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.s...@imail.org 801.408.8111 > -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-boun...@r- > project.org] On Behalf Of Jong-Hoon Kim > Sent: Sunday, January 25, 2009 6:58 PM > To: r-help@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@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. ______________________________________________ R-help@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.
