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] 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".

μ

be a latent variable we don't observe, but we know it has a certain prior distribution

p ( μ )

x = μ + ϵ

ϵ ∼

is a Gaussian noise variable (so

ρ ( x ) = ∫ p ( x

be the probability density of

, then the posterior mean and variance of

∇ ρ ( x )

ρ ( x )

ρ ( x )

ρ ( x )

∇ ρ ( x ) ∇ ρ ( x

ρ ( x

The posterior higher order moments of

are also obtainable as algebraic expressions of

∇ ρ , ρ ,

∇ ρ ( x )

ρ ( x )

where we have used Bayes' theorem to write

Tweedie's formula is used in empirical Bayes method and diffusion models.