Parametric statistical models - Parametric models I...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Parametric statistical models 1 / 11 Parametric models A (statistical) model P = { P θ : θ Θ } is a family of probability distributions indexed by a set Θ (the parameter space ). In a parametric (statistical) model , the distributions are indexed by a finite number of parameters (i.e., Θ R k for some k < ). Examples: Bernoulli distributions on { 0 , 1 } Poisson distributions on Z + = { 0 , 1 , 2 , . . . } Gaussian distributions on R Multivariate Gaussian distributions on R d 2 / 11 Poisson distributions Poi( λ ) on Z + Indexed by positive scalar θ = λ > 0 called the rate parameter . The distribution P λ is supported (i.e., non-zero) on Z + . P λ ( x ) = exp( - λ ) λ x x ! . 3 / 11 Gaussian distributions N( μ, σ 2 ) on R Indexed by θ = ( μ, σ 2 ) : μ R is the mean , σ 2 > 0 is the variance . The distribution P μ,σ 2 has the probability density ϕ μ,σ 2 ( x ) = 1 2 πσ 2 exp - ( x - μ ) 2 2 σ 2 . 4 / 11
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Model fitting (parameter estimation) Suppose we have an observation x , and a parametric model P with parameter space Θ .
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern