Probability VS Likelihood
By: Harshit Dawar
Tags: Deep Learning, Statistics, Mathematics, Data Science, Machine Learning

Important note!

The biggest problem which restricts someone to understand the concepts of Data Science is the wrong approach towards learning & understanding it.

Most of the people today just rush for implementing the algorithms of the data science without understanding the internal working of the particular algorithm. This new approach of learning data science is completely wrong, & according to me it is the worst approach, but the sad reality is that most of the people are following this wrong/worst approach only.

One hype is created in the mindset of the majority of the people, & the hype is that at the majority of the places/situations/scenarios Deep Learning helps, then at few situations, Machine Learning helps, & at the last, at very few situations, Statistics helps. This hype/mindset is completely wrong & the reality is exactly opposite to this hype.

In reality, Deep Learning is the subset of the Machine Learning, & Machine Learning itself is completely dependent on Statistics. Now, here if you think logically, then you will understand the fact that, if you didn’t understand the Statistics, then how you will be able to understand Machine Learning by its core.

That is why it is been preferred that the internal working of the algorithms should be very much clear, & it is possible only when you understand Statistics. This blog topic i.e “Probability VS Likelihood” is a Statistics topic, it might be the case that some of the readers of this blog are not interested in Data Science, they are just interested in this small part, but the actual truth is this small part acts as fundamentals or building blocks in the Data Science part. It is completely fine if you are among the persons who are not interested in Data Science, but even though you will understand some of the logic or building blocks of the Data Science field.

It is very important to understand the difference between Probability & the Likelihood, so that being said, let’s begin understanding the difference between the two.

Difference between the Probability & Likelihood!

Probability corresponds to finding the chance of something given a sample distribution of the data, while on the other hand, Likelihood refers to finding the best distribution of the data given a particular value of some feature or some situation in the data.

Example of Probability!

Consider a dataset containing the heights of the people of a particular country. Let’s say the mean of the data is 170 & the standard deviation is 3.5.

When Probability has to be calculated of any situation using this dataset, then the dataset features will be constant i.e. mean & standard deviation of the dataset will be constant, they will not be altered. Let’s say the probability of height > 170 cm has to be calculated for a random record in the dataset, then that will be calculated using the information shown below:

Calculating Probability [Image by Author!]

In the above image, “mu” represents mean & “sigma” represents Standard Deviation.

While calculating probability, feature value can be varied, but the characteristics(mean & Standard Deviation) of the data distribution cannot be altered.

If in the same dataset, the probability of height > 190 cm has to be calculated, then in the above equation, only the height part would have changed.

Example of Likelihood!

Likelihood calculation involves calculating the best distribution or best characteristics of data given a particular feature value or situation.

Consider the exactly same dataset example as provided above for probability, if their likelihood of height > 170 cm has to be calculated then it will be done using the information shown below:

Likelihood calculation [Image by Author!]

In the calculation of the Likelihood, the equation of the conditional probability flips as compared to the equation in the probability calculation.

Here, the dataset features will be varied, i.e. Mean & Standard Deviation of the dataset will be varied in order to get the maximum likelihood for height > 170 cm.