[PPT] - Game-changers: . Detecting shifts in the flow of campaign PowerPoint Presentation

SLIDE 1

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Game-changers:

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Detecting shifts in the flow of campaign contributions

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University of Rochester

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Matthew Blackwell

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APWG

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March 8th, 2013

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Why not polls?

. Lack of variation .1. . Cheap talk .

2.

. Data (un)availability .

3.

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Why not polls?

. Lack of variation .1. . Cheap talk .

2.

. Data (un)availability .

3.

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Why not polls?

. Lack of variation .1. . Cheap talk .

2.

. Data (un)availability .

3.

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Why not polls?

. Lack of variation .1. . Cheap talk .

2.

. Data (un)availability .

3.

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SLIDE 9

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A measurement question

. When do campaigns take off or fall flat? . When do campaign contributions take off or fall flat? . Tools: Bayesian nonparametric model for overdispersed count data.

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A measurement question

. When do campaigns take off or fall flat? . When do campaign contributions take off or fall flat? . Tools: Bayesian nonparametric model for overdispersed count data.

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A measurement question

. When do campaigns take off or fall flat? . When do campaign contributions take off or fall flat? . Tools: Bayesian nonparametric model for overdispersed count data.

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Why contributions?

. Lots of variation .1. . Costly participation .

2.

. Data availability .

3.

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Why contributions?

. Lots of variation .1. . Costly participation .

2.

. Data availability .

3.

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Why contributions?

. Lots of variation .1. . Costly participation .

2.

. Data availability .

3.

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Why contributions?

. Lots of variation .1. . Costly participation .

2.

. Data availability .

3.

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. . .

50

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100

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150

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200

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500

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1000

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1500

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2000

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Why changepoint models?

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The challenges

. Modeling daily contribution counts . Choosing the number of changepoints

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The challenges

. Modeling daily contribution counts . Choosing the number of changepoints

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Number of

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Contributions

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Apr 11

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Jul 11

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Oct 11

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Jan 12

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500

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1000

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1500

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2000

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2500

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Overdispersion in campaign contributions

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Bayesian model for overdispersed counts

. For observations 𝑢 in {1, … , 𝑈}: . [𝑧𝑢|𝜃𝑢, 𝛾, 𝜍, 𝑌] ∼ Poisson(𝜃𝑢𝜇𝑢) . (data) . 𝜇𝑢 = exp(𝑌𝑢𝛾) . (link function) . [𝜃𝑢|𝜍] ∼ Gamma(𝜍, 𝜍) . (random effect) . [𝑧𝑢|𝛾, 𝜍, 𝑌] ∼ NegBin(𝜍, 𝜍/(𝜍 + 𝜇𝑢)) . marginal distribution of 𝑧:

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Bayesian model for overdispersed counts

. For observations 𝑢 in {1, … , 𝑈}: . [𝑧𝑢|𝜃𝑢, 𝛾, 𝜍, 𝑌] ∼ Poisson(𝜃𝑢𝜇𝑢) . (data) . 𝜇𝑢 = exp(𝑌𝑢𝛾) . (link function) . [𝜃𝑢|𝜍] ∼ Gamma(𝜍, 𝜍) . (random effect) . [𝑧𝑢|𝛾, 𝜍, 𝑌] ∼ NegBin(𝜍, 𝜍/(𝜍 + 𝜇𝑢)) . marginal distribution of 𝑧:

SLIDE 22

.

Bayesian model for overdispersed counts

. For observations 𝑢 in {1, … , 𝑈}: . [𝑧𝑢|𝜃𝑢, 𝛾, 𝜍, 𝑌] ∼ Poisson(𝜃𝑢𝜇𝑢) . (data) . 𝜇𝑢 = exp(𝑌𝑢𝛾) . (link function) . [𝜃𝑢|𝜍] ∼ Gamma(𝜍, 𝜍) . (random effect) . [𝑧𝑢|𝛾, 𝜍, 𝑌] ∼ NegBin(𝜍, 𝜍/(𝜍 + 𝜇𝑢)) . marginal distribution of 𝑧:

SLIDE 23

.

Bayesian model for overdispersed counts

. For observations 𝑢 in {1, … , 𝑈}: . [𝑧𝑢|𝜃𝑢, 𝛾, 𝜍, 𝑌] ∼ Poisson(𝜃𝑢𝜇𝑢) . (data) . 𝜇𝑢 = exp(𝑌𝑢𝛾) . (link function) . [𝜃𝑢|𝜍] ∼ Gamma(𝜍, 𝜍) . (random effect) . [𝑧𝑢|𝛾, 𝜍, 𝑌] ∼ NegBin(𝜍, 𝜍/(𝜍 + 𝜇𝑢)) . marginal distribution of 𝑧:

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Generalize to a mixture model

. [𝑧𝑢|𝑡𝑢, 𝜃𝑢, 𝛾, 𝜍, 𝑌] ∼ Poisson(𝜃𝑢𝜇𝑢) . (data) . 𝑡𝑢 = 𝑙 . regimes . (1, … , 𝐿) . 𝜇𝑢 = exp(𝑌𝑢𝛾𝑙) . (link function) . [𝜃𝑢|𝜍, 𝑡𝑢] ∼ Gamma(𝜍𝑙, 𝜍𝑙) . (random effect) . Pr(𝑡𝑢+􏷡 = 𝑙 | 𝑡𝑢 = 𝑙) = 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑙 + 1 | 𝑡𝑢 = 𝑙) = 1 − 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑘 | 𝑡𝑢 = 𝑙) = 0 . (∀𝑘 ∉ {𝑙, 𝑙 + 1})

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Generalize to a mixture model

. [𝑧𝑢|𝑡𝑢, 𝜃𝑢, 𝛾, 𝜍, 𝑌] ∼ Poisson(𝜃𝑢𝜇𝑢) . (data) . 𝑡𝑢 = 𝑙 . regimes . (1, … , 𝐿) . 𝜇𝑢 = exp(𝑌𝑢𝛾𝑙) . (link function) . [𝜃𝑢|𝜍, 𝑡𝑢] ∼ Gamma(𝜍𝑙, 𝜍𝑙) . (random effect) . Pr(𝑡𝑢+􏷡 = 𝑙 | 𝑡𝑢 = 𝑙) = 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑙 + 1 | 𝑡𝑢 = 𝑙) = 1 − 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑘 | 𝑡𝑢 = 𝑙) = 0 . (∀𝑘 ∉ {𝑙, 𝑙 + 1})

SLIDE 26

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Generalize to a mixture model

. [𝑧𝑢|𝑡𝑢, 𝜃𝑢, 𝛾, 𝜍, 𝑌] ∼ Poisson(𝜃𝑢𝜇𝑢) . (data) . 𝑡𝑢 = 𝑙 . regimes . (1, … , 𝐿) . 𝜇𝑢 = exp(𝑌𝑢𝛾𝑙) . (link function) . [𝜃𝑢|𝜍, 𝑡𝑢] ∼ Gamma(𝜍𝑙, 𝜍𝑙) . (random effect) . Pr(𝑡𝑢+􏷡 = 𝑙 | 𝑡𝑢 = 𝑙) = 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑙 + 1 | 𝑡𝑢 = 𝑙) = 1 − 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑘 | 𝑡𝑢 = 𝑙) = 0 . (∀𝑘 ∉ {𝑙, 𝑙 + 1})

SLIDE 27

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Generalize to a mixture model

. [𝑧𝑢|𝑡𝑢, 𝜃𝑢, 𝛾, 𝜍, 𝑌] ∼ Poisson(𝜃𝑢𝜇𝑢) . (data) . 𝑡𝑢 = 𝑙 . regimes . (1, … , 𝐿) . 𝜇𝑢 = exp(𝑌𝑢𝛾𝑙) . (link function) . [𝜃𝑢|𝜍, 𝑡𝑢] ∼ Gamma(𝜍𝑙, 𝜍𝑙) . (random effect) . Pr(𝑡𝑢+􏷡 = 𝑙 | 𝑡𝑢 = 𝑙) = 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑙 + 1 | 𝑡𝑢 = 𝑙) = 1 − 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑘 | 𝑡𝑢 = 𝑙) = 0 . (∀𝑘 ∉ {𝑙, 𝑙 + 1})

SLIDE 28

.

