Adding Bias To Random Walk

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?

[TADA]

take a look at that file exchange:

https://www.mathworks.com/matlabcentral/fileexchange/22003-random-walks-in-matlab

[Kelly McGuire]

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]

Sorry, I was sure there was bias implementation there...

Answer 1

[TADA]

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

[TADA]

i think the continous step would be less biased because of adding the random value which is not biased

[Kelly McGuire]

Great! Since I'm still a novice at programming in Matlab, to create biases to the west, south, and east, I would just add a couple more lines of:

bias = [ones(1, 34), repmat([2 3 4], 1, (100-34)/3)], but with 22 instead of 34? Or because there is now a 34% bias to the north, that leaves a 22% bias in the other 3 directions?

[TADA]

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]

Excellent! That is great, thank you.

[TADA]

Cheers! Good Luck

Answer 2

[Walter Roberson]

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) ?

[Kelly McGuire]

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]

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)];