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How Company Leaders and Data Scientists Work Together

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How Company Leaders and Data Scientists Work Together

Business leaders across platforms are hungrily eyeing data-driven decision making for its ability to transform businesses. But what needs to be taken into account is the opinion of data scientists in the core company teams for they are the experts in the field and whatever they have to say regarding data driven decisions should be the final word in these matters.

“The ideal scenario is all parties in complete alignment. This can be envisioned as a perfect rectangle, with business leaders’ expectations at the top, fully supported by a foundation of data science capabilities — for example, when data science and AI can achieve management’s goal of reducing customer retention costs by automating identification and outreach to at-risk customers,”says a report.

The much sought after rectangle, however, is rarely achieved. “A more workable shape is the rhombus, depicting the push-and-pull of expectations and deliverables.”

Using the power of your company’s data.

Business leaders must have patience with developments on the part of data scientists for what they expect is usually not in sync with the deliverables on the ground.

“Over the last few years, an automaker, for example, dove into data science on leadership’s blind faith that analytics could revolutionize the driver experience. After much trial and error, the results fell far short of adding anything meaningful to what drivers found valuable behind the wheel of a car.”

Appreciate Small Improvements

Also, what must be appreciated are small improvements made impactful. For instance, “slight increases in profitability per customer or conversion rates” are things that should be taken into account despite the fact that they might be modest gains in comparison to what business leaders had invested in analytics. “Applied over a large population of customers, however, those small improvements can yield big results. Moreover, these improvements can lead to gains elsewhere, such as eliminating ineffective business initiatives.”

Healthy Competition

However, it is advisable for business leaders to constantly push their data scientists to strive for more deliverables and improve their tally with a framework of healthy competition in place. In fact, big companies form data science centers of excellence, “while also creating a healthy competitive atmosphere that encourages data scientists to push each other to find the best tools, strategies, and techniques for solving problems and implementing solutions.”

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Here are three ways to inspire data scientists

  1. Both sides must work together –Take the example of a data science team with expertise in building models to improve customers’ shopping experiences. “Business leaders might assume that a natural next step is to use AI to enhance all customer service needs.”However, AI and machine learning cannot answer the ‘why’ or ‘how’ of the data insights. Human beings have to delve into those aspects by studying the AI output. And on the other hand, data scientists also must understand why business leaders expect so much from them and how to achieve a middle path with regard to expectations and deliverables.
  2. Gain from past successes and achievements – “There is value in small data projects to build capabilities and understanding and to help foster a data-driven culture.”The best policy for firms to follow is to initially keep modest expectations. After executing and implementing the analytics projects, they should conduct a brutally honest anatomy of the successes and failures, and then build business expectations at the same time as analytics investment.
  3. Let data scientists spell out the delivery of analytics results – “Communication around what is reasonable and deliverable given current capabilities must come from the data scientists — not the frontline marketing person in an agency or the business unit leader.” Before signing any contract or deal with a client, it is advisable to allow the client to have a discussion with the data scientists so that there is no conflict of ideas between what the data science team spells out and what the marketing team has in mind. For this, data scientists will have to work on their soft skills and improve their ability to “speak business” regarding specific projects.


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Statistical Application in R & Python: EXPONENTIAL DISTRIBUTION

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Statistical Application in R & Python: EXPONENTIAL DISTRIBUTIONStatistical Application in R & Python: EXPONENTIAL DISTRIBUTION

In this blog, we will explore the Exponential distribution. We will begin by questioning the “why” behind the exponential distribution instead of just looking at its PDF formula to calculate probabilities. If we can understand the “why” behind every distribution, we will have a head start in figuring out its practical uses in our everyday business situations.

Much could be said about the Exponential distribution. It is an important distribution used quite frequently in data science and analytics. Besides, it is also a continuous distribution with one parameter “λ” (Lambda). Lambda as a parameter in the case of the exponential distribution represents the “rate of something”. Essentially, the exponential distribution is used to model the decay rate of something or “waiting times”.

