Mathias Brandewinder on .NET, F#, VSTO and Excel development, and quantitative analysis / machine learning.
16. April 2011 17:27

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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10. April 2011 12:09

One of my initial goals for 2011 was to get my feet wet with Python, but after the last (and excellent) San Francisco F# user group meetup, dedicated to F# for Python developers, I got all excited about F# again, and dug back my copy of Programming F#.

The book contains a Sequence example which I found inspiring:

open System

let RandomSequence =
let random = new Random()
seq {
while true do
yield random.NextDouble() }

What’s nice about this is that it is a lazy sequence; each element of the Sequence will be pulled in memory “on demand”, which makes it possible to work with Sequences of arbitrary length without running into memory limitation issues.

This formulation looks a lot like a simulation, so I thought I would explore that direction. What about modeling the weather, in a fictional country where 60% of the days are Sunny, and the others Rainy?

Keeping our weather model super-simple, we could do something along these lines: we define a Weather type, which can be either Sunny or Rainy, and a function WeatherToday, which given a probability, returns the adequate Weather.

type Weather = Sunny | Rainy

let WeatherToday probability =
if probability < 0.6 then Sunny
else Rainy

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