MATLAB: How to create a Markov Matrix with variables instead of numbers for probabilities

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How do I create a Markov Matrix with variables instead of numbers where the probabilities should go?

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If your goal is to manipulate P symbolically (i.e., algebraically, rather than numerically), then you'll need to use Matlab's symbolic toolbox if you have it. In that case,

P = sym('p',[4,4]);

creates a symbolic matrix P with element (i,j) denoted by pi_j.

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MATLAB: How to do bivariate numerical integration in Matlab for computing joint probabilities

These can all be expressed in terms of the 'mvncdf' function. For (1) it would be:

 P1 = mvncdf(-b,mu,sigma);

For (4) it would be: (I assume you meant "Pr(u_1>-c(i,1);-b(i,2)<=u_2<=-c(i,2))" rather than "Pr(u_1>-c(i,1);-b(:,2)<=u_2<=-c(i,2))" .)

 P4 = mvncdf([-c(:,1),-b(:,2)],[repmat(inf,size(b,1),1),-c(:,2)],mu,sigma);

This latter uses the "rectangle" form of the 'mvncdf' call.

I think you should be able to work out the remaining cases for yourself using the concepts demonstrated here.

MATLAB: What are target variables, predictor variables and prior probabilities

Hi Lester, There are a lot of phrases here and I will try to explain them in that order with some context.

Target variable, in the machine learning context is the variable that is or should be the output. For example it could be binary 0 or 1 if you are classifying or it could be a continuous variable if you are doing a regression. In statistics you also refer to it as the response variable.

Predictor variables in the machine learning context the the input data or the variables that is mapped to the target variable through an empirical relation ship usually determined through the data. In statistics you you refer to them as predictors. Each set of predictors may be called as an observation.

Prior probability usually comes from the Bayesian Inference where you have prior belief that the probabilities of the parameters (or weights) come from a certain distribution.

You see that there are couple of different terminologies and this is because we have different branches fields like machine learning and statistics with different nomenclature. I would be able to clarify this further if you define what your training methods are and what your data looks like.

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MATLAB: What are target variables, predictor variables and prior probabilities

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