chapter 2

Question 1

what are 2 approaches to probability?

Answer 1

• Frequentist interpretation
• Bayesian interpretation

Question 2

describe the Frequentist interpretation.

Answer 2

• probabilities represent long run frequencies of events.
• For example: if we flip the coin many times, we expect it to land heads about half the time.

Question 3

describe the Bayesian interpretation.

Answer 3

• probability is used to quantify our uncertainty about something; hence it is fundamentally related to information rather than repeated trials.
• For example: if we flip the coin we believe the coin is equally likely to land heads or tails on the next toss.

Question 4

______ can be used to model uncertainty about events that do not have long term frequencies? give example.

Answer 4

• Bayesian interpretation
• For example, we might have received a specific email message, and want to compute the probability it is spam.

Question 5

how can we calculate union probability?

Answer 5

p(A ∨ B) = p(A) + p(B) − p(A ∧ B)

Question 6

how can we calculate joint probability?

Answer 6

• p(A ∧ B) = p(A|B) * p(B)
• p(A ∧ B) = p(B|A) * p(A)

Question 7

how can we calculate conditional probability?

Answer 7

• p(A|B) = p(A n B) / p(B) …. if p(B) > 0
• prob of a given b

Question 8

describe bayes Prior / state of nature?

Answer 8

• Is the probability of an event occurring before new data is collected, based on current knowledge
• reflect the prior knowledge of how likely we will get sth
• Priors are known before the training process
• The state of nature is a random variable P(wi).
• If there are only two classes, the sum of the priors is P(w1) + P(w2) = 1

Question 9

describe bayes Likelihood / Class conditional probabilities?

Answer 9

• It represents the probability of how likely a feature x occurs given that it belongs to the particular class, wi.
• It is denoted by, P(X|wi)
• It is the quantity that we have to evaluate while training the data.

Question 10

describe bayes Evidence

Answer 10

• It is the probability of occurrence of a particular feature i.e. P(X).
• We also figure out evidence values during training.

Question 11

how can we calculate evidence in Bayes theory?

Answer 11

using the chain rule as, P(X) = Σin P(X|wi)P(wi)

Question 12

describe Bayes Posterior Probabilities?

Answer 12

 It is the probability of occurrence of Class wi when certain Features are given P(wi|X)

 It is what we aim at computing in the test phase in which we have testing input [ features ] and we have to find how likely trained model can predict features belonging to the particular class wi.

Question 13

what should our predictions be in the case of:
1. P(ω1)»> P(ω2)
2. P(ω1)= P(ω2)
3. the probability of error

Answer 13

1. decision should favor of ω1
2. it is half probable for our prediction being right
3. the minimum of P(ω1) and P(ω2)