Generalize to a mixture model

. [𝑧𝑢|𝑡𝑢, 𝜃𝑢, 𝛾, 𝜍, 𝑌] ∼ Poisson(𝜃𝑢𝜇𝑢) . (data) . 𝑡𝑢 = 𝑙 . regimes . (1, … , 𝐿) . 𝜇𝑢 = exp(𝑌𝑢𝛾𝑙) . (link function) . [𝜃𝑢|𝜍, 𝑡𝑢] ∼ Gamma(𝜍𝑙, 𝜍𝑙) . (random effect) . Pr(𝑡𝑢+􏷡 = 𝑙 | 𝑡𝑢 = 𝑙) = 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑙 + 1 | 𝑡𝑢 = 𝑙) = 1 − 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑘 | 𝑡𝑢 = 𝑙) = 0 . (∀𝑘 ∉ {𝑙, 𝑙 + 1})

SLIDE 29

.

Generalize to a mixture model

. [𝑧𝑢|𝑡𝑢, 𝜃𝑢, 𝛾, 𝜍, 𝑌] ∼ Poisson(𝜃𝑢𝜇𝑢) . (data) . 𝑡𝑢 = 𝑙 . regimes . (1, … , 𝐿) . 𝜇𝑢 = exp(𝑌𝑢𝛾𝑙) . (link function) . [𝜃𝑢|𝜍, 𝑡𝑢] ∼ Gamma(𝜍𝑙, 𝜍𝑙) . (random effect) . Pr(𝑡𝑢+􏷡 = 𝑙 | 𝑡𝑢 = 𝑙) = 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑙 + 1 | 𝑡𝑢 = 𝑙) = 1 − 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑘 | 𝑡𝑢 = 𝑙) = 0 . (∀𝑘 ∉ {𝑙, 𝑙 + 1})

SLIDE 30

.

Generalize to a mixture model

. [𝑧𝑢|𝑡𝑢, 𝜃𝑢, 𝛾, 𝜍, 𝑌] ∼ Poisson(𝜃𝑢𝜇𝑢) . (data) . 𝑡𝑢 = 𝑙 . regimes . (1, … , 𝐿) . 𝜇𝑢 = exp(𝑌𝑢𝛾𝑙) . (link function) . [𝜃𝑢|𝜍, 𝑡𝑢] ∼ Gamma(𝜍𝑙, 𝜍𝑙) . (random effect) . Pr(𝑡𝑢+􏷡 = 𝑙 | 𝑡𝑢 = 𝑙) = 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑙 + 1 | 𝑡𝑢 = 𝑙) = 1 − 𝑞𝑙 . Pr(𝑡𝑢+􏷡 = 𝑘 | 𝑡𝑢 = 𝑙) = 0 . (∀𝑘 ∉ {𝑙, 𝑙 + 1})

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.

Traditional changepoint models

. 1 . Regimes . 2 . 3 . 4 . (𝛾􏷡, 𝜍􏷡) . Regimes . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . (𝛾􏷤, 𝜍􏷤) . Units . 1 . 2 . 3 . 𝑞􏷡 . 1 − 𝑞􏷡 . changepoint . ⋯ . N . Must be in the last regime

SLIDE 32

.

Traditional changepoint models

. 1 . Regimes . 2 . 3 . 4 . (𝛾􏷡, 𝜍􏷡) . Regimes . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . (𝛾􏷤, 𝜍􏷤) . Units . 1 . 2 . 3 . 𝑞􏷡 . 1 − 𝑞􏷡 . changepoint . ⋯ . N . Must be in the last regime

SLIDE 33

.

Traditional changepoint models

. 1 . Regimes . 2 . 3 . 4 . (𝛾􏷡, 𝜍􏷡) . Regimes . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . (𝛾􏷤, 𝜍􏷤) . Units . 1 . 2 . 3 . 𝑞􏷡 . 1 − 𝑞􏷡 . changepoint . ⋯ . N . Must be in the last regime

SLIDE 34

.

Traditional changepoint models

. 1 . Regimes . 2 . 3 . 4 . (𝛾􏷡, 𝜍􏷡) . Regimes . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . (𝛾􏷤, 𝜍􏷤) . Units . 1 . 2 . 3 . 𝑞􏷡 . 1 − 𝑞􏷡 . changepoint . ⋯ . N . Must be in the last regime

SLIDE 35

.

Traditional changepoint models

. 1 . Regimes . 2 . 3 . 4 . (𝛾􏷡, 𝜍􏷡) . Regimes . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . (𝛾􏷤, 𝜍􏷤) . Units . 1 . 2 . 3 . 𝑞􏷡 . 1 − 𝑞􏷡 . changepoint . ⋯ . N . Must be in the last regime

SLIDE 36

.

Traditional changepoint models

. 1 . Regimes . 2 . 3 . 4 . (𝛾􏷡, 𝜍􏷡) . Regimes . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . (𝛾􏷤, 𝜍􏷤) . Units . 1 . 2 . 3 . 𝑞􏷡 . 1 − 𝑞􏷡 . changepoint . ⋯ . N . Must be in the last regime

SLIDE 37

.

Traditional changepoint models

. 1 . Regimes . 2 . 3 . 4 . (𝛾􏷡, 𝜍􏷡) . Regimes . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . (𝛾􏷤, 𝜍􏷤) . Units . 1 . 2 . 3 . 𝑞􏷡 . 1 − 𝑞􏷡 . changepoint . ⋯ . N . Must be in the last regime

SLIDE 38

.

Traditional changepoint models

. 1 . Regimes . 2 . 3 . 4 . (𝛾􏷡, 𝜍􏷡) . Regimes . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . (𝛾􏷤, 𝜍􏷤) . Units . 1 . 2 . 3 . 𝑞􏷡 . 1 − 𝑞􏷡 . changepoint . ⋯ . N . Must be in the last regime

SLIDE 39

.

Traditional changepoint models

. 1 . Regimes . 2 . 3 . 4 . (𝛾􏷡, 𝜍􏷡) . Regimes . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . (𝛾􏷤, 𝜍􏷤) . Units . 1 . 2 . 3 . 𝑞􏷡 . 1 − 𝑞􏷡 . changepoint . ⋯ . N . Must be in the last regime

SLIDE 40

.

Traditional changepoint models

. 1 . Regimes . 2 . 3 . 4 . (𝛾􏷡, 𝜍􏷡) . Regimes . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . (𝛾􏷤, 𝜍􏷤) . Units . 1 . 2 . 3 . 𝑞􏷡 . 1 − 𝑞􏷡 . changepoint . ⋯ . N . Must be in the last regime

SLIDE 41

.

Bayesian nonparametric priors

Model assumptions: 𝑧𝑢 ∼ 𝐻 i.i.d. from an unknown distribution

𝐻.

Parametric structure on our priors puts limitations on the

posterior inferences.

Bayesian nonparametrics: priors over distributions and, thus, an

infinite number of parameters.

SLIDE 42

.

Bayesian nonparametric priors

Model assumptions: 𝑧𝑢 ∼ 𝐻 i.i.d. from an unknown distribution

𝐻.

Parametric structure on our priors puts limitations on the

posterior inferences.

Bayesian nonparametrics: priors over distributions and, thus, an

infinite number of parameters.

SLIDE 43

.

Bayesian nonparametric priors

Model assumptions: 𝑧𝑢 ∼ 𝐻 i.i.d. from an unknown distribution

𝐻.

Parametric structure on our priors puts limitations on the

posterior inferences.

Bayesian nonparametrics: priors over distributions and, thus, an

infinite number of parameters.

SLIDE 44

.

Dirichlet process prior

. regimes: 𝑡𝑢 ∈ {1, … , ∞} . Pr(𝑡𝑢+􏷡 = 𝑙 | 𝑡𝑢 = 𝑙) =

𝑜𝑙 𝑢−􏷡+𝑐

. Pr(𝑡𝑢+􏷡 = 𝑙+1 | 𝑡𝑢 = 𝑙) =

𝑐 𝑢−􏷡+𝑐

Dirichlet process prior clusters units into a countably infinite set
f groups.
Obviously we only observe a finite number of these groups, but

the number is determined by the data and the prior, not exclusively from the prior.

