#### An Introduction To Probability And Statistics For Data Science

*We* already know that * data science* is one of the most trending buzzwords in today’s tech world, with an exceptional potential of opportunities for aspirants. If you belong to this league and are planning to pursue a career in this field, being familiar with the fundamental concepts is of utmost importance. You mayn’t need a Ph.D. to excel in

*, but you’ve to have a solid understanding of the basic algorithms.*

**data science**If you’ve just entered the field, you probably have come across people saying * probability* and

*are the crucial prerequisites for*

**statistics****and they are correct. Having a good understanding of these two aspects would not only arm you with the concepts but will also help you attain your goal of**

*data science*,

**becoming a data science professional.**In this post, we’re going to explain the basics of **probability** and **statistics** in the context of **data science** with some advanced concepts.

*1- Probability*

*1- Probability*

* Probability *stands for the chance that something will happen and calculates how likely it is for that event to happen. It’s an intuitive concept that we use on a regular basis without actually realizing that we’re speaking and implementing

**probability**at work.

*1.1- The need of probability*

*1.1- The need of probability*

*Randomness* and uncertainty are imperative in the world and thus, it can prove to be immensely helpful to understand and know the chances of various events. Learning of **probability** helps you in making informed decisions about likelihood of events, based on a pattern of collected data.

In the context of **data science**, statistical inferences are often used to analyze or predict trends from data, and these inferences use **probability** distributions of data. Thus, your efficacy of working on **data science** problems depends on **probability** and its applications to a good extent.

*1.2- Conditional probability*

*1.2- Conditional probability*

*They* naturally arise in the investigation of experiments where a trial’s outcome may affect subsequent trials’ outcomes. It’s a measure of the **probability** of a particular situation occurring (an event) given that (by evidence, assertion, presumption, or assumption) another event has occurred. Now, if the **probability** of the event modifies when the first event is taken into consideration, it can be said that the **probability** of the second event is dependent on the occurrence of the first event.

*1.3- Conditional probability and data science*

*1.3- Conditional probability and data science*

*A number* of * data science techniques* depend on

*. It’s a formula that demonstrates the probability of an event depending on the prior knowledge about the conditions that might be associated with the event. Reverse probabilities can be found out using the Bayes theorem if the conditional*

**Bayes theorem****probability**is known to us. With the help of this theorem, it’s possible to develop a learner that is capable of predicting the

**probability**of the response variable of some class, given a fresh set of attributes.

*interconnect the knowing possibilities.*

**Implementing of code***1.4- Random variables*

*1.4- Random variables*

*To* calculate the likelihood of an event’s occurrence, a framework needs to be put to express the outcome. And random variables are numerical descriptions of these outcomes.

It’s a set of possible values derived from a random experiment. It’s a variable whose possible values are a random phenomenon’s outcomes. Random variables are divided into two categories namely *continuous* and *discrete.*

A continuous random variable is the one that considers an infinite number of possible values. These variables are usually measurements such as weight, height, and time needed to run a mile, among others.

A discrete random variable is the one that may just take on countable quantity of different values like 2, 3, 4, 5 etc. These variables are usually counts such as the number of children in a family, the number of faulty light bulbs in a box of ten etc.

*1.5- Probability** distribution*

*1.5- Probability*

*distribution*

* Probability distribution* is a function that describes all the possible likelihoods and values that can be taken by a random variable within a given range. For a continuous random variable, the

**probability**distribution is described by the

**probability**density function. And for a discrete random variable, it’s a

**probability**mass function that defines the

**probability**distribution.

**Probability** distributions are categorized into different classifications like binomial distribution, chi-square distribution, normal distribution, Poisson distribution etc. Different **probability** distributions represent different data generation process and cater to different purposes. For instance, the binomial distribution evaluates the **probability** of a particular event occurring many times over a given number of trials as well as given the **probability** of the event in each trial. The normal distribution is symmetric about the mean, demonstrating that the data closer to the mean are more recurrent in occurrence compared to the data far from the mean.

