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Inferring a Gaussian distribution Thomas P. Minka 1 Introduction
Inferring a Gaussian distribution Thomas P. Minka 1 Introduction

... p(V|X). It also derives p(X|Gaussian), the probability that the data came from any Gaussian whatsoever. From this we can get the posterior predictive density p(x|X), which has the most practical importance. The analysis is done for noninformative priors and for arbitrary conjugate priors. The presen ...
Week1_Lecture 3_post
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... From it, we can see 1) The SD always equals to zero if the all the values in a particular dataset are the same (i.e. no spread in value) 2) The SD will be very large if the values in the dataset vary a lot from each other. (i.e. a huge spread in value) Therefore, in this sense, we use SD as a measur ...
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... ‰ P = the probability that a randomly selected value of a variable X falls between a and b. f(x) = the probability density function. ‰ The probability function has to be integrated over distinct limits to obtain a probability. ‰ The probability for X to have a particular value is ZERO. ‰ Two importa ...
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... with many well-known run and scan statistics as well as with analogous statistics not yet discussed in the literature but which may be useful at a practical level. Moreover, using the algorithms provided here, it is possible to apply the approach in many real situations also if the limits concerning ...
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Lecture 5 - Bauer College of Business

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Bayesian estimation of diameter distribution during harvesting

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CRYSTAL BALL ARTICLES Simulation Techniques for Risk

... In order to describe the distribution types of the "uncertain" variables in our model, we need additional data about the uncertain variables. There are several sources for this additional data: Analysis of Historical Data: If an organization has historical data describing an uncertain variable, a si ...
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Document

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File

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Gibbs sampling

In statistics and in statistical physics, Gibbs sampling or a Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm for obtaining a sequence of observations which are approximated from a specified multivariate probability distribution (i.e. from the joint probability distribution of two or more random variables), when direct sampling is difficult. This sequence can be used to approximate the joint distribution (e.g., to generate a histogram of the distribution); to approximate the marginal distribution of one of the variables, or some subset of the variables (for example, the unknown parameters or latent variables); or to compute an integral (such as the expected value of one of the variables). Typically, some of the variables correspond to observations whose values are known, and hence do not need to be sampled.Gibbs sampling is commonly used as a means of statistical inference, especially Bayesian inference. It is a randomized algorithm (i.e. an algorithm that makes use of random numbers, and hence may produce different results each time it is run), and is an alternative to deterministic algorithms for statistical inference such as variational Bayes or the expectation-maximization algorithm (EM).As with other MCMC algorithms, Gibbs sampling generates a Markov chain of samples, each of which is correlated with nearby samples. As a result, care must be taken if independent samples are desired (typically by thinning the resulting chain of samples by only taking every nth value, e.g. every 100th value). In addition (again, as in other MCMC algorithms), samples from the beginning of the chain (the burn-in period) may not accurately represent the desired distribution.
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