SLIDE 45

.

Dirichlet process prior

. regimes: 𝑡𝑢 ∈ {1, … , ∞} . Pr(𝑡𝑢+􏷡 = 𝑙 | 𝑡𝑢 = 𝑙) =

𝑜𝑙 𝑢−􏷡+𝑐

. Pr(𝑡𝑢+􏷡 = 𝑙+1 | 𝑡𝑢 = 𝑙) =

𝑐 𝑢−􏷡+𝑐

Dirichlet process prior clusters units into a countably infinite set
f groups.
Obviously we only observe a finite number of these groups, but

the number is determined by the data and the prior, not exclusively from the prior.

SLIDE 46

.

Dirichlet process prior

. regimes: 𝑡𝑢 ∈ {1, … , ∞} . Pr(𝑡𝑢+􏷡 = 𝑙 | 𝑡𝑢 = 𝑙) =

𝑜𝑙 𝑢−􏷡+𝑐

. Pr(𝑡𝑢+􏷡 = 𝑙+1 | 𝑡𝑢 = 𝑙) =

𝑐 𝑢−􏷡+𝑐

Dirichlet process prior clusters units into a countably infinite set
f groups.
Obviously we only observe a finite number of these groups, but

the number is determined by the data and the prior, not exclusively from the prior.

SLIDE 47

.

Dirichlet process prior

. regimes: 𝑡𝑢 ∈ {1, … , ∞} . Pr(𝑡𝑢+􏷡 = 𝑙 | 𝑡𝑢 = 𝑙) =

𝑜𝑙 𝑢−􏷡+𝑐

. Pr(𝑡𝑢+􏷡 = 𝑙+1 | 𝑡𝑢 = 𝑙) =

𝑐 𝑢−􏷡+𝑐

Dirichlet process prior clusters units into a countably infinite set
f groups.
Obviously we only observe a finite number of these groups, but

the number is determined by the data and the prior, not exclusively from the prior.

SLIDE 48

.

Dirichlet process prior

. 1 . Regimes . (infinite) . 2 . 3 . ⋯ . ⋯ . ⋯ . (𝛾􏷡, 𝜍􏷡) . Regimes . (infinite) . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . ⋯ . ⋯ . ⋯ . Units . 1 . 2 . 3 .

𝑜􏷫/(𝑢 − 􏷡 + 𝑐)

.

𝑐/(𝑢 − 􏷡 + 𝑐)

. changepoint . ⋯ . N . (𝛾􏷡􏷠, 𝜍􏷡􏷠) . Number of regimes can vary

SLIDE 49

.

Dirichlet process prior

. 1 . Regimes . (infinite) . 2 . 3 . ⋯ . ⋯ . ⋯ . (𝛾􏷡, 𝜍􏷡) . Regimes . (infinite) . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . ⋯ . ⋯ . ⋯ . Units . 1 . 2 . 3 .

𝑜􏷫/(𝑢 − 􏷡 + 𝑐)

.

𝑐/(𝑢 − 􏷡 + 𝑐)

. changepoint . ⋯ . N . (𝛾􏷡􏷠, 𝜍􏷡􏷠) . Number of regimes can vary

SLIDE 50

.

Dirichlet process prior

. 1 . Regimes . (infinite) . 2 . 3 . ⋯ . ⋯ . ⋯ . (𝛾􏷡, 𝜍􏷡) . Regimes . (infinite) . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . ⋯ . ⋯ . ⋯ . Units . 1 . 2 . 3 .

𝑜􏷫/(𝑢 − 􏷡 + 𝑐)

.

𝑐/(𝑢 − 􏷡 + 𝑐)

. changepoint . ⋯ . N . (𝛾􏷡􏷠, 𝜍􏷡􏷠) . Number of regimes can vary

SLIDE 51

.

