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Published byRodolfo Heckstall Modified about 1 year ago

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By C. Yeshwanth and Mohit Gupta

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An inference method that uses Bayes’ rule to update prior beliefs based on data Allows a-priori information about the parameters to be used in the analysis method A posterior distribution over the hypothesis space is obtained using the Bayesian update rule Conjugate priors are priors which result in a posterior distribution belonging to the same family after the Bayesian update

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The Pearson distribution is a family of continuous probability distributions These are used to fit a distribution given the mean, the variance, the skewness and the kurtosis of the distribution. There are many families included in Pearson curves like Beta distribution, gamma distribution and Inverse gamma distribution

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Depending on the first four moments, it is decided that which Pearson curve will best fit the given data After fixing the type of the distribution, the parameters of that distribution are calculated to obtain the exact distribution.

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We did not use the alternative for 2 reasons The family of densities described by the alternative approaches is a subset of the families described in the first approach The computational costs of using the second approach are too high

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Number of SamplesEstimate of AlphaEstimate of Theta The actual values used for the shape and scale parameters were 5 and 5 respectively

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Actual Value of ShapeEstimated Value of Shape Estimated Value of Scale The number of samples was fixed to when performing this estimation and the scale parameter was fixed to 5

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Actual Value of ScaleEstimated Value of Shape Estimated Value of Scale The number of samples was fixed to when performing this estimation and the shape parameter was fixed to 5

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The accuracy of the point estimates increases with increasing the number of samples Credible confidence intervals are difficult to extract from the raw distributions especially for the scale parameter We attempted to fit a Pearson Curve to the distributions to extract the confidence interval This is because of the skewed nature of the Pearson estimate of the posterior density

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“Bayesian Analysis of the Two-Parameter Gamma Distribution” by Robert B. Miller “Conjugate classes for gamma distributions” by Eivind Damsleth. ution tion xchange/26516-pearspdf

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