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Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Fundamentally, Bayesian inference uses prior knowledge, in the form of a prior distribution in order to estimate posterior probabilities. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability".
Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geometallurgy, geography, forestry, environmental control, landscape ecology, soil science, and agriculture. Geostatistics is applied in varied branches of geography, particularly those involving the spread of diseases (epidemiology), the practice of commerce and military planning (logistics), and the development of efficient spatial networks. Geostatistical algorithms are incorporated in many places, including geographic information systems (GIS).
In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by recording states from the chain. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Various algorithms exist for constructing chains, including the Metropolis–Hastings algorithm.
In statistics, originally in geostatistics, kriging or Kriging, also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances. Under suitable assumptions of the prior, kriging gives the best linear unbiased prediction (BLUP) at unsampled locations. Interpolating methods based on other criteria such as smoothness may not yield the BLUP. The method is widely used in the domain of spatial analysis and computer experiments. The technique is also known as Wiener–Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov.
In digital image processing and computer vision, image segmentation is the process of partitioning a digital image into multiple image segments, also known as image regions or image objects. The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. Image segmentation is typically used to locate objects and boundaries in images. More precisely, image segmentation is the process of assigning a label to every pixel in an image such that pixels with the same label share certain characteristics.
Mark and recapture is a method commonly used in ecology to estimate an animal population's size where it is impractical to count every individual. A portion of the population is captured, marked, and released. Later, another portion will be captured and the number of marked individuals within the sample is counted. Since the number of marked individuals within the second sample should be proportional to the number of marked individuals in the whole population, an estimate of the total population size can be obtained by dividing the number of marked individuals by the proportion of marked individuals in the second sample. Other names for this method, or closely related methods, include capture-recapture, capture-mark-recapture, mark-recapture, sight-resight, mark-release-recapture, multiple systems estimation, band recovery, the Petersen method, and the Lincoln method.
Spatial analysis is any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques using different analytic approaches, especially spatial statistics. It may be applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, or to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is geospatial analysis, the technique applied to structures at the human scale, most notably in the analysis of geographic data. It may also be applied to genomics, as in transcriptomics data.
The modifiable areal unit problem (MAUP) is a source of statistical bias that can significantly impact the results of statistical hypothesis tests. MAUP affects results when point-based measures of spatial phenomena are aggregated into spatial partitions or areal units as in, for example, population density or illness rates. The resulting summary values are influenced by both the shape and scale of the aggregation unit.
Spatial epidemiology is a subfield of epidemiology focused on the study of the spatial distribution of health outcomes; it is closely related to health geography.
Data fusion is the process of integrating multiple data sources to produce more consistent, accurate, and useful information than that provided by any individual data source.
In data analysis, anomaly detection is generally understood to be the identification of rare items, events or observations which deviate significantly from the majority of the data and do not conform to a well defined notion of normal behavior. Such examples may arouse suspicions of being generated by a different mechanism, or appear inconsistent with the remainder of that set of data.
In statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone. Unlike a statistical ensemble in statistical mechanics, which is usually infinite, a machine learning ensemble consists of only a concrete finite set of alternative models, but typically allows for much more flexible structure to exist among those alternatives.
A boundary problem in analysis is a phenomenon in which geographical patterns are differentiated by the shape and arrangement of boundaries that are drawn for administrative or measurement purposes. The boundary problem occurs because of the loss of neighbors in analyses that depend on the values of the neighbors. While geographic phenomena are measured and analyzed within a specific unit, identical spatial data can appear either dispersed or clustered depending on the boundary placed around the data. In analysis with point data, dispersion is evaluated as dependent of the boundary. In analysis with areal data, statistics should be interpreted based upon the boundary.
Cross-species transmission (CST), also called interspecies transmission, host jump, or spillover, is the transmission of an infectious pathogen, such as a virus, between hosts belonging to different species. Once introduced into an individual of a new host species, the pathogen may cause disease for the new host and/or acquire the ability to infect other individuals of the same species, allowing it to spread through the new host population. The phenomenon is most commonly studied in virology, but cross-species transmission may also occur with bacterial pathogens or other types of microorganisms.
David Brian Dunson is an American statistician who is Arts and Sciences Distinguished Professor of Statistical Science, Mathematics and Electrical & Computer Engineering at Duke University. His research focuses on developing statistical methods for complex and high-dimensional data. Particular themes of his work include the use of Bayesian hierarchical models, methods for learning latent structure in complex data, and the development of computationally efficient algorithms for uncertainty quantification. He is currently serving as joint Editor of the Journal of the Royal Statistical Society, Series B.
Sudipto Banerjee is an Indian-American statistician best known for his work on Bayesian hierarchical modeling and inference for spatial data analysis. He is Professor of Biostatistics and Senior Associate Dean in the School of Public Health at the University of California, Los Angeles. He served as the Chair of the Department of Biostatistics at UCLA from 2014 through 2023. He served as the elected President of the International Society for Bayesian Analysis in 2022.
Alan Enoch Gelfand is an American statistician, and is currently the James B. Duke Professor of Statistics and Decision Sciences at Duke University. Gelfand’s research includes substantial contributions to the fields of Bayesian statistics, spatial statistics and hierarchical modeling.
Bayesian history matching is a statistical method for calibrating complex computer models. The equations inside many scientific computer models contain parameters which have a true value, but that true value is often unknown; history matching is one technique for learning what these parameters could be.
Roderick Joseph Alexander Little is an academic statistician, whose main research contributions lie in the statistical analysis of data with missing values and the analysis of complex sample survey data. Little is Richard D. Remington Distinguished University Professor of Biostatistics in the Department of Biostatistics at the University of Michigan, where he also holds academic appointments in the Department of Statistics and the Institute for Social Research.
Jorge Mateu is a Spanish mathematician, author, and academic. He is a professor of Statistics within the Department of Mathematics at University Jaume I of Castellon and Director of the Unit Eurocop for Data Science in criminal activities in the same department.
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