singular. The FIM for a N-variate multivariate normal distribution, has a special form.

Search algorithm

searchsearchingkeyword search
There are also search methods designed for quantum computers, like Grover's algorithm, that are theoretically faster than linear or brute-force search even without the help of data structures or heuristics. * hardware *, also use statistical methods to rank results in very large data sets *, necessary for executing certain search algorithms Categories: Problems in combinatorial optimization, such as:. The vehicle routing problem, a form of shortest path problem.


racistracial prejudiceracial discrimination
A neuroimaging study on amygdala activity during racial matching activities found increased activity to be associated with adolescent age as well as less racially diverse peer groups which the author conclude suggest a learned aspect of racism. A meta analysis of neuroimaging studies found amygdala activity correlated to increased scores on implicit measures of racial bias. It was also argued amygdala activity in response to racial stimuli represents increased threat perception rather than the traditional theory of the amygdala activity represented ingroup-outgroup processing. Racism has also been associated with lower childhood IQ in an analysis of 15,000 people in the UK.

Computational sociology

computational social sciencecomputationalcomputationally
Gender bias, readability, content similarity, reader preferences, and even mood have been analyzed based on text mining methods over millions of documents. The analysis of readability, gender bias and topic bias was demonstrated in Flaounas et al. showing how different topics have different gender biases and levels of readability; the possibility to detect mood shifts in a vast population by analysing Twitter content was demonstrated as well. The analysis of vast quantities of historical newspaper content has been pioneered by Dzogang et al., which showed how periodic structures can be automatically discovered in historical newspapers.


wikipedia.orgparody of WikipediaBeersheba University
It may more specifically follow the biases of Internet culture, inclining to being young, male, English-speaking, educated, technologically aware, and wealthy enough to spare time for editing. Biases of its own may include over-emphasis on topics such as pop culture, technology, and current events. Taha Yasseri of the University of Oxford, in 2013, studied the statistical trends of systemic bias at Wikipedia introduced by editing conflicts and their resolution. His research examined the counterproductive work behavior of edit warring.

Robert Tibshirani

Tibshirani, RobertRobert J. Tibshirani
His son, Ryan Tibshirani, with whom he occasionally publishes scientific papers, is currently an Associate Professor at Carnegie Mellon University in the department of Statistics, jointly in the Machine Learning Department. Tibshirani received the COPSS Presidents' Award in 1996. Given jointly by the world's leading statistical societies, the award recognizes outstanding contributions to statistics by a statistician under the age of 40. He is a fellow of the Institute of Mathematical Statistics, the American Statistical Association, and a (Canadian) Steacie award winner. He was elected a Fellow of the Royal Society of Canada in 2001 and a member of the National Academy of Sciences in 2012.

Feature selection

variable selectionselectingfeature
In traditional statistics, the most popular form of feature selection is stepwise regression, which is a wrapper technique. It is a greedy algorithm that adds the best feature (or deletes the worst feature) at each round. The main control issue is deciding when to stop the algorithm. In machine learning, this is typically done by cross-validation. In statistics, some criteria are optimized. This leads to the inherent problem of nesting. More robust methods have been explored, such as branch and bound and piecewise linear network. Subset selection evaluates a subset of features as a group for suitability. Subset selection algorithms can be broken up into Wrappers, Filters and Embedded.

Ensemble learning

ensembleensembles of classifiersmachine learning ensemble
Python: Scikit-learn, a package for machine learning in Python offers packages for ensemble learning including packages for bagging and averaging methods. MATLAB: classification ensembles are implemented in Statistics and Machine Learning Toolbox. Ensemble averaging (machine learning). Bayesian structural time series (BSTS).

Sampling bias

ascertainment biasbiased samplebias
Indeed, biases sometimes come from deliberate intent to mislead or other scientific fraud. In statistical usage, bias merely represents a mathematical property, no matter if it is deliberate or unconscious or due to imperfections in the instruments used for observation. While some individuals might deliberately use a biased sample to produce misleading results, more often, a biased sample is just a reflection of the difficulty in obtaining a truly representative sample, or ignorance of the bias in their process of measurement or analysis. An example of how ignorance of a bias can exist is in the widespread use of a ratio (a.k.a. 'fold change) as a measure of difference in biology.

Linear predictor function

In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables (independent variables), whose value is used to predict the outcome of a dependent variable. This sort of function usually comes in linear regression, where the coefficients are called regression coefficients. However, they also occur in various types of linear classifiers (e.g. logistic regression, perceptrons, support vector machines, and linear discriminant analysis), as well as in various other models, such as principal component analysis and factor analysis. In many of these models, the coefficients are referred to as "weights".

Lasso (statistics)

LASSOLASSO method\ell_1 penalty
In statistics and machine learning, lasso (least absolute shrinkage and selection operator; also Lasso or LASSO) is a regression analysis method that performs both variable selection and regularization in order to enhance the prediction accuracy and interpretability of the statistical model it produces. It was originally introduced in geophysics literature in 1986, and later independently rediscovered and popularized in 1996 by Robert Tibshirani, who coined the term and provided further insights into the observed performance.

Educational data mining

Learning analytics. Machine learning. Statistics.

ENSAE ParisTech

ENSAEÉcole Nationale de la Statistique et de l'Administration ÉconomiqueEcole Nationale de la Statistique
ENSAE ParisTech is known as the branch school of École Polytechnique for statistics, data science and machine learning. It is one of France's top schools of economics and statistics and is directly attached to France's Institut national de la statistique et des études économiques (INSEE) and the French Ministry of Economy and Finance. Students are given a proficient training both in economics and statistics and they can specialize in macroeconomics, microeconomics, statistics or finance. The ENSAE has the ability to train its students for the French actuary graduation (Institut des Actuaires).

Statistical learning theory

statistical machine learning
Statistical learning theory is a framework for machine learning drawing from the fields of statistics and functional analysis. Statistical learning theory deals with the problem of finding a predictive function based on data. Statistical learning theory has led to successful applications in fields such as computer vision, speech recognition, bioinformatics and baseball. The goals of learning are understanding and prediction. Learning falls into many categories, including supervised learning, unsupervised learning, online learning, and reinforcement learning. From the perspective of statistical learning theory, supervised learning is best understood.

Regularization (mathematics)

Bias–variance tradeoff. Matrix regularization. Regularization by spectral filtering. Regularized least squares.

Online machine learning

online learningon-line learningonline
In computer science, online machine learning is a method of machine learning in which data becomes available in a sequential order and is used to update our best predictor for future data at each step, as opposed to batch learning techniques which generate the best predictor by learning on the entire training data set at once. Online learning is a common technique used in areas of machine learning where it is computationally infeasible to train over the entire dataset, requiring the need of out-of-core algorithms.