Re: [Help-mcsim] R?p. : MCSim and mixture models

[Bill Harris]

Frederic Bois <address@hidden> writes:

> Regarding my previous message: for the indicator variable it would be
> enough to sample it
> uniform (0, 1) and then to partition the [0,1] interval in as many
> segments as there are models.
> If the indicator is less than, say, 0.1 use model 1, else less than
> 0.2 use model 2 etc. You could
> use segments of different length to given different prior
> probabilities to your models. You could
> also parametrize the segment lengths, etc.

Frédéric,

Nice idea.  I'll think about it or perhaps try it.

I came up with an electrical network that approximates a problem I am
considering.

If you have a fixed-width font, this may make sense.

             \
    I1        \   +--------+
  +------+--   \--+  R2    +--------+-------------+
  |      |   S1   +--------+        |             |
  |      |                          |             |
  |    +-+--+                       |           +-+--+
V1|    |    |                       |           |    |
__|__  |    |                     __|___        |    |
 ---   | R3 |                   C __ ___        | R1 |
-----  |    |                       |           |    |
 -+-   +-+--+                       |           +-+--+
  |      |                          |             |
  |      |                          |             |
 _|_    _|__                      __|___          |
                                                  ^
                                                  V2

Imagine that V1 is fixed (say, 10 volts), that R1, R2, and R3 are fixed
but noisy, that C is fixed, that R1 >> R1, and that R1+R2 ≅ R3.

Imagine that V2 varies.

Finally, S1 switches on and off, but we don't know when.

I want to know I1, the current out of battery V1, as well as S1, the
probability that switch S1 is closed at any particular time, with V2 as
the only predictor variable.

When S1 is open, I1 = (V1 / R3) + epsilon

When S1 closes, I1 is initially (V1 / R3) + (V1 / R2), as C1 initially
acts like a short.  Eventually I1 becomes (V1 / R3) + ((V1 - V2) / (R2 +
R3)) + epsilon.

Does that clarify things?  When it's not so late, I'll write out the
data likelihood.

Bill
--
Bill Harris
Facilitated Systems
http://makingsense.facilitatedsystems.com/