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Adding Bias To Random Walk

Asked by Kelly McGuire on 14 Jan 2019
Latest activity Commented on by TADA
on 14 Jan 2019
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 Comments

TADA
on 14 Jan 2019
take a look at that file exchange:
https://www.mathworks.com/matlabcentral/fileexchange/22003-random-walks-in-matlab
Hey TADA, thanks for the link. I didn't find anything about adding a bias in each direction. Could you point that out for me?
TADA
on 14 Jan 2019
Sorry, I was sure there was bias implementation there...

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2 Answers

TADA
Answer by TADA
on 14 Jan 2019
Edited by TADA
on 14 Jan 2019
 Accepted Answer

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 Comments

TADA
on 14 Jan 2019
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.
Excellent! That is great, thank you.
TADA
on 14 Jan 2019
Cheers! Good Luck

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Answer by Walter Roberson
on 14 Jan 2019

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 Comments

Thanks for the response! Any one of the directions can be the 34%, and the other three can have the 22%. For now, it doesn't matter, I just need one of the directions to be more probable than the other three. I'd like to add the bias to the code that I attached, because that code does everything exactly the way I want, just need to add some bias.
Walter Roberson
on 14 Jan 2019
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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