By C. Yeshwanth and Mohit Gupta.  An inference method that uses Bayes’ rule to update prior beliefs based on data  Allows a-priori information about.

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Presentation transcript:

By C. Yeshwanth and Mohit Gupta

 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

 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

 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.

 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

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

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

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

 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

 “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