by | May 6, 2019 | Data Analytics

One of the most useful discoveries in the probability and statistics is the Bayesian statistics. The development of this decision theory has immensely increased the power of decision-making and solved many issues faced with frequentist statistics.

The Bayes theorem of Bayesian Statistics often goes by different names such as posterior statistics, inverse probability, or revised probability.

Although the development of Bayesian method has divided data scientists in two group – Bayesians and frequentists but the importance of Bayes theorem are unmatched. In some uncertain instances, it’s not possible to come to a conclusion without Bayesian.

Hence, if you are looking forward to becoming a data scientist, machine learning engineer, or data engineer, Bayesian statistics is an important concept to learn. Knowing what is Bayesian statistics, how it works, and all the essential aspects of the topic are the key to clearing the interview process. Date: 5th Oct, 2020 (Saturday)
Time: 10:30 AM - 11:30 AM (IST/GMT +5:30)
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Therefore, we’ve created a simple guide containing crucial interview questions based on Bayes theorem. Briefly study these questions and answers to perform well in your machine-learning interview.

## Bayesian Statistics Interview Questions and Answers

### 1. Explain the introduction to Bayesian Statistics And Bayes Theorem?

It calculates the degree of belief in a certain event and gives a probability of the occurrence of some statistical problem.

Let’s consider an example:

Suppose, from 4 basketball matches, John won 3 and Harry won only one.

Now, if you have to bet on either John or Harry. So, what would you do?

The answer is obvious – John.

But, let’s add another factor to the match, which is rain. When Harry won, it was raining. But, when John won, out of 3 matches, 1 time it was raining.

If the weather forecast says that there is an extremely high possibility of rain on the day of the next match. So, who would you bet on?

Even without using it, you can tell that the comparison basis has changed and chances of Harry winning have increased.

That is where Bayesian statistics PDF helps. Hence, the exact probability can be calculated with Bayes theorem.

#### Introduction to Bayes Theorem Bayes Theorem Source Wikipedia

The Bayes theorem is:

P (A/B) = P(B/A)P(A) / P(B)

Considering the above example, here’s what the values are:

•        P(A) = ¼, Harry won one out of 4 matches.
•        P(B) = ½, it rained two times out of 4 match days.
•        P(B/A) = 1, when Harry won it was raining.

Placing the values in the formula, the chances of Harry winning will become 50%, which was only 25% earlier.

### 2. Explain The Bayes’ Box

The Bayes’ box is a method of representing and solving probability through Bayes theorem.

 Hypothesis Prior Likelihood Likelihood x Prior Posterior A 0.75 1 0.75 0.857 B 0.25 0.5 0.125 0.143 Total 0.875 1

The prior probabilities are assumed values without additional factors.

The likelihood is nothing but the probability of A and B.

The posterior probabilities are results after considering added information. (For instance, rain in the above example). Bayesian Statistics PDF is a good resource to understand this concept with thorough details.

### 3. Which Is Better Bayesian Or Frequentist Statistics?

It shows a degree of belief, which means that it reflects our everyday knowledge of probability. When a person, who doesn’t know either frequentist or Bayesian, thinks of probability, then it will be Bayesian. These statistics give a value to your belief.

Frequentists only find the probability of events or observations like a 50% probability of tails in a coin toss.

Answering how much is the probability of a certain coin showing tails is not possible in frequentists. It will automatically assume prior values to be 0.5 in this case.

### 4. How Bayesian Statistics Is Related To Machine Learning? Bayesian Inference

Machine learning simply tries to predict something about a certain system based on data available. But Bayesian statistics, on the other hand, is the degree of belief.

Bayesian machine learning is useful when there are fewer data available. So, using this method, it is predicted what the model will look like based on prior knowledge.

For instance, predicting whether a coin will land on tails lead to uncertainty. The scope of the answer will be limited. If you flip this coin 100 times and receive 50 tails and 50 heads, then you can say the probability is 50%. But, what if the result is 70 times tails and 30 times heads?

We all know the probability of heads and tails while flipping a coin is 50-50. With less data, you have the chances of landing on an incorrect conclusion. Date: 5th Oct, 2020 (Saturday)
Time: 10:30 AM - 11:30 AM (IST/GMT +5:30)
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Using Bayesian inference, will lead to an answer, which says, “If the coin is not biased, the probability is 70-30.” Hence, Bayesian induces uncertainty in answer to make it more relevant.

### 5. Explain Naive Bayes Classifier Naive Bayes Classifier Source Wikipedia

There are three naïve Bayes classifiers:

1. The Multinomial classifier uses multinomial distribution on each word of a sentence. Every word is treated independently rather than being treated as a part of the sentence.
2. The Gaussian classifier is utilized with continuous data. It assumes that each data class is distributed as a Gaussian distribution.
3. The Bernoulli classifier assumes that every feature present is binary, which means it can only take either of the two values.