Dirichlet process prior

. 1 . Regimes . (infinite) . 2 . 3 . ⋯ . ⋯ . ⋯ . (𝛾􏷡, 𝜍􏷡) . Regimes . (infinite) . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . ⋯ . ⋯ . ⋯ . Units . 1 . 2 . 3 .

𝑜􏷫/(𝑢 − 􏷡 + 𝑐)

.

𝑐/(𝑢 − 􏷡 + 𝑐)

. changepoint . ⋯ . N . (𝛾􏷡􏷠, 𝜍􏷡􏷠) . Number of regimes can vary

SLIDE 52

.

Dirichlet process prior

. 1 . Regimes . (infinite) . 2 . 3 . ⋯ . ⋯ . ⋯ . (𝛾􏷡, 𝜍􏷡) . Regimes . (infinite) . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . ⋯ . ⋯ . ⋯ . Units . 1 . 2 . 3 .

𝑜􏷫/(𝑢 − 􏷡 + 𝑐)

.

𝑐/(𝑢 − 􏷡 + 𝑐)

. changepoint . ⋯ . N . (𝛾􏷡􏷠, 𝜍􏷡􏷠) . Number of regimes can vary

SLIDE 53

.

Dirichlet process prior

. 1 . Regimes . (infinite) . 2 . 3 . ⋯ . ⋯ . ⋯ . (𝛾􏷡, 𝜍􏷡) . Regimes . (infinite) . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . ⋯ . ⋯ . ⋯ . Units . 1 . 2 . 3 .

𝑜􏷫/(𝑢 − 􏷡 + 𝑐)

.

𝑐/(𝑢 − 􏷡 + 𝑐)

. changepoint . ⋯ . N . (𝛾􏷡􏷠, 𝜍􏷡􏷠) . Number of regimes can vary

SLIDE 54

.

Dirichlet process prior

. 1 . Regimes . (infinite) . 2 . 3 . ⋯ . ⋯ . ⋯ . (𝛾􏷡, 𝜍􏷡) . Regimes . (infinite) . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . ⋯ . ⋯ . ⋯ . Units . 1 . 2 . 3 .

𝑜􏷫/(𝑢 − 􏷡 + 𝑐)

.

𝑐/(𝑢 − 􏷡 + 𝑐)

. changepoint . ⋯ . N . (𝛾􏷡􏷠, 𝜍􏷡􏷠) . Number of regimes can vary

SLIDE 55

.

Dirichlet process prior

. 1 . Regimes . (infinite) . 2 . 3 . ⋯ . ⋯ . ⋯ . (𝛾􏷡, 𝜍􏷡) . Regimes . (infinite) . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . ⋯ . ⋯ . ⋯ . Units . 1 . 2 . 3 .

𝑜􏷫/(𝑢 − 􏷡 + 𝑐)

.

𝑐/(𝑢 − 􏷡 + 𝑐)

. changepoint . ⋯ . N . (𝛾􏷡􏷠, 𝜍􏷡􏷠) . Number of regimes can vary

SLIDE 56

.

Dirichlet process prior

. 1 . Regimes . (infinite) . 2 . 3 . ⋯ . ⋯ . ⋯ . (𝛾􏷡, 𝜍􏷡) . Regimes . (infinite) . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . ⋯ . ⋯ . ⋯ . Units . 1 . 2 . 3 .

𝑜􏷫/(𝑢 − 􏷡 + 𝑐)

.

𝑐/(𝑢 − 􏷡 + 𝑐)

. changepoint . ⋯ . N . (𝛾􏷡􏷠, 𝜍􏷡􏷠) . Number of regimes can vary

SLIDE 57

.

Dirichlet process prior

. 1 . Regimes . (infinite) . 2 . 3 . ⋯ . ⋯ . ⋯ . (𝛾􏷡, 𝜍􏷡) . Regimes . (infinite) . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . ⋯ . ⋯ . ⋯ . Units . 1 . 2 . 3 .

𝑜􏷫/(𝑢 − 􏷡 + 𝑐)

.

𝑐/(𝑢 − 􏷡 + 𝑐)

. changepoint . ⋯ . N . (𝛾􏷡􏷠, 𝜍􏷡􏷠) . Number of regimes can vary

SLIDE 58

.