*2- Statistics*

*2- Statistics*

* Statistics* is the study of collection, interpretation, organization analysis and organization of data and thus,

**data science professionals**need to have solid grasp of

**statistics**.

Descriptive **statistics** together with **probability** theory can help them in making forward-looking business decisions. Core statistical concepts are needed to be learned in order to excel in the field. There’re some basic algorithms and theorems that form the foundation of different libraries that are widely used in * data science*. Let’s have a look at some common statistical techniques widely used in the field.

*2.1- Classification*

*2.1- Classification*

*It’s* a * data mining technique*, which assigns categories to a collection of data to help in more accurate analysis and predictions. Known as a Decision Tree as well, it’s one of the many methods meant for making the analysis of massive datasets effective. Classification techniques are divided into two major categories namely

*discriminant analysis*and

*logistic regression*.

*2.2- Linear Regression*

*2.2- Linear Regression*

*In* **statistics**, Linear Regression is a method used to predict the target variable after insertion of the best linear relationship between those variables. *Simple Linear Regression* is where a single independent is used while in *Multiple Linear Regression*, many independent variables are used to predict a dependent variable.

*2.3- Resampling Methods*

*2.3- Resampling Methods*

*It’s* a non-parametric method pertaining to statistical inference wherein repeated samples are drawn from the actual data samples. Here, the utilization of generic distribution tables in order to compute approximate p **probability** values doesn’t happen.

It can develop a unique sampling distribution based on the original data by using experimental methods. Having a good understanding of terms Cross-Validation and Bootstrapping can help you develop the concept of Resampling Methods.

*2.4- Bootstrapping*

*2.4- Bootstrapping*

*It’s* a technique that aids in different situations like validation of performance of a predictive model, ensemble methods etc. It performs by sampling with replacements from the actual data, “not chosen” data points are considered here as test cases.

*2.5- Cross-Validation*

*2.5- Cross-Validation*

*It’s* a technique followed for validating the model performance. It’s done by splitting the training data into k parts. The k-1 parts are considered as the training set while the “held out” part is considered as the test set.

*2.6- Tree-Based Methods*

*2.6- Tree-Based Methods*

*Tree-Based* Methods are used to solve both regression and classification problems. Here, the predictor space gets segmented into various simple regions together with a set of splitting rules that is summarized in a tree.

These kinds of approaches are referred to as Decision-Tree methods and they develop multiple trees that are merged to obtain a single consensus prediction. *Random forest algorithm*, *Boosting* and *Bagging* are the major approaches used here.

*2.7- Bagging*

*2.7- Bagging*

*Bagging* essentially stands for creating multiple models of a single algorithm – such as a Decision Tree. Every single model is trained on a sample data different in nature (called bootstrap sample). As a result, every Decision Tree is developed using different sample data, which solves the issue of overfitting to the sample size. This grouping of Decision Trees essentially helps in decreasing the total error, as there’s a reduction in the overall variance with the addition of every new tree. A random forest is what we call a bag of such Decision Trees.

In * data science*, a lot of other concepts and techniques of

**statistics**are used apart from the above. It’s also important to note that if you obtain a good grasp of

**statistics**in the context of

**data science**, working with

*can be one of the best ideas. Once you’ve learned the core concepts of*

**machine learning models****statistics**, you can try to implement some

**models right from the beginning to develop a good foundational knowledge about their underlying mechanics.**

*machine learning**Key takeaway*

*Key takeaway*

*This* was a fundamental rundown of some basic concepts and techniques of **probability** and **statistics** used in the context of **data science**. This understanding can help aspiring **data science professionals** to obtain a clear and better knowledge of the field.

When it comes to **probability**, a huge portion of **data science** relies on estimating the **probability** of occasions – from the likelihood of disappointment for a segment in the production system, to the chances of an advertisement getting tapped on. And once you’ve developed a good grasp of likelihood hypothesis, you can gradually move forward to find out about the measurements – which will lead you toward deciphering information and helping stakeholders in making informed business decisions.

Simply put, having a good comprehension of the concepts, strategies, and techniques utilized in both **probability** and **statistics** greatly helps you in gaining better and deeper insights. However, apart from these two subjects, you also need to master other fields like mathematics, **machine learning**, programming etc to rise above the competition when you’ll actually start working in the field of **data science**. And * data science bootcamp* is the most convenient way to learn these fields.