[R] Why two curves and numerical integration look so different?

[C W]

I want to do numerical integration w.r.t. mu: P(mu) × N(mu, 0.00001)

Because the variance is small, it results in density like: 7.978846e+94

Is there any good suggestion for this?

Thanks so much!


On Thu, Feb 11, 2016 at 9:14 AM, C W <tmrsg11 at gmail.com> wrote:

> Wow, thank you, that was very clear.  Let me give it some more runs and
> investigate this.
>
> On Thu, Feb 11, 2016 at 12:31 AM, William Dunlap <wdunlap at tibco.com>
> wrote:
>
>> Most of the mass of that distribution is within 3e-100 of 2.
>> You have to be pretty lucky to have a point in sequence
>> land there.  (You will get at most one point there because
>> the difference between 2 and its nearest neightbors is on
>> the order of 1e-16.)
>>
>> seq(-2,4,len=101), as used by default in curve, does include 2
>> but seq(-3,4,len=101) and seq(-2,4,len=100) do not so
>> curve(..., -3, 4, 101) and curve(..., -2, 4, 100) will not show the bump.
>> The same principal holds for numerical integration.
>>
>>
>> Bill Dunlap
>> TIBCO Software
>> wdunlap tibco.com
>>
>> On Wed, Feb 10, 2016 at 6:37 PM, C W <tmrsg11 at gmail.com> wrote:
>>
>>> Dear R,
>>>
>>> I am graphing the following normal density curve.  Why does it look so
>>> different?
>>>
>>> # the curves
>>> x <- seq(-2, 4, by=0.00001)
>>> curve(dnorm(x, 2, 10^(-100)), -4, 4)  #right answer
>>> curve(dnorm(x, 2, 10^(-100)), -3, 4)  #changed -4 to -3, I get wrong
>>> answer
>>>
>>> Why the second curve is flat?  I just changed it from -4 to -3.  There is
>>> no density in that region.
>>>
>>>
>>> Also, I am doing numerical integration.  Why are they so different?
>>>
>>> > x <- seq(-2, 4, by=0.00001)
>>> > sum(x*dnorm(x, 2, 10^(-100)))*0.00001
>>> [1] 7.978846e+94
>>> > x <- seq(-1, 4, by=0.00001) #changed -2 to -1
>>> > sum(x*dnorm(x, 2, 10^(-100)))*0.00001
>>> [1] 0
>>>
>>> What is going here?  What a I doing wrong?
>>>
>>> Thanks so much!
>>>
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>>>
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>>
>>
>

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