O'Reilly logo

Statistical Methods for Fuzzy Data by Reinhard Viertl

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

21.7 Problems

a. Assume the probability density fx(·|θ) is determined by a parameter vector ψ which is depending on the regression parameters θ = (θ0, θ1,…,θk), i.e. fxi(·|θ) = g(·|ψ(θ, xi)).

Which form has the likelihood function for observed data (x1, y1),…,(xn, yn)? How does Bayes’ theorem look in this situation?

b. Let the dependent quantity Yx have an exponential distribution Exτ with density Assuming a regression line θ0 + θ1 · x for the mean value τ, i.e. τ(x) = θ0 + θ1 · x and therefore calculate the likelihood function and write down Bayes’ theorem for this special case for data points (x1, y1),…,(xn, yn) in the plane 2.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required