Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI...

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Lecture 2: probability concepts II.

Transcript of Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI...

Page 1: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Lecture 2: probability concepts II.

Page 2: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Kolmogorov: axioms of probability theory and the Bayesian viewpoint

Page 3: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

(Ω, F, P) probability space:

• sample space Ω (set of all possible outcomes)• set of events F • each event is a subset of Ω containing zero or more outcomes• probability measure P: probability of some event A is P(A)

union of mutually exclusive

Kolmogorov probability concept

(satisfied by frequentist definition of probabilities)

disjoint

Page 4: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Kolmogorov probability concept

Page 5: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Kolmogorov probability concept

A or B A and B

http://www.math.uah.edu/stat/

Venn diagrams at web site ofProbability, Mathematical Statistics, Stochastic Processes:

Page 6: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Kolmogorov probability concept

Page 7: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Kolmogorov probability concept

Page 8: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Kolmogorov probability concept

Page 9: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Kolmogorov probability concept

Page 10: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Kolmogorov probability concept

Page 11: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Kolmogorov probability concept

Page 12: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Bayes’ theorem

Page 13: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

?

Bayes’ theorem

Page 14: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Bayes’ theorem

Page 15: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Bayes’ theorem

Page 16: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Bayes’ theorem

Page 17: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Bayes’ theorem

Page 18: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually

Bayes’ theorem


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Card Motor New - SMC ETech · Maximum pushing force P hi 6 N ... Component supply to tape Workpiece alignment ... Time while pushing force is applied Time 5nC 20nC 40nC

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, J. X. Prochaska , N. H. P. Rhodin , , T. Zafar arXiv:1711.00407v1 … · 2018-10-09 · Cooke et al. 2010; Zafar et al. 2011). Mapping of the HI 21cm ab-sorptionagainst the extended

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PageRank. s1s1 p 12 p 21 s2s2 s3s3 p 31 s4s4 p 41 p 34 p 42 p 13 x 1 = p 21 p 34 p 41 + p 34 p 42 p 21 + p 21 p 31 p 41 + p 31 p 42 p 21 / Σ x 2 = p 31.

PageRank. s1s1 p 12 p 21 s2s2 s3s3 p 31 s4s4 p 41 p 34 p 42 p 13 x 1 = p 21 p 34 p 41 + p 34 p 42 p 21 + p 21 p 31 p 41 + p 31 p 42 p 21 / Σ x 2 = p 31.

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