Mixture distribution rejection sampling
I have a mixture density $f_X(x)$ (it is comprised of several normals) which I need to sample from. My proposal distribution for rejection sampling is given by $g(x)$, where $g(x)$ has two parameters which need to be chosen such that the acceptance probability is maximised. I need to calculate $u = underset{x}{text{sup}} frac{f_X(x)}{g(x)}$ in order to calculate the acceptance probability.
I am stuck conceptually here. I don't understand how I am supposed to maximise the acceptance probability, without first knowing what $u$ is - and I am unable to find $u$ because the expression has these two unknown tuning parameters.
statistics
asked Dec 8 at 23:14
mrnovice
5,3781326
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I have a mixture density $f_X(x)$ (it is comprised of several normals) which I need to sample from. My proposal distribution for rejection sampling is given by $g(x)$, where $g(x)$ has two parameters which need to be chosen such that the acceptance probability is maximised. I need to calculate $u = underset{x}{text{sup}} frac{f_X(x)}{g(x)}$ in order to calculate the acceptance probability.
I am stuck conceptually here. I don't understand how I am supposed to maximise the acceptance probability, without first knowing what $u$ is - and I am unable to find $u$ because the expression has these two unknown tuning parameters.
statistics
asked Dec 8 at 23:14
mrnovice
5,3781326
add a comment |
I have a mixture density $f_X(x)$ (it is comprised of several normals) which I need to sample from. My proposal distribution for rejection sampling is given by $g(x)$, where $g(x)$ has two parameters which need to be chosen such that the acceptance probability is maximised. I need to calculate $u = underset{x}{text{sup}} frac{f_X(x)}{g(x)}$ in order to calculate the acceptance probability.
I am stuck conceptually here. I don't understand how I am supposed to maximise the acceptance probability, without first knowing what $u$ is - and I am unable to find $u$ because the expression has these two unknown tuning parameters.
statistics
asked Dec 8 at 23:14
mrnovice
5,3781326
I have a mixture density $f_X(x)$ (it is comprised of several normals) which I need to sample from. My proposal distribution for rejection sampling is given by $g(x)$, where $g(x)$ has two parameters which need to be chosen such that the acceptance probability is maximised. I need to calculate $u = underset{x}{text{sup}} frac{f_X(x)}{g(x)}$ in order to calculate the acceptance probability.
I am stuck conceptually here. I don't understand how I am supposed to maximise the acceptance probability, without first knowing what $u$ is - and I am unable to find $u$ because the expression has these two unknown tuning parameters.
statistics
statistics
asked Dec 8 at 23:14
mrnovice
5,3781326
asked Dec 8 at 23:14
mrnovice
5,3781326
asked Dec 8 at 23:14
mrnovice
5,3781326
asked Dec 8 at 23:14
mrnovice
5,3781326
asked Dec 8 at 23:14
mrnovice
5,3781326
5,3781326
add a comment |
add a comment |
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