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]]
>
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