simulating an unbias coin with a bias coin flip

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Genus 2014-4-28

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https://ww2.mathworks.cn/matlabcentral/answers/127432-simulating-an-unbias-coin-with-a-bias-coin-flip

评论： Andrew Newell 2014-5-2

Hello, I have a question about achieving an unbias coin with a bias coin flip for N = 1000 tosses, for a set of I have written code for unknown bias probabilities p = [ 0.5 0.4 0.3 0.2 0.1].I would like to choose these arbitrarily to achieve an unbias coin for each. I visited this site to read about the process http://www.pcoder.net/change-an-unfairly-biased-coin-to-a-fair-coin-a-classical-randomized-algorithm/#axzz308a9TpBx but im confuse about the implementation in matlab. thanks in advance for any feedback. thanks

if true
% calling the function
p = [ 0.5 0.4 0.3 0.2 0.1];
N = 1000;
for i = 1:length(p)
   function outcome = mysim(p, N)
P = cumsum(p); 
u = rand(1, N); 
outcome = zeros(1, N); % A blank array for holding the outcomes 
for n=100:100:N, 
   h = find(u(n)<P, 1 );
    outcome(n) = h;
end % code
  end

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Genus 2014-4-28

I implemented your recommendation however there is an error at outcome(i) = mysim(p, N); it states the variable appears to change size on every loop iteration (within a script) consider preallocating for speed. What are your reccomendations for rectifying this issue, thanks

Andrew Newell 2014-4-28

在 MATLAB Online 中打开

That's not an error, just a suggestion. You can preallocate outcome by adding the line

outcome = zeros(size(p));

before the loop.

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Answer 1

Andrew Newell 2014-4-28

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/127432-simulating-an-unbias-coin-with-a-bias-coin-flip#answer_134888

编辑：Andrew Newell 2014-5-1

在 MATLAB Online 中打开

I think that the simplest approach is to write a little function to simulate a single toss, and then build up your simulation from that. Here is that function:

function side = simulateOneToss
% Make two tosses (outcomes 0 and 1 could stand for heads and tails)
twoTosses = round(rand(1,2));
 % If outcome is not HT or TH (both of which sum to 1), try again.
while sum(twoTosses) ~= 1
    twoTosses = round(rand(1,2));
end
 % Take first of the two tosses as the answer.
side = twoTosses(1);

Based on the comments below, here is a version that allows a probability other than 0.5:

function side = simulateOneToss(p)
% Make two tosses (outcomes 0 and 1 could stand for heads and tails)
twoTosses = rand(1,2)<p;
% If outcome is not HT or TH (both of which sum to 1), try again.
while sum(twoTosses) ~= 1
  twoTosses = rand(1,2)<p;
end
% Take first of the two tosses as the answer.
side = twoTosses(1);

Note that I don't round before comparing with the probability (otherwise you'll always get p=0.5 in effect). Now this can be used in a simulator:

function outcomes = simulateTosses(p,nTosses,nTrials)
tosses = zeros(nTosses,nTrials);
for i=1:numel(tosses)
  tosses(i) = simulateOneToss(p);
end
outcomes = sum(tosses>p);

Finally, you can run it and plot the results as follows:

nTosses = 100;
nTrials = 10;
p = 0.6;
outcomes = simulateTosses(p,nTosses,nTrials);
bar(1:nTrials,outcomes)

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Genus 2014-5-2

在 MATLAB Online 中打开

excellent, it works. I have a question about descision or hypothesis testing. suppose I have a conditional probability defined by the binomial probability

    function [p] = calculateInputProbability(N, T)
     inputP = [];
    for i=1:N+1
        combo = nchoosek(N,i-1);
        temp  = combo * power(T , i-1);
        temp1  = temp * power((1-T), N-(i-1));
        inputP(i) = temp1;          
    end
    p  = inputP;

end

im hoping to do hypothesis testing with H0 vs H1 the same specifications as before. but now with theta is in[0,1];. Ho having the conditional probability and theta = 1/2 and for H1 defined by the same conditional probability but theta =[ 0.5 0.4 0.3 0.2 0.1];

1) suppose we have 5 bias coins corresponding to each bias element theta =[ 0.5 0.4 0.3 0.2 0.1] and unbias coin corresponding to theta = 1/2. 2) we would like to choose an arbitrary bias single coin from the 5 coins and flip it 100 times and determine if the coin is bias or unbias. if its unbias probability is 1/2 otherwise bias. 3) we would like for each selected coin to simulate it from 100 to 1000 in steps of 100. . how do i rate you on this site. you have helped me greatly. here is my code so far. thanks

%% Input Values n0 = 0.5; n1 = [0.4 0.3 0.2 0.1]; nTosses = [100 200 300 400 500 600 700 800 900 1000]; nTrials = 1; for i = 1:length(n1) for j = 1: length(nToses) outcomes = simulateTosses(n1(i),nTosses(j),nTrials); end %% Calculate the prbability [p] = calculateInputProbability(nTosses(j), n1(i)); % code end

Andrew Newell 2014-5-2

Genus, now you're on to a question on hypothesis testing, which should be posted separately. But first, I would recommend reading up on the relevant statistical methods. For example, there is a Wikipedia page Checking whether a coin is fair.

I'm glad I have been able to help you. We don't have ratings as such, but you can click on the "Accept this answer" button.

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