What type of probability is the probability that an email which contains the word Viagra is spam?

For example, if an email contains the word Viagra, we classify it as spam. If on the other hand, an email contains the word money, then there's an 80% chance that it's spam. According to Bayes Theorem, the probability that an email is spam given that it contains “word”.

Which method is used for calculating the probability that a certain email is spam?

With Bayes' Rule, we want to find the probability an email is spam, given it contains certain words. We do this by finding the probability that each word in the email is spam, and then multiply these probabilities together to get the overall email spam metric to be used in classification.

What is the symbolic notation of conditional probability?

This revised probability that an event A has occurred, considering the additional information that another event B has definitely occurred on this trial of the experiment, is called the conditional probability of A given B and is denoted by P(A|B).

What type of probability is Bayes Theorem?

Bayes' Theorem, named after 18th-century British mathematician Thomas Bayes, is a mathematical formula for determining conditional probability. Conditional probability is the likelihood of an outcome occurring, based on a previous outcome having occurred in similar circumstances.

What is naive Bayes assumption How does it help explain with an example?

In simple terms, a Naive Bayes classifier assumes that the presence of a particular feature in a class is unrelated to the presence of any other feature. For example, a fruit may be considered to be an apple if it is red, round, and about 3 inches in diameter.

2 Joint Conditional Probability Part 1 Dot Product

What is posterior probability in Naive Bayes?

What Is a Posterior Probability? A posterior probability, in Bayesian statistics, is the revised or updated probability of an event occurring after taking into consideration new information. The posterior probability is calculated by updating the prior probability using Bayes' theorem.

Is Naive Bayes probabilistic?

A Naive Bayes classifier is a probabilistic machine learning model that's used for classification task. The crux of the classifier is based on the Bayes theorem.

What does unconditional probability mean?

An unconditional probability is the chance that a single outcome results among several possible outcomes. The term refers to the likelihood that an event will take place irrespective of whether any other events have taken place or any other conditions are present.

What is conditional probability in naïve Bayes Theorem?

The conditional probability is the probability of one event given the occurrence of another event, often described in terms of events A and B from two dependent random variables e.g. X and Y.

What is dependent probability?

Dependent events in probability means events whose occurrence of one affect the probability of occurrence of the other. For example suppose a bag has 3 red and 6 green balls. Two balls are drawn from the bag one after the other.

What is conditional probability?

Conditional probability is known as the possibility of an event or outcome happening, based on the existence of a previous event or outcome. It is calculated by multiplying the probability of the preceding event by the renewed probability of the succeeding, or conditional, event.

What is a complement probability?

Two events are said to be complementary when one event occurs if and only if the other does not. The probabilities of two complimentary events add up to 1. For example, rolling a 5 or greater and rolling a 4 or less on a die are complementary events, because a roll is 5 or greater if and only if it is not 4 or less.

How do you do conditional probability?

The formula for conditional probability is derived from the probability multiplication rule, P(A and B) = P(A)*P(B|A). You may also see this rule as P(A∪B). The Union symbol (∪) means “and”, as in event A happening and event B happening.

What is the probability that a message is spam given that it contains the word free?

Expert-verified answer

3.57% of all messages contain the word “free” and are marked as spam. To Find: the probability that a message contains the word “free”, given that it is spam.

What is Bayes spam probability?

Bayesian spam filtering is based on Bayes rule, a statistical theorem that gives you the probability of an event. In Bayesian filtering it is used to give you the probability that a certain email is spam.

What Gaussian Naive Bayes?

Gaussian Naive Bayes supports continuous valued features and models each as conforming to a Gaussian (normal) distribution. An approach to create a simple model is to assume that the data is described by a Gaussian distribution with no co-variance (independent dimensions) between dimensions.

What is Bayes Theorem example?

Bayes theorem is also known as the formula for the probability of “causes”. For example: if we have to calculate the probability of taking a blue ball from the second bag out of three different bags of balls, where each bag contains three different colour balls viz. red, blue, black.

What is hypothesis in Bayes Theorem?

Bayes' Theorem relates the "direct" probability of a hypothesis conditional on a given body of data, P_E(H), to the "inverse" probability of the data conditional on the hypothesis, P_H(E).

Is conditional probability independent or dependent?

Conditional probability can involve both dependent and independent events. If the events are dependent, then the first event will influence the second event, such as pulling two aces out of a deck of cards. A dependent event is when one event influences the outcome of another event in a probability scenario.

What is marginal probability with example?

Marginal probability: the probability of an event occurring (p(A)), it may be thought of as an unconditional probability. It is not conditioned on another event. Example: the probability that a card drawn is red (p(red) = 0.5). Another example: the probability that a card drawn is a 4 (p(four)=1/13).

What is conditional vs unconditional probability?

Unconditional probability refers to a probability that is unaffected by previous or future events. The unconditional probability of event “A” is denoted as P(A). A conditional probability, contrasted to an unconditional probability, is the probability of an event that would be affected by another event.

What is conditional and unconditional?

A conditional offer means you still need to meet the requirements – usually exam results. An unconditional offer means you've got a place, although there might still be a few things to arrange.

Why Naive Bayes is called naïve?

Naive Bayes is called naive because it assumes that each input variable is independent. This is a strong assumption and unrealistic for real data; however, the technique is very effective on a large range of complex problems.

What do naïve and Bayes stand for?

A naive Bayes classifier is an algorithm that uses Bayes' theorem to classify objects. Naive Bayes classifiers assume strong, or naive, independence between attributes of data points. Popular uses of naive Bayes classifiers include spam filters, text analysis and medical diagnosis.

What is meant by Naive Bayes?

Naïve Bayes is a simple learning algorithm that utilizes Bayes rule together with a strong assumption that the attributes are conditionally independent, given the class. While this independence assumption is often violated in practice, naïve Bayes nonetheless often delivers competitive classification accuracy.