6

The probability density is used to 'measure how good' the parameters are because it is a natural way of quantifying if these parameters are good for the observed data. Also, as the notation often causes some confusion, $L(\theta | x)$ denotes the probability of all of your observed data, not just one value. Also the "$|$" may cause confusion as it ...


2

The idea behind this kind of reasoning is that there is a "true" distribution (unknown to us, mere mortals) and that the data is generated following this distribution. But what we don't really know the shape of the distribution, all we know is the distribution of the data that we have. This is called the empirical distribution. Let's see a simple ...


2

And that's all, we can infer P(x|y=c) and P(c) from the data. I don't see where the MLE shows its role. Maximum likelihood estimate is used for this very purpose, i.e. to estimate the conditional probability $p(x_j \mid y)$ and marginal probability $p(y)$ . In Naive Bayes Algorithm ,using the properties of conditional probability, we can estimate the joint ...


1

Note first that the first $=$ (equals) in $\frac{dl(\theta)}{d\theta} = 0 = −\frac{1}{2\sigma^2}(0−2X^TY + X^TX \theta)$ should be interpreted as a "is set to", that is, we set $\frac{dl(\theta)}{d\theta} = 0$. Given that (apparently) $\frac{dl(\theta)}{d\theta} = −\frac{1}{2\sigma^2}(0−2X^TY + X^TX \theta)$, $\frac{dl(\theta)}{d\theta} = 0$ is ...


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