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For instance, you might be interested in predicting answers to the below-mentioned situations:

  • The amount of time until the customer finishes browsing and actually purchases something in your store (success).
  • The amount of time until the hardware on AWS EC2 fails (failure).
  • The amount of time you need to wait until the bus arrives (arrival).

In all of the above cases if we can estimate a robust value for the parameter lambda, then we can make the predictions using the probability density function for the distribution given below:

Application:-

Assume that a telemarketer spends on “average” roughly 5 minutes on a call. Imagine they are on a call right now. You are asked to find out the probability that this particular call will last for 3 minutes or less.

 

 

Below we have illustrated how to calculate this probability using Python and R.

Calculate Exponential Distribution in R:

In R we calculate exponential distribution and get the probability of mean call time of the tele-caller will be less than 3 minutes instead of 5 minutes for one call is 45.11%.This is to say that there is a fairly good chance for the call to end before it hits the 3 minute mark.

Calculate Exponential Distribution in Python:

We get the same result using Python.

Conclusion:

We use exponential distribution to predict the amount of waiting time until the next event (i.e., success, failure, arrival, etc).

Here we try to predict that the probability of the mean call time of the telemarketer will be less than 3 minutes instead of 5 minutes for one call, with the help of Exponential Distribution. Similarly, the exponential distribution is of particular relevance when faced with business problems that involve the continuous rate of decay of something. For instance, when attempting to model the rate with which the batteries will run out. 

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Hopefully, this blog has enabled you to gather a better understanding of the exponential distribution. For more such interesting blogs and useful insights into the technologies of the age, check out the best Analytics Training institute Gurgaon, with extensive Data Science Courses in Gurgaon and Data analyst course in Delhi NCR.

Lastly, let us know your opinions about this blog through your comments below and we will meet you with another blog in our series on data science blogs soon.

 

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The Rising Popularity of Python in Data Science

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The Rising Popularity of Python in Data Science

Python is the preferred programming language for data scientists. They need an easy-to-use language that has decent library availability and great community participation. Projects that have inactive communities are usually less likely to maintain or update their platforms, which is not the case with Python.

What exactly makes Python so ideal for data science? We have examined why Python is so prevalent in the booming data science industry — and how you can use it for in your big data and machine learning projects.

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Why Python is Dominating?

Python has long been known as a simple programming language to pick up, from a syntax point of view, anyway. Python also has an active community with a vast selection of libraries and resources. The result? You have a programming platform that makes sense of how to use emerging technologies like machine learning and data science.

Professionals working with data science applications don’t want to be bogged down with complicated programming requirements. They want to use programming languages like Python and Ruby to perform tasks in a hassle-free way.

Ruby is excellent for performing tasks such as data cleaning and data wrangling, along with other data pre-processing tasks. However, it doesn’t feature as many machine learning libraries as Python. This gives Python the edge when it comes to data science and machine learning.

Python also enables developers to roll out programs and get prototypes running, making the development process much faster. Once a project is on its way to becoming an analytical tool or application, it can be ported to more sophisticated languages such as Java or C, if necessary.

Newer data scientists gravitate toward Python because of its ease of use, which makes it accessible.

Why Python is Ideal for Data Science?

Data science involves extrapolating useful information from massive stores of statistics, registers, and data. These data are usually unsorted and difficult to correlate with any meaningful accuracy. Machine learning can make connections between disparate datasets but requires serious computational sophistry and power.

Python fills this need by being a general-purpose programming language. It allows you to create CSV output for easy data reading in a spreadsheet. Alternatively, more complicated file outputs that can be ingested by machine learning clusters for computation.

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Consider the Following Example:

Weather forecasts rely on past readings from a century’s worth of weather records. Machine learning can help make more accurate predictive models based on past weather events. Python can do this because it is lightweight and efficient at executing code, but it is also multi-functional. Also, Python can support object-orientated and functional styles, meaning it can find an application anywhere.

There are now over 70,000 libraries in the Python Package Index, and that number continues to grow. As previously mentioned, Python offers many libraries geared toward data science. A simple Google search reveals plenty of Top 10 Python libraries for data science lists. Arguably, the most popular data analysis library is an open-source library called pandas. It is a high-performance set of applications that make data analysis in Python a much simpler task.

