Adding Bias To Random Walk
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How would add a bias or probability of 34%, 22%, 22%, and 22% for each of the four directions in the attached random walk code?
3 个评论
TADA
2019-1-14
take a look at that file exchange:
https://www.mathworks.com/matlabcentral/fileexchange/22003-random-walks-in-matlab
Kelly McGuire
2019-1-14
TADA
2019-1-14
Sorry, I was sure there was bias implementation there...
采纳的回答
you can make a step & bias vector:
stepCoordinates = [1,0;0,1;-1,0;0,-1];
% this creates the bias to the north
bias = [ones(1, 34), repmat([2 3 4], 1, (100-34)/3)];
then when you generate the actual steps in your loop use this instead of what you had:
stepBiasIndex = randi(100, 1, numberOfSteps);
stepCoordIndex = bias(stepBiasIndex);
delta = stepCoordinates(stepCoordIndex,:);
if continuousSteps
signOfStep = sign(delta);
plusminusRandSign = [-1 1];
indicesWithSignZero = signOfStep == 0;
signOfStep(indicesWithSignZero) = plusminusRandSign(randi(2, size(signOfStep(indicesWithSignZero))));
delta = delta - signOfStep.*rand(numberOfSteps, 2);
end
deltax = delta(:,2)';
deltay = delta(:,1)';
You can vectorize the rest of it but you said it does what you want so i didn't touch anything else
In this specific solution the bias is only in percentage because the bias vector is a 1x100 vector
so if you want to be more specific about it you can make it a 1x1000 for promils or 1x10000 for higher precision...
I attached the edited file
5 个评论
TADA
2019-1-14
i think the continous step would be less biased because of adding the random value which is not biased
Kelly McGuire
2019-1-14
编辑：Kelly McGuire
2019-1-14
TADA
2019-1-14
That's Right Ecause That The Bias Of North Is 34 It Eaves 66/3 For HE Other Three....
You Can Easily Change The Content Of That Vector To Add Bias In Any Direction, For Instance
bias = [ones(1,34),repmat(2,1,40),repmat(3,1,13),repmat(4,1,13)];
Now That Would Be 34% North, 40% East And 13% West And South.
Kelly McGuire
2019-1-14
TADA
2019-1-14
Cheers! Good Luck
更多回答（1 个）
Walter Roberson
2019-1-14
There was a recent question in which someone asked for going immediately back to be prohibitted and for the probability of going forward to be doubled. My suggestion then was:
dd = randi(4)
for ss = 1:500
rr = rand;
if rr < 1/4
dd = 1+mod(dd,4) %next higher direction
elseif rr < 1/2
dd = 1+mod(dd-2,4) %next lower direction
end % 50 percent stays same direction
if dd==1
yy=yy+1; %north
elseif dd==2
xx=xx+1; %east
elseif dd==3
yy=yy-1; %south
else
xx=xx-1; %west
end
plot here probably
end
The initial dd is about picking some initial direction. The directions are numbered 1 (north), 2 (east), 3 (south), 4 (west), and the new direction is computed as a change of 0, -1 or +1 to the current direction (-2 was ruled out by not being permitted to go backwards.) You can modify the rr tests for whatever probabilities you want.
It is not clear to me in your question whether the 34% should be for a particular fixed direction (e.g., prefer to head east), or for a relative direction (e.g., prefer to go straight) ?
2 个评论
Kelly McGuire
2019-1-14
编辑：Kelly McGuire
2019-1-14
Walter Roberson
2019-1-14
randsample() the direction numbers with a weights matrix.
Or construct
dv = [1*ones(1,34), 2*ones(1,22), 3*ones(1,22), 4*ones(1,22)]; %direction 1 is overrepresented
dx = [-1 0 1 0]; dy = [0 1 0 -1];
rand_direction = randi(length(dv), 1, num_steps_needed);
rand_dx = dx(rand_direction);
rand_dy = dy(rand_direction);
x_positions = [initial_x, cumsum(rand_dx)];
y_positions = [initial_y, cumsum(rand_dy)];
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