monte carlo simulation notion it is not sufficient to produce good answer we have to have valid reason to be confident that it is in fact good answer and when we drop large enough number of needlesthe small standard deviation gives us reason to be confident that we have correct answer rightnot exactly having small standard deviation is necessary condition for having confidence in the validity of the result it is not sufficient condition the notion of statistically valid conclusion should never be confused with the notion of correct conclusion each statistical analysis starts with set of assumptions the key assumption here is that our simulation is an accurate model of reality recall that the design of our buffon-laplace simulation started with little algebra demonstrating how we could use the ratio of two areas to find the value of we then translated this idea into code that depended upon little geometry and the randomness of random random let' see what happens if we get any of this wrong supposefor examplewe replace the in the last line of throwneedles by and again run estpi( this time it prints est std dev needles est std dev needles est std dev needles est std dev needles est std dev needles est std dev needles the standard deviation for mere , needles suggests that we should have fair amount of confidence in the estimate but what does that really meanit means that we can be reasonably confident that if we were to draw more samples from the same distributionwe would get similar value it says nothing about whether or not this value is close to the actual value of statistically valid conclusion should not be confused with correct conclusion before believing the results of simulationwe need to have confidence both that our conceptual model is correct and that we have correctly implemented that model whenever possibleone should attempt to validate results against reality in this caseone could use some other means to compute an approximation to the area of circle ( physical measurementand check that the computed value of is at least in the right neighborhood some closing remarks about simulation models for most of the history of sciencetheorists used mathematical techniques to construct purely analytical models that could be used to predict the behavior of system from set of parameters and initial conditions this led to the development of important mathematical tools ranging from calculus to probability theory these tools helped scientists develop reasonably accurate understanding of the macroscopic physical world