In my last post, I looked into running a simple simulation using F# sequences; our model mapped a sequence of random numbers to 2 states, Rainy and Sunny.

What if we wanted to model something a bit more realistic, like a system where the weather tomorrow depends on the weather today? Let’s say, for instance, that if the weather is Sunny today, there is a 60% chance that it’s still Sunny tomorrow, but if it’s Rainy today, we have a 70% chance that tomorrow is Rainy.

*Technicality: we will also assume that if we know today’s weather, what happened yesterday brings us no additional information on the probability of rain or sun tomorrow.*

Let’s start like last time, and define first a Weather type, with 2 states, Rainy and Sunny, and represent the transitions from state to state, using pattern matching:

type Weather = Sunny | Rainy let NextDay today proba = match today with | Rainy -> if proba < 0.7 then Rainy else Sunny | Sunny -> if proba < 0.6 then Sunny else Rainy

Armed with this, starting from an initial state, we want to generate the next state, based on the current state and the next probability coming from the sequence of random numbers. This part got me stumped for a while. Using a **Sequence map** is clearly not going to work, because, unlike in the previous post, we can’t determine the Weather based on the probability alone, we need both the probability and the previous Weather. Conversely, **Sequence unfold** has the opposite problem: it generates a sequence of states based on the previous State, but doesn’t take in another Sequence as input.

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