Dirichlet process prior

. 1 . Regimes . (infinite) . 2 . 3 . ⋯ . ⋯ . ⋯ . (𝛾􏷡, 𝜍􏷡) . Regimes . (infinite) . (𝛾􏷢, 𝜍􏷢) . (𝛾􏷣, 𝜍􏷣) . ⋯ . ⋯ . ⋯ . Units . 1 . 2 . 3 .

𝑜􏷫/(𝑢 − 􏷡 + 𝑐)

.

𝑐/(𝑢 − 􏷡 + 𝑐)

. changepoint . ⋯ . N . (𝛾􏷡􏷠, 𝜍􏷡􏷠) . Number of regimes can vary

SLIDE 59

.

Your lunch is never free

DPP has a rich-get-richer property:

Pr(𝑡𝑢+􏷡 = 𝑙 | 𝑡𝑢 = 𝑙) = 𝑜𝑙 𝑢 − 1 + 𝑐

No free lunch theorem: All nonparametric priors place

assumptions on the clustering algorithm and no algorithm is

ptimal across the space of all problems.

SLIDE 60

.

Your lunch is never free

DPP has a rich-get-richer property:

Pr(𝑡𝑢+􏷡 = 𝑙 | 𝑡𝑢 = 𝑙) = 𝑜𝑙 𝑢 − 1 + 𝑐

No free lunch theorem: All nonparametric priors place

assumptions on the clustering algorithm and no algorithm is

ptimal across the space of all problems.

SLIDE 61

.

Monte Carlo evidence

.

Probability of

.

Changepoint

. Negative Binomial . .

50

.

100

.

150

.

200

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

1.0

.

Monte Carlo evidence

SLIDE 62

. .

Monte Carlo evidence

.

. .

Probability of

.

Changepoint

. Negative Binomial . .

50

.

100

.

150

.

200

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

1.0

.

Monte Carlo evidence

SLIDE 63

.

. .

Probability of

.

Changepoint

. Negative Binomial . .

50

.

100

.

150

.

200

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

1.0

.

Probability of

.

Changepoint

. Poisson . .

50

.

100

.

150

.

200

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

1.0

.

Monte Carlo evidence

SLIDE 64

.

SLIDE 65

.

The rise and fall of Herman Cain

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

Suspends candidacy

SLIDE 66

.

The rise and fall of Herman Cain

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

Suspends candidacy

SLIDE 67

.

The rise and fall of Herman Cain

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

Suspends candidacy

SLIDE 68

.

The rise and fall of Herman Cain

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

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Apr 11

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Jul 11

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Oct 11

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Jan 12

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100

.

200

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300

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400

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500

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Fox News Debate

.

Announces candidacy

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

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0.4

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0.6

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0.8

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Number of

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Contributions

.

Jan 11

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Apr 11

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Jul 11

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Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

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0.4

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0.6

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0.8

.

Number of

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Contributions

.

Jan 11

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Apr 11

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Jul 11

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Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

.

0.8

.

Number of

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Contributions

.

Jan 11

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Apr 11

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Jul 11

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Oct 11

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Jan 12

. .

100

.

200

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300

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400

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500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

Suspends candidacy

SLIDE 69

.

The rise and fall of Herman Cain

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

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0.4

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0.6

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0.8

.

Number of

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Contributions

.

Jan 11

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Apr 11

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Jul 11

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Oct 11

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Jan 12

. .

100

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200

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400

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500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

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0.4

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0.8

.

Number of

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Contributions

.

Jan 11

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Apr 11

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Jul 11

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Oct 11

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Jan 12

. .

100

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200

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400

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500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

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Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

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0.4

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.

Number of

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Contributions

.

Jan 11

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Apr 11

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Jul 11

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Oct 11

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Jan 12

. .

100

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200

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500

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. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

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0.4

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.

Number of

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Contributions

.

Jan 11

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Apr 11

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Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

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500

.

Fox News Debate

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

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0.8

.

Number of

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Contributions

.

Jan 11

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Apr 11

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Jul 11

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Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

Announces candidacy

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

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0.8

.

Number of

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Contributions

.