No matter what data scientists are looking to do with Python, be it predictive causal analytics or prescriptive analytics, Python has the toolset to perform a variety of powerful functions. It’s no wonder why data scientists embrace Python.

If you are interested in Python Certification Training in Delhi, drop by DexLab Analytics. With a team of expert consultants, we provide state-of-the-art Machine Learning Using Python training courses for aspiring candidates. Check out our course itinerary for more information.

 

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Basics of a Two-Variable Regression Model: Explained

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Basics of a Two-Variable Regression Model: Explained

In continuation of the previous Regression blog, here we are back again to discuss the basics of a two-variable regression model. To read the first blog from the Regression series, click here www.dexlabanalytics.com/blog/a-regression-line-is-the-best-fit-for-the-given-prf-if-the-parameters-are-ols-estimations-elucidate.

In Data Science, regression models are the major driver to interpret the model with necessary statistical methods, practically as well as theoretically. One, who works extensively with business data metrics, will be able to solve various tough problems with the help of a regression theory. The key insight of the regression models lies in interpreting the fitness of the models. But it differs from the standard machine learning techniques such that, for improvement in the performance of the model being predicted, the major interpretable coefficients are never sacrificed. Thus, a sense in regression models can be considered as the most important tool to be chosen for solving any practical problem.

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Let’s consider a simple example to understand regression analysis from scratch. Say, we want to predict the sales of a Softlines eCommerce company for this year during the festivals of Diwali. There are a lot of factors to generate impacts on the sales value, as there are hundreds of factors persisting within the model. We can consider our own judgement to get the impacting factors. Now, here in our model, the value of sales that we want to predict is the dependent variable, whereas the impacting factors are considered as the independent variables. To analyse this model in terms of regression, we need to gather all the information about the independent variables from the past few years, and then act on it according to the regression theory.

Before getting into the core theory, there are some basic assumptions for such a two-variable regression model and they are as follows:

  • Variables are linearly related: The variables in a 2-variable Regression Model are linearly related, the linearity being in parameters, though not always in variables, i.e. the power in which the parameters appear should be of 1 only and should not be multiplied or divided by any other parameters. These linearly related variables are basically of two types (i) independent or explanatory variables & (ii) dependent or response variables.
  • Variables can be represented graphically: The idea behind this assumption guarantees that observations must be real numbers represented on graph papers.
  • Residual term and the estimated value of the variables are uncorrelated.
  • Residual terms and explanatory variables are uncorrelated.
  • Error variables are uncorrelated with mean 0 & common variance σ2

Deep Learning and AI using Python

Now, how can a PRF for expanding an economic relationship between 2 variables be specified?

Well, Population regression function, or more generally, the population regression curve, is defined as the locus of the conditional means of the dependent variables, for a fixed value of the explanatory variables. More simply, it is the curve connecting the means of the sub-populations of Y corresponding to the given values of the regressor X.

Formally, a PRF is the locus of all conditional means of the dependent variables for a given value of the explanatory variables. Thus; the PRF as economic theory would suggest would be:

Where 9(X) is expected to be an increasing function of X, if the conditional expectation is linear in X. then

Hence, for any ith observations:

However, the actual observation for the dependent variable is Yi. Therefore; Yi – E(Y/Xi) = ui, which is the disturbance term or the stochastic term of the Regression Model.

Thus,

…………………… (A)

  • is the population regression function and this form of specifying the population regression function is called the stochastic specification of the PRF.

Stochastic Specification of the Model:

Yi = α + βXi + ui is referred to as the stochastic specification of the Population Regression Function, where ui is the stochastic or the random disturbance term. It explains everything’s net influence other than X variable on the ith observation. Thus, ui is a surrogate or proxy for all omitted or neglected variables which may affect Y but is not included in the model. The random disturbance term is incorporated into the model with the following assumptions:-

Proof:

Taking conditional expectation as both sides, we get:

Hence; E(ui) = 0

cov(ui,uj) = E(ui uj ) = 0 ∀ i ≠ j i.e. the disturbance terms are distributed independently of each other.

