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fixed broken link to Wikipedia
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edit approved Feb 4 at 10:02
The Amplitwist
edit approved Feb 4 at 10:02
The Amplitwist
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I have a stupid question about the Metropolis-Hastings sampling algorithmMetropolis-Hastings sampling algorithm.

If I got this right, for every variable $X$ in turn, which currently has value $x_{old}$, you generate a new sample $x_{new}$. To do that, you draw $x_{new}$ from the proposal distribution $Q(x_{new}\mid x_{old})$, then you draw a number $\alpha$ uniformly at random from the range between $0$ and $1$. Then, accept $x_{new}$ if $\alpha < \min{1,\frac{P(x_{new})}{P(x_{old})}\frac{Q(x_{old}\mid x_{new})}{Q(x_{new}\mid x_{old})}}$

The second ratio does not really make sense to me: Why are we more likely to accept if $Q(x_{new}\mid x_{old})$ is low?

I have a stupid question about the Metropolis-Hastings sampling algorithm.

If I got this right, for every variable $X$ in turn, which currently has value $x_{old}$, you generate a new sample $x_{new}$. To do that, you draw $x_{new}$ from the proposal distribution $Q(x_{new}\mid x_{old})$, then you draw a number $\alpha$ uniformly at random from the range between $0$ and $1$. Then, accept $x_{new}$ if $\alpha < \min{1,\frac{P(x_{new})}{P(x_{old})}\frac{Q(x_{old}\mid x_{new})}{Q(x_{new}\mid x_{old})}}$

The second ratio does not really make sense to me: Why are we more likely to accept if $Q(x_{new}\mid x_{old})$ is low?

I have a stupid question about the Metropolis-Hastings sampling algorithm.

If I got this right, for every variable $X$ in turn, which currently has value $x_{old}$, you generate a new sample $x_{new}$. To do that, you draw $x_{new}$ from the proposal distribution $Q(x_{new}\mid x_{old})$, then you draw a number $\alpha$ uniformly at random from the range between $0$ and $1$. Then, accept $x_{new}$ if $\alpha < \min{1,\frac{P(x_{new})}{P(x_{old})}\frac{Q(x_{old}\mid x_{new})}{Q(x_{new}\mid x_{old})}}$

The second ratio does not really make sense to me: Why are we more likely to accept if $Q(x_{new}\mid x_{old})$ is low?

oops
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Frankie
Frankie
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I have a stupid question about the Metropolis-Hastings sampling algorithm.

If I got this right, for every variable $X$ in turn, which currently has value $x_{old}$, you generate a new sample $x_{new}$. To do that, you draw $x_{new}$ from the proposal distribution $Q(x_{new}\mid x_{old})$, then you draw a number $\alpha$ uniformly at random from the range between $0$ and $1$. Then, rejectaccept $x_{new}$ if $\alpha < \min{1,\frac{P(x_{new})}{P(x_{old})}\frac{Q(x_{old}\mid x_{new})}{Q(x_{new}\mid x_{old})}}$

The second ratio does not really make sense to me: Why are we more likely to reject if $Q(x_{old}\mid x_{new})$ is high? A new value $x_{new}$ is badaccept if it's easy to get back to $x_{old}$ from there? Conversely, a new value $x_{new}$$Q(x_{new}\mid x_{old})$ is perfect if we cannot get back to $x_{old}$ from it at alllow? I must be misunderstanding something ...

I have a stupid question about the Metropolis-Hastings sampling algorithm.

If I got this right, for every variable $X$ in turn, which currently has value $x_{old}$, you generate a new sample $x_{new}$. To do that, you draw $x_{new}$ from the proposal distribution $Q(x_{new}\mid x_{old})$, then you draw a number $\alpha$ uniformly at random from the range between $0$ and $1$. Then, reject $x_{new}$ if $\alpha < \min{1,\frac{P(x_{new})}{P(x_{old})}\frac{Q(x_{old}\mid x_{new})}{Q(x_{new}\mid x_{old})}}$

The second ratio does not really make sense to me: Why are we more likely to reject if $Q(x_{old}\mid x_{new})$ is high? A new value $x_{new}$ is bad if it's easy to get back to $x_{old}$ from there? Conversely, a new value $x_{new}$ is perfect if we cannot get back to $x_{old}$ from it at all? I must be misunderstanding something ...

I have a stupid question about the Metropolis-Hastings sampling algorithm.

If I got this right, for every variable $X$ in turn, which currently has value $x_{old}$, you generate a new sample $x_{new}$. To do that, you draw $x_{new}$ from the proposal distribution $Q(x_{new}\mid x_{old})$, then you draw a number $\alpha$ uniformly at random from the range between $0$ and $1$. Then, accept $x_{new}$ if $\alpha < \min{1,\frac{P(x_{new})}{P(x_{old})}\frac{Q(x_{old}\mid x_{new})}{Q(x_{new}\mid x_{old})}}$

The second ratio does not really make sense to me: Why are we more likely to accept if $Q(x_{new}\mid x_{old})$ is low?

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Frankie
Frankie
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Question about this ratio in Metropolis-Hastings MCMC algorithm

I have a stupid question about the Metropolis-Hastings sampling algorithm.

If I got this right, for every variable $X$ in turn, which currently has value $x_{old}$, you generate a new sample $x_{new}$. To do that, you draw $x_{new}$ from the proposal distribution $Q(x_{new}\mid x_{old})$, then you draw a number $\alpha$ uniformly at random from the range between $0$ and $1$. Then, reject $x_{new}$ if $\alpha < \min{1,\frac{P(x_{new})}{P(x_{old})}\frac{Q(x_{old}\mid x_{new})}{Q(x_{new}\mid x_{old})}}$

The second ratio does not really make sense to me: Why are we more likely to reject if $Q(x_{old}\mid x_{new})$ is high? A new value $x_{new}$ is bad if it's easy to get back to $x_{old}$ from there? Conversely, a new value $x_{new}$ is perfect if we cannot get back to $x_{old}$ from it at all? I must be misunderstanding something ...