cauchy(0,a) prior

[Joe King]

What exactly is the role of a in the cauchy(0,a) prior ? What is it's density function ?

[Bob Carpenter]

On 10/23/12 4:27 PM, Joe King wrote:
> What exactly is the role of a in the cauchy(0,a) prior ? What is it's density function ?

As much as we'd like to help, we really don't have time to
act as a general stats help desk!

First, you need to learn what a density function is, and then
look up the density function p_X(x) for X ~ cauchy(m,a).

- Bob

[Joe King]

Hi Bob

Thanks for your answer.

I know what a density function is, and I know that the cauchy distribution is "special" in the sense that the integral that defines its expectations diverges. Wikipedia and probability books that I have looked at all define the pdf as the integral over -infty to +infty of x/(pi(1+x^2)) dx but this doesn't shed light on what a is when you write cauchy(0,a)

If you can point me to a suitable reference I would be humbly grateful.

Thanks
JK

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From: Bob Carpenter <ca...@alias-i.com>
To: stan-...@googlegroups.com
Sent: Tuesday, October 23, 2012 9:34 PM
Subject: Re: [stan-users] cauchy(0,a) prior

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[Andrew Gelman]

Hi, for our distributions we use the notation in Appendix A of Bayesian Data Analysis unless otherwise stated.

See you

A

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[Bob Carpenter]

On 10/23/12 4:40 PM, Joe King wrote:
...

> I know what a density function is, and I know that the cauchy distribution is "special" in the sense that the integral
> that defines its expectations diverges. Wikipedia and probability books that I have looked at all define the pdf as the
> integral over -infty to +infty of x/(pi(1+x^2)) dx but this doesn't shed light on what a is when you write cauchy(0,a)

>> On 10/23/12 4:27 PM, Joe King wrote:
>> > What exactly is the role of a in the cauchy(0,a) prior ? What is it's density function ?

Sorry -- I interpreted "it's" to mean "a", which doesn't have
a density function here. I didn't think you'd be
asking for a function definition that's in our manual.

- Bob

[Joe King]

Oh, it's a comedy of errors....you thought I was asking "what is a pdf" !?! Haha. I might not have gone to university (yet) but I do know a little bit more than the average high school student :-) However now I feel really stupid that the answer is in your manual. Sorry !

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From: Bob Carpenter <ca...@alias-i.com>
To: stan-...@googlegroups.com

Sent: Tuesday, October 23, 2012 9:48 PM

Subject: Re: [stan-users] cauchy(0,a) prior

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