Can "normal_lpdf" give a positive result? Strange error

[Ste]

In attempting to calculate the probability of a 2D number to belong to a 2D cluster I am using normal_lpdf

transformed parameters{

for(i in 1:I) {

vector<upper=0>[2] cluster_log[G*P];

cluster_log[i,1] = normal_lpdf(.. | .., ..);

cluster_log[i,2] = normal_lpdf(.. | .., ..);

}

}

How is possible that normal_lpdf gives a positive result?

ERROR: cluster_log[k0__][1] is 1.45791, but must be less than or equal to 0" 

Thanks.

[Ben Goodrich]

On Tuesday, April 11, 2017 at 3:34:25 AM UTC-4, Ste wrote:

How is possible that normal_lpdf gives a positive result?

Since a PDF is the slope of the CDF, it can go above 1 for a subset of the parameter space, in which case the log is positive. See for example

dnorm(0, mean = 0, sd = 0.25, log = TRUE) # 0.467

Ben

[stefano]

Thank Ben,

So how can I translate that quantity in probability of a number to belong to a distribution?

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[Ben Goodrich]

On Tuesday, April 11, 2017 at 5:03:44 AM UTC-4, Ste wrote:

So how can I translate that quantity in probability of a number to belong to a distribution?

You can't.

Ben

[Aki Vehtari]

Slightly longer answer: you need to understand the difference between probability density and probability mass. Density can be get values larger than 1, while probabilities are constrained to be less than or equal to 1.

See more, e.g., in https://en.wikipedia.org/wiki/Probability_density_function

[stefano]

Thanks to both,

actually the short answer is the one I was also expecting. Thanks for the link!

Stefano Mangiola

Data analyst (MSc, MPhil, PhD candidate)
@ Melbourne University

Hovens lab - Papenfuss lab

Royal Melbourne Hospital - WEHI

+61 (0)450135954

[Bob Carpenter]

You can in many cases look at posterior probabilities of mixture
responsibilities even for continuous outcomes. That may be what
you want and it's explained in the manual chapter on mixtures (or
the chapter on clustering).

We have to just guess when people send us fragments with no
explanation of their goals.

- Bob

> On Apr 11, 2017, at 6:35 AM, stefano <mangiol...@gmail.com> wrote:
>
> Thanks to both,
>
> actually the short answer is the one I was also expecting. Thanks for the link!
>
> Stefano Mangiola
>
> Data analyst (MSc, MPhil, PhD candidate)
> @ Melbourne University
> Hovens lab - Papenfuss lab
> Royal Melbourne Hospital - WEHI
> +61 (0)450135954
>
> 2017-04-11 20:15 GMT+10:00 Aki Vehtari <aki.v...@aalto.fi>:
> Slightly longer answer: you need to understand the difference between probability density and probability mass. Density can be get values larger than 1, while probabilities are constrained to be less than or equal to 1.
> See more, e.g., in https://en.wikipedia.org/wiki/Probability_density_function
>
>
> On Tuesday, April 11, 2017 at 12:19:05 PM UTC+3, Ben Goodrich wrote:
> On Tuesday, April 11, 2017 at 5:03:44 AM UTC-4, Ste wrote:
> So how can I translate that quantity in probability of a number to belong to a distribution?
>
> You can't.
>
> Ben
>
>
> --
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> To unsubscribe from this topic, visit https://groups.google.com/d/topic/stan-users/xahTgpKimBk/unsubscribe.

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>
>

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