Search results
Results from the WOW.Com Content Network
Here i represents the equation number, r = 1, …, R is the individual observation, and we are taking the transpose of the column vector. The number of observations R is assumed to be large, so that in the analysis we take R → ∞ {\displaystyle \infty } , whereas the number of equations m remains fixed.
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to ...
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.
Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling.Given a hypothesis about a population, for which we wish to draw inferences, statistical inference consists of (first) selecting a statistical model of the process that generates the data and (second) deducing propositions from the model.
Bayesian inference using Gibbs sampling (BUGS) is a statistical software for performing Bayesian inference using Markov chain Monte Carlo (MCMC) methods. It was developed by David Spiegelhalter at the Medical Research Council Biostatistics Unit in Cambridge in 1989 and released as free software in 1991.
Simple cases, where observations are complete, can be dealt with by using the sample covariance matrix. The sample covariance matrix (SCM) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in R p × p ; however, measured using the intrinsic geometry of ...
Variational Bayesian methods are a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning.They are typically used in complex statistical models consisting of observed variables (usually termed "data") as well as unknown parameters and latent variables, with various sorts of relationships among the three types of random variables, as ...
) The vector is modelled as a linear function of its previous value. The vector's components are referred to as y i,t, meaning the observation at time t of the i th variable. For example, if the first variable in the model measures the price of wheat over time, then y 1,1998 would indicate the price of wheat in the year 1998.