[R] generic questions about probability and simulation -- not directly related to R

[Greg Snow]

If the time until change is exponentially distributed with a mean of 3, then the probability of changing in the first day is:

> pexp(1,1/3)
[1] 0.2834687

The same idea will work for all the other statements below (none of which are true) including for time steps greater than 3 days.

Hope this helps,

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111


> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Jong-Hoon Kim
> Sent: Sunday, January 25, 2009 6:58 PM
> To: r-help at r-project.org
> Subject: [R] generic questions about probability and simulation -- not
> directly related to R
> 
> Dear helpers,
> 
> As the title says, my question is not directly related to R.
> I find, however, that there are many people who are both knowledgeable
> and
> kind in this email list, and so decided to give it a try.
> 
> I do stochastic simulations.  Parameter values used in simulation often
> come
> from the observations of the real word phenomena.
> Parameter values are often given as "rates" (of change), "time", or
> "probabilities".
> I am confused about how I go about converting parameters given with
> different units.
> 
> For example, I have a discrete time Markov model that describes the
> following process:
> 
> A -> B -> C
> 
> Let's suppose that I am given average time that individuals stay at A,
> "dA",
> as 3 days.  We assume that "dA" is exponentially distributed.
> Similarly, "dB" follows an exponential distribution with average 1000
> days.
> 
> 
> I decide to simulate the model with a time step corresponding to one
> day.
> 
> Would any of the following be correct?
> a. A probability an individual makes transitions from A to B is 1/3.
> Likewise, transition from B to C occurs with probability 1/1000.
> b. If I reduce the size of time step as 0.1 day, then the transition
> probability from A to B is 0.1*(1/3).  Likewise,  transition
> probability
> from B to C is 0.1*(1/1000)
> c. The size of time step must not be larger than 3 day, which makes the
> transition probability to 1.
> d. if parameters values are given rates of change, then I can directly
> translate them to a probabilities per unit time.  There is no
> difference
> between a rate and probability per time.
> 
> How do we know about the reasonable size of time steps?
> 
> Any help would be greatly appreciated.  Also, could anybody suggest
> pointers
> or books that can be useful in this regard?
> 
> Sincerely,
> 
> -- JH
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-
> guide.html
> and provide commented, minimal, self-contained, reproducible code.