tronter
Jan23-08, 04:04 PM
Let \bold{X} be a discrete random variable whose set of possible values is \bold{x}_j, \ j \geq 1 . Let the probability mass function of \bold{X} be given by P \{\bold{X} = \bold{x}_j \}, \ j \geq 1 , and suppose we are interested in calculating \theta = E[h(\bold{X})] = \sum_{j=1}^{\infty} h(\bold{x}_j) P \{\bold{X} = \bold{x}_j \} .
In some cases, why are Markov Chains better for estimating \theta as opposed to Monte-Carlo simulations? If we wanted to calculate E[\bold{X}] there would not be any need to use simulation at all, right?
And \lim_{n \to \infty} \frac{h(\bold{x}_j)}{n} \approx \theta \ \? ?
In some cases, why are Markov Chains better for estimating \theta as opposed to Monte-Carlo simulations? If we wanted to calculate E[\bold{X}] there would not be any need to use simulation at all, right?
And \lim_{n \to \infty} \frac{h(\bold{x}_j)}{n} \approx \theta \ \? ?