Proof:

Two variables are said to be independently distributed, or stochastically independent; if the conditional distributions are equal to the corresponding marginal distributions.

Hence; cov(ui,uj )= E(ui uj ) = 0 Thus, no auto correction is present among ui,s i.e. ui,s. s are identically and independently distributed Random Variables. Hence, ui,s are all Random Samples.

Proof:

The conditional variance between two error terms can be given as given independence &

 

 

All these assumptions can be embodied in the simple statement: ui~N(0,σ2) where ui,s are iid’s ∀ I, Which heads “the ui are independently distributed identically distributed with mean 0 & variance σ2”.

Last Notes

The benefits of regression analysis are immense. Today’s business houses literally thrive on such analysis. For more information, follow us at DexLab Analytics. We are a leading data science training institute headquartered in Delhi NCR and our team of experts take pride in crafting the most insight-rich blogs. Currently, we are working on Regression Analysis. More blogs are to be followed on this model. Keep watching!

 

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A Regression Line Is the Best Fit for the Given PRF If the Parameters Are OLS Estimations – Elucidate

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A Regression Line Is the Best Fit for the Given PRF If the Parameters Are OLS Estimations - Elucidate

Regression analysis is extensively used in business applications. It’s one of the most integral statistical techniques that help in estimating the direction and strength between two or more (financial) variables – thus determining a company’s sales and profits over the past few years.

In this blog, we have explained how a regression line is the best fit for a given PRF if the parameters are all OLS estimations.

The OLS estimators for a given regression line has been obtained as: a = y ̅ – bx ̅ and b = (Cov(x,y))/(v(x)). The regression line on the basis of these OLS estimate has been given as: Y ̂_ i-Y ̅ = b(x_i-x ̅ )….. (1)

The regression line (1) constructed above is a function of the least square i.e. the parameters of the regression equation have been selected so that the residual sum of squares is minimized. Thus, the estimators ‘a’ & ‘b’ explains the population parameters, the best relative to any other parameters. Given, the linearity of the parameters, these estimators share the minimum variations with the population parameters, i.e. they explain the maximum variations in the model, in relation to the population parameters, as compared to any other estimators, in a class of unbiased estimators.

Thus, the regression line would be the ‘best fit’ for a given PRF. If ‘a’ & ‘b’ are best linear unbiased estimators for  respectively. Thus, to show ‘best fit’, we need to prove:

  1. To ‘b’ is Best unbiased estimator for :-

From the OLS estimation; we have ‘b’ as:

i.e.b is a linear combination of w’is & y’is.

Hence; ‘b’ is a linear estimator for β. Therefore, the regression line would be linear in parameters as far as ‘b’ is concerned.

Now,

Let us test for the prevalence of this conditions:

For unbiasedness, we must have :- E(b)=β. To test this, we take expectation on both sides of (3) & get:

From (1) & (4) we can say that ‘b’ is a linear unbiased estimator for β.

To check whether ‘b’ is the best estimator or not we need to check whether it has the minimum variance in a class of linear unbiased estimator.

Thus, we need to calculate the variance for ‘b’ & show that it is the minimum in a class of unbiased estimations. But, first, we need to calculate the variance for ‘b’.

Now; we need to construct another linear unbiased estimator and find its variance.

Let another estimator be: b^*=∑ci yi….(6)  For unbiasedness ∑ci =0,∑cixi =1.

Now; from (6) we get:

∴b* is an unbiased estimator for  Now; the variance for  can be calculated as:-

Now;

Hence; from (9) we can say V(b) is the least among a class of unbiasedness estimators.

Therefore, ‘b’ is the best linear unbiased estimator for  in a class of linear unbiased estimators.

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  1. To prove ‘a’ is the best linear unbiased estimator for α:-

Form the OLS estimation we have ‘a’ as:-

Here; ‘b’ is a function of Y and Y is a linear function of X(orUi).

‘a’ is also a linear function of Y. i.e. has linearity.