### 6. Explain The Strength Of Bayesian Statistics

It is sometimes preferred over other methods, here’s why:

1. Bayesian gives intuitive and direct inferences. It meaningfully tells the probability of a hypothesis being true.
2. Introduction to Bayesian statistics enhanced the power of answering complicated questions easily and clearly.
3. Bayesian uses every available information to find the probability. This indicates that apart from data, the method uses prior information as well.
4. The method enhances decision-making. When there is a lack of parameters and facts, Bayesian quantify uncertainties using available evidence.

### 7. Do You Think That Bayesian Statistics Has The Power To Replace Frequentists?

Both frequentists and Bayesian statistics have specific applications, which is why these methods are used frequently. For instance, if you can solve a certain problem with both Bayesian and frequentists, use the one that does it simply.

Suppose, when you have to solve huge problems that have streaming data, Bayesian will only give an approximation.

### 8. Explain The Difference Between Maximum Likelihood Estimation (MLE) And Bayesian Statistics Maximum Likelihood Estimation

Suppose, you tossed a coin 10 times, the result was 7 heads and 3 tails. This means that the probability of getting a “head” is 70% and “tail” is 30% in the 11th toss. This is one of the many possible arrangements and related estimation. The method is called maximum likelihood estimation.

Now, since we know that the possibility of heads and tails is 50%, we can consider this prior information. Then, calculate what will be the outcome in the 11th toss. This method is Bayesian statistics.

Bayesian Statistics PDF can provide you with detailed information on this.

### 9. What Are Some Unique Applications Of Bayesian Statistics And Bayes Theorem?

There are various unique applications of it and Bayes theorem. Here are some of these:

1. It can be used to decide whether a project will finish on time or not? There are only two possible outcomes, either it will finish on/before time or it will not.
2. Using multiple blood samples to decide diseases.
3. Utilizing it as a spam filter considering previous patterns.
4. It is used to detect whether a certain water body is fit for various purposes such as drinking, agriculture, etc. Since, due to the presence of various pollutants, it is not possible to give an exact quantifier, the Bayesian method is used.

### 10. Why Bayesian Statistics Is Important?

It is fundamentally sound and at some times, highly useful.

In addition, it uses the rigid format of the likelihood of the outcome and prior knowledge of a possible situation. Then, the posterior probability is calculated. This rigid nature of the method sometimes helps in solving complex models.

In addition, it is really essential in some instances because it quantifies a degree of belief. Hence, it can quantify and find the probability of if a certain belief is true or not. If we look at frequentist statistics, it can only quantify events and not a hypothesis.

### 11. Explain The Difference Between Bayes Theorem And Conditional Probability Bayes Theorem And Conditional Probability Source Wikimedia

Conditional probability finds the probability of an event A in accordance with the occurrence of other event B. It is represented as:

P(A|B) = P(A∩B)/P(B)

P(A∩B) is the probability of both A and B occurring at the same time.

P(A/B) is the probability of occurrence of A when B has already occurred.

For example, you went to the market to buy cheese and butter. We know P(Cheese ∩ Butter) is 0.3, P(Cheese) is 0.4, and P(Butter) is 0.6.

P( Cheese/Butter) = 1/2

P(Butter/ Cheese) = 3/4

Bayes theorem is actually an extension of conditional probability. It is represented as:

P(A|B) = P(B|A) * P(A)/P(B)

Here, The conditional probability answers the probability of occurrence of A when B has already occurred. In that case, the Bayes theorem answers using prior beliefs and comes to a posterior conclusion.

### 12. Explain The Inconsistencies In Bayesian Inference

There are various loopholes in Bayesian inference:

• In most real-world examples, obtaining the prior probability is often hard.
• When both prior and likelihood become too complicated, MCMC (Markov chain Monte Carlo) sampling is used. This is extremely slow in real instances.
• In order to quantify the prior knowledge, the user can influence the result, unknowingly or knowingly.

## Conclusion Date: 5th Oct, 2020 (Saturday)
Time: 10:30 AM - 11:30 AM (IST/GMT +5:30)
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Questions related to what is Bayesian statistics can come up in various technical interviews. In conclusion, whether you are going for the interview of a data scientist or engineer, you should be well acquainted with the topic.

Hence, thoroughly understand the above aspects of introduction to Bayesian Statistics. Learn more about – what is Bayesian statistics, Bayes theorems, and frequentist statistics, brush up your knowledge and hence prepare to excel in your interview.

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