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Maurice Charles Kenneth Tweedie (30 September 1919 – 14 March 1996) was a British medical physicist and statistician from the University of Liverpool. He was known for research into the exponential family probability distributions.[1][2]
Maurice Charles Kenneth Tweedie | |||||
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Born | |||||
Died | 14 March 1996 76) | (aged||||
Education | University of Reading | ||||
Known for | Inverse Gaussian distribution Tweedie distributions | ||||
Scientific career | |||||
Institutions | Virginia Tech University of Manchester University of Liverpool | ||||
Academic advisors | Paul White Boyd Harshbarger |
Tweedie read physics at the University of Reading and attained a BSc (general) and BSc (special) in physics in 1939 followed by a MSc in physics 1941. He found a career in radiation physics, but his primary interest was in mathematical statistics where his accomplishments far surpassed his academic postings.
Tweedie's contributions included pioneering work with the Inverse Gaussian distribution.[3][4] Arguably his major achievement rests with the definition of a family of exponential dispersion models characterized by closure under additive and reproductive convolution as well as under transformations of scale that are now known as the Tweedie exponential dispersion models.[1][5] As a consequence of these properties the Tweedie exponential dispersion models are characterized by a power law relationship between the variance and the mean which leads them to become the foci of convergence for a central limit like effect that acts on a wide variety of random data.[6] The range of application of the Tweedie distributions is wide and includes:
Tweedie is credited for a formula first published in Robbins (1956),[15] which offers "a simple empirical Bayes approach to correcting selection bias".[16] Let be a latent variable we don't observe, but we know it has a certain prior distribution . Let be an observable, where is a Gaussian noise variable (so ) . Let be the probability density of , then the posterior mean and variance of given the observed are: The posterior higher order moments of are also obtainable as algebraic expressions of .
Using , we get where we have used Bayes' theorem to write
Tweedie's formula is used in empirical Bayes method and diffusion models.[17]
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