There, ‘a’ is a linear estimator for   ……. (11)

Now, for ‘a’ to be an unbiased estimator; we must have From (10) we have:-

Taking expectations on both sides of the equation; we get:

Therefore, ‘a’ is an unbiased estimator for  ……… (12)

From (11) & (12) ‘a’ is a linear unbiased estimator for

Now, if ‘a’ is to be the best estimator for then is most have the minimum variance. Thus; we first need to calculate the variance of ‘a’.

Now, 

Now; let us consider an estimator in the class of linear unbiased estimator.

Further we know,

Now;

Hence;

Now;

Therefore;

Hence; from (16) we can say that is the Min Variance Unbiased estimator in a class of unbiased estimator.

Hence; we can now safely conclude that a regression line composed of OLS estimators is the ‘best fit’ line for a given PRF, compared to any other estimator.

Thus, the best-fit regression line can be depicted as

Thus, a regression line is the best fit for a given PRF if the estimators are OLS.

End Notes

The beauty and efficiency of Regression method of forecasting never fail to amaze us. The way it crunches the data to help make better decisions and improve the current position of the business is incredible. If you are interested in the same, follow us at DexLab Analytics. A continues blog series on regression model and analysis is upcoming. Watch this space for more.

DexLab Analytics offers premium data science courses in Gurgaon crafted by the experts. After thorough research, each course is prepared keeping student’s needs and industry demands in mind. You can check out our course offerings here.

 

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Demand for Data Analysts is Skyrocketing – Explained

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Demand for Data Analysts is Skyrocketing - Explained

The salary of analytics professionals outnumbers that of software engineers by more than 26%. The wave of big data analytics is taking the world by storm. If you follow the latest studies, you will discover that there has been a prominent growth in median salary over several experience levels in the past three years (2016 to 2018). In 2019, the average analytics salary has been capped at 12.6 lakh per annum.

The key takeaway is that the salary structure of analytics professionals continues to beat other tech-related job roles. In fact, data analysts are found out-earning their Java correspondents by nearly 50% in India alone. A latest survey provides an encompassing view of base and compensation salaries in data science along with median salaries followed across diverse job categories, regions, education profiles, experience, tools and skills.

In this regard, a spokesperson of a prominent data analytics learning institute was found saying, “The demand for AI skills is expected to increase rapidly, which is also reflected by the fact that AI engineers command a higher salary than peers.” She further added, “Many of our clients have realized that investing in data-driven skills at the leadership level is a determining factor for the success of digital and AI initiatives in the organization. With the increasing adoption of digital technologies, we expect an enduring growth of Data Science and AI initiatives to offer exciting and lucrative career options to new age professionals,”

Over time, we are witnessing how markets are evolving while the demand for skilled data scientists is following an upward trend. It is not only the technology firms that are posting job offers, but the change is also evident across industries, like retail, medical, retail and CPG amongst others. These sectors are enhancing their analytical capabilities implying an automatic increase in the number of data-centric jobs and recruitment of data scientists.

Points to Consider:

  • In the beginning, nearly 76% of data analysts earn 6-lakh figure per annum.
  • The average analytics salary observed in 2018-19 is 12.6 lakh.
  • In terms of analytics career, Mumbai offers the highest compensation of 13.7 lakh yearly, followed by Bangalore at 13 lakh.
  • Mid-level professionals proficient in data analytics are more in demand.
  • Knowing Python is an added advantage; Python Programming training will help you earn more. Expect a package of 15.1 lakh.
  • Nevertheless, we often see a pay disparity for female data scientists against their male counterparts. While women’s take-home salary is 9.2 lakh, male from the same designation and profession earns 13.7 lakh per annum.

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As endnotes, the demand for data science skills is skyrocketing. If you want to enter into this flourishing job market, this is the best time! Enroll in a good data analyst course in Delhi and mould your career in the shape of success! DexLab Analytics is a top-notch data analyst training institute that offers a plethora of in-demand skill training courses. Reach us for more.

 

This article has been sourced from — www.tribuneindia.com/news/jobs-careers/data-analytics-professionals-ride-the-big-data-wave/759602.html

 

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The Almighty Central Limit Theorem

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The Almighty Central Limit Theorem

The Central Limit Theorem (CLT) is perhaps one of the most important results in all of the statistics. In this blog, we will take a glance at why CLT is so special and how it works out in practice. Intuitive examples will be used to explain the underlying concepts of CLT.

