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  1. J

    Likelihood function confusion over definition

    When we have a likelihood, say L(theta| x) would we say that L is the likelihood of (x1,x2) or (X1,X2) or neither? Where X1,X2 are the unobserved random variables and x1,x2 the observed values.
  2. J

    posterior distribution conditioned on a second parameter

    If you have 2 parameters a and b and a observed data set x, and wish to calculate the posterior distribution of a given b is the following true P(a|b,x) proportional to P(a,b| x) Where proportionality is in a. I had wrote this down somewhere but can't remember why or if it is right...
  3. J

    What counts as a high dimensional problem in sequential importance sampling?

    I've read a lot about how sequential importance sampling isn't useful in high dimensions, but not what is considered high. The reason for me asking is that I'm interested in fitting a state space model with 50 dimensions and 60 time points, but I'm not sure how useful sequential importance...
  4. J

    Multivariate normal distribution, not full rank, probability density function

    If X has a multivariate distribution of full rank and Y is the sum of the elements of X. Then (X,Y) is a multivariate normal distribution but not of full rank, then as I understand you can not calculate a density function for it. However would I be able to say the density function of (X,Y) is...
  5. J

    How to apply MCMC/Metropolis Hastings with a constraint

    I have 4 random variables, say A,B,C and D and some data X. I can obtain the conditional pdfs P(A|B,C,D,X),..., P(D|A,B,C,X) up to proportionality. I would like to sample from the joint pdf P(A,B,C,D|X). This can easily be done via metropolis hastings. However I wish to also have the...
  6. J

    Independent Metropolis Hastings, not jumping

    I'm trying to sample from a posterior (with 50 dimensions) and I've got a proposal distribution which gives a overall acceptance rate of 0.3. However when I take 20000 draws, there are a couple occasions where the proposal is rejected 500-1000 times consecutively. I haven't much experience in...
  7. J

    Multiple prioir/posterior distributions, with Data that depends on 2 of the variables

    Hi, I have 10 prior distributions one for each of theta1, theta2..... . The prior distribution for theta1 is Gamma(a1,b1), and the others are described similarly. Now I have an observation x, where X~Poisson(theta1 +theta2). I would like to get separate posterior distribution for theta1...
  8. J

    Goodness of Fit test with 2 sets of data, not sure how many degrees of freedom I have

    I have two data sets, one with 1000 observations and the other with 50. The observations can equal A, B, C or D. Now using the first set of data I calculate the probabilities P(A)=(freq of A)/100 and similarly for P(B),P(C) and P(D). I now want to use these probabilities to model the second...