Jan 11

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Apr 11

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Jul 11

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Oct 11

.

Jan 12

. .

100

.

200

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300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

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Contributions

.

Jan 11

.

Apr 11

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Jul 11

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Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

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Apr 11

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Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

Suspends candidacy

SLIDE 70

.

The rise and fall of Herman Cain

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

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0.4

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0.6

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0.8

.

Number of

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Contributions

.

Jan 11

.

Apr 11

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Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

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500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

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0.8

.

Number of

.

Contributions

.

Jan 11

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Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

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500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

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0.8

.

Number of

.

Contributions

.

Jan 11

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Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

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500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

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Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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Number of

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Contributions

.

Jan 11

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Apr 11

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Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

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500

.

Fox News Debate

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

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0.8

.

Number of

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Contributions

.

Jan 11

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Apr 11

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Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

Announces candidacy

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

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0.4

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0.6

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0.8

.

Number of

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Contributions

.

Jan 11

.

Apr 11

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Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

Suspends candidacy

SLIDE 71

.

The rise and fall of Herman Cain

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

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Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

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0.4

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0.6

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Number of

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Contributions

.

Jan 11

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Apr 11

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Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

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500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

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0.8

.

Number of

.

Contributions

.

Jan 11

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Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

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500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

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0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

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500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

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0.8

.

Number of

.

Contributions

.

Jan 11

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Apr 11

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Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

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400

.

500

.

Fox News Debate

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

Announces candidacy

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

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Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

Suspends candidacy

SLIDE 72

.

The rise and fall of Herman Cain

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

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0.4

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0.6

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0.8

.

Number of

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Contributions

.

Jan 11

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Apr 11

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Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

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500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

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Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

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Apr 11

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Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

.

0.8

.

Number of

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Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

Announces candidacy

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

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0.8

.

Number of

.

Contributions

.

Jan 11

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Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

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Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

Suspends candidacy

SLIDE 73

.

The rise and fall of Herman Cain

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

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Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

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500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

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0.6

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0.8

.

Number of

.

Contributions

.

Jan 11

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Apr 11

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Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

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300

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400

.

500

.

Fox News Debate

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

. .

Probability of

.

Changepoint

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

.

0.0

.

0.2

.

0.4

.

0.6

.

0.8

.

Number of

.

Contributions

.

Jan 11

.

Apr 11

.

Jul 11

.

Oct 11

.

Jan 12

. .

100

.

200

.

300

.

400

.

500

.

Fox News Debate

.

Announces candidacy

.

Wins FL straw poll

.

Misconduct allegations

.

Suspends candidacy

SLIDE 74

.

. .

Jan 07

.

Apr 07

.

Jul 07

.

Oct 07

.

Jan 08

.

Apr 08

.

Jul 08

.

Oct 08

.

Negative

.

Changepoint

.

Positive

.

Changepoint

.

All Senate changepoints

SLIDE 75

.

. . .

500

.

1000

.

1500

.

0.0

.

0.1

.

0.2

.

0.3

.

0.4

.

0.5

.

Probability of

.

Changepoint

.

Number of Frontrunner words on campaign

.

More attention around changepoints

SLIDE 76

.

The path forward.

. Run on all (digitzed) Congressional races to find more sys- tematic variation. .1. . Compare changepoints for time-series of different types of voters, PACs. .

2.

. Generalize the Bayesian nonparametric approach beyond count data. .

3.

SLIDE 77

.

The path forward.

. Run on all (digitzed) Congressional races to find more sys- tematic variation. .1. . Compare changepoints for time-series of different types of voters, PACs. .

2.

. Generalize the Bayesian nonparametric approach beyond count data. .

3.

SLIDE 78

.

The path forward.

. Run on all (digitzed) Congressional races to find more sys- tematic variation. .1. . Compare changepoints for time-series of different types of voters, PACs. .

2.

. Generalize the Bayesian nonparametric approach beyond count data. .

3.

SLIDE 79

.

The path forward.

. Run on all (digitzed) Congressional races to find more sys- tematic variation. .1. . Compare changepoints for time-series of different types of voters, PACs. .

2.

. Generalize the Bayesian nonparametric approach beyond count data. .