First, let us take a look at why CLT is so significant. Firstly, CLT affords us the flexibility of not knowing the underlying distribution of any data set provided if the sample is large enough. Secondly, it enables us to make “Large sample inference” about the population parameters such as its mean and standard deviation.

The obvious question anybody would be asking themselves is why it is useful not to know the underlying distribution of a given data set?

To put it simply in real life, often times than not the population size of anything will be unknown. Population size here refers to the entire collection of something, like the exact number of cars in Gurgaon, NCR at any given day. It would be very cumbersome and expensive to get a true estimate of the population size. If the population size is unknown its underlying distribution will be known too and so will be its standard deviation. Here, CLT is used to approximate the underlying unknown distribution to a normal distribution. In a nutshell, we don’t have to worry about knowing the size of the population or its distribution. If the sample sizes are large enough, i.e. – we have a lot of observed data, it takes the shape of a symmetric bell-shaped curve. 

Now let’s talk about what we mean by “Large sample inference”. Imagine slicing up the data into ‘n’ number of samples as below:

Now, each of these samples will have a mean of their own.

Therefore, effectively the mean of each sample is a random variable which follows the below distribution:

Imagine, plotting each of the sample mean on a line plot, and as “n”, i.e. the number of samples goes to infinity or a large number the distribution takes a perfect bell-shaped curve, i.e – it tends to a normal distribution.

Large sample inferences could be drawn about the population from the above distribution of x̅. Say, if you’d like to know the probability that any given sample mean will not exceed quantity or limit.

The Central Limit Theorem has vast application in statistics which makes analyzing very large quantities easy through a large enough sample. Some of these we will meet in the subsequent blogs.

Try this for yourself: Imagine the average number of cars transiting from Gurgaon in any given week is normally distributed with the following parameter . A study was conducted which observed weekly car transition through Gurgaon for 4 weeks. What is the probability that in the 5th week number of cars transiting through Gurgaon will not exceed 113,000?

If you liked this blog, then do please leave a comment or suggestions below.

About the Author: Nish Lau Bakshi is a professional data scientist with an actuarial background and a passion to use the power of statistics to tackle various pressing, daily life problems.

About the Institute: DexLab Analytics is a premier data analytics training institute headquartered in Gurgaon. The expert consultants working here craft the most industry-relevant courses for interested candidates. Our technology-driven classrooms enhance the learning experience.

 

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Upskill and Upgrade: The Mantra for Budding Data Scientists

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Upskill and Upgrade: The Mantra for Budding Data Scientists

Have the right skills? Then the hottest jobs of the millennium might be waiting for you! The job profiles of data analysts, data scientists, data managers and statisticians harbour great potentials.

However, the biggest challenge in today’s age lies in preparing novice graduates for Industry 4.0 jobs. Although no one has yet cleared which roles will cease to exist and which new roles will be created, the consultants have started advising students to imbibe necessary skills and up-skill in domains that are likely to influence and carve the future jobs. Becoming adaptive is the best way to sail high in the looming technology-dominated future.

Data Science and Future

In this context, data science has proved to be one of the most promising fields of technology and science that exhibits a wide gap between demand and supply yet an absolute imperative across disciplines. “Today there is no shortage of data or computing abilities but there is a shortage of workforce equipped with the right skill set that can interpret data and get valuable insights,” revealed James Abdey, assistant professorial lecturer Statistics, London School of Economics and Political Science (LSE).

He further added that data science is a multidisciplinary field – drawing collectives from Economics, Mathematics, Finance, Statistics and more.

As a matter of fact, anyone, who has the right skill and expertise, can become a data scientist. The required skills are analytical thinking, problem-solving and decision-making aptitude. “As everything becomes data-driven, acquiring analytical and statistical skill sets will soon be imperative for all students, including those pursuing Social Sciences or Liberal Arts and also for professionals,” said Jitin Chadha, founder and director, Indian School of Business and Finance (ISBF).

