How do we know which type of probability model to use? In our introduction to statistical inference, the lecturer said

In statistics we assume a certain type of probability model generates
  observed data and we use a collection of observations to estimate
  which particular model is most plausible, ...

This does not seem sensible to me. How can one just "assume" a certain type of probability model generates observed data? Surely there is a rigorous way of knowing which probability model fits the observed data rather than just assuming? Can someone please provide a better explanation of this?
 A: *

*In some situations the characteristics of the situation will suggest a model.
For example, imagine you have a situation where events occurring in time have characteristics like - the rate at which events happen is close to constant; events occur independently, at constant average rate and the probability of at least one event in a small interval of time will be proportional to the length of the interval. Then the number of events per unit time will be close to Poisson-distributed, the time between events will be close to exponentially distributed, the distribution of events within a fixed interval of time will be uniform. There are a variety of other such simple models (for other circumstances) from which a number of distributions arise, and which may often be reasonable models in a number of real situations. 
You might like to read, for example, about Bernoulli trials -- which are a kind of idealized situation with a sequence of outcomes of two kinds; from this a variety of distributions occur, depending on what things you look at (number of outcomes of one type in a fixed number of trials, or perhaps the number of trials until you see an outcome of a particular kind, for example).

*In other situations a distribution may have been found to work well in practice, or a distribution shape is suggested by observation (possibly from previous studies). This may happen without there necessarily being a model of a process that implies that distribution -- a distribution is used because it works fairly well in that situation. It seems like this is the case when the Weibull distribution is used for wind speeds, for example (at least I haven't seen a theoretical derivation of it).
Sometimes models arise as a mix of both -- an initial theoretical model is considered as an approximation, then a similar but more complex model is used which better approximates the actual circumstances.
Or it might happen that theoretical considerations narrow things down somewhat ("we need a family of right skewed continuous distributions with constant coefficient-of variation", for example) but doesn't of itself suggest a specific family, and it may be that a number of simple choices seem to describe the data sets we have reasonably well. Then the choice of distribution family may come down to what is easiest to fit, or convenient to perform particular kinds of calculations on or is most familiar to our audience, as long it also works well enough for our purposes.