DexLab Analytics is one of the most prominent deep learning training institutes seated in the heart of Delhi. We offer state-of-the-art in-demand skill training courses to all the interested candidates.

The Challenges Ahead

The dearth of expert training faculty and obsolete curriculum acts as major roadblocks to the success of data science training. Such hindrances cause difficulty in preparing graduates for Industry 4.0. In this regard, Chiraag Mehta from ISBF shared that by increasing international collaborations and intensifying industry-academia connect, they can formulate an effective solution and bring forth the best practices to the classrooms. “With international collaborations, higher education institutes can bring in the latest curriculum while a deeper industry-academia connect including, guest lecturers from industry players and internships will help students relate the theory to real-world applications, ” shared Mehta during an interview with Education Times.

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Industry 4.0: A Brief Overview

The concept Industry 4.0 encompasses the potential of a new industrial revolution – where gathering and analyzing data across machines will become the order of the day. The rise of this new digital industrial revolution is expected to facilitate faster, more flexible and efficient processes to manufacture high-quality products at reduced costs – thus, increasing productivity, switch economies, stimulate industrial growth and reform workforce profile.

Want to know more about data science courses in Gurgaon? Feel free to reach us at DexLab Analytics.

 

The blog has been sourced from ― timesofindia.indiatimes.com/home/education/news/learn-to-upskill-and-be-adaptive/articleshow/68989949.cms

 

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Bayes’ Theorem: A Brief Explanation

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Bayes’ Theorem: A Brief Explanation

(This is in continuation of the previous blog, which was published on 22nd April, 2019 – www.dexlabanalytics.com/blog/a-beginners-guide-to-learning-data-science-fundamentals )

In this blog, we’ll try to get a hands-on understanding of the Bayes’ Theorem. While doing so, hopefully we’ll be able to grasp a basic understanding of concepts such as Prior odds ratio, Likelihood ratio and Posterior odds ratio.

Arguably, a lot of classification problems have their root in Bayes’ Theorem. Reverend T. Bayes came up with this superior logical function, which mathematically deducts the probability of an event occurring from a larger set by “flipping” the conditional probabilities.

 


 

Consider,  E1, E2, E3,……..En to be a partition a larger set “S” and now define an Event – A, such that A is a subset of S.

Let the square be the larger set “S” containing mutually exclusive events Ei’s.  Now, let the yellow ring passing through all Ei’s be an event – A.

Using conditional probabilities, we know,

Also, the relationship:

Law of total probability states:

Rearranging the values of  &  gives us the Bayes Theorem:

The values of  are also known as prior probabilities, the event A is some event, which is known to have occurred and the conditional probability   is known as the posterior probability.

Now that, you’ve got the maths behind it, it’s time to visualise its practical application. Bayesian thinking is a method of applying Bayes’ Theorem into a practical scenario to make sound judgements.

The next blog will be dedicated to Bayesian Thinking and its principles.

For now, imagine, there have been news headlines about builders snooping around houses they work in. You’ve got a builder in to work on something in your house. There is room for all sorts of bias to influence you into believing that the builder in your house is also an opportunistic thief.

However, if you were to apply Bayesian thinking, you can deduce that only a small fraction of the population are builders and of that population, a very tiny proportion is opportunistic thieves. Therefore, the probability of the builder in your house being an opportunistic thief is actually a product of the two proportions, which is indeed very-very small.

Technically speaking, we call the resulting posterior odds ratio as a product of prior odds ratio and likelihood ratio. More on applying Bayesian Thinking coming up in the next blog.

In the meantime try this exercise and leave your comments below in the comments section.

2

In the above example on “snooping builders”, what are your:

  • Ei’s
  • Event – A
  • “S”

About the Author: Nish Lau Bakshi is a professional data scientist with an actuarial background and a passion to use the power of statistics to tackle various pressing, daily life problems.

About the Institute: DexLab Analytics is a premier data analyst training institute in Gurgaon specializing in an enriching array of in-demand skill training courses for interested candidates. Skilled industry consultants craft state-of-the-art big data courses and excellent placement assistance ensures job guarantee.

For more from the tech series, stay tuned!

 

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