. Game-changers: . Detecting shifts in the flow of campaign contributions . University of Rochester . Matthew Blackwell . APWG . March 8th, 2013
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. Why not polls? . Lack of variation . 1. . Cheap talk . 2. . Data (un)availability . 3.
. Why not polls? . Lack of variation . 1. . Cheap talk . 2. . Data (un)availability . 3.
. Why not polls? . Lack of variation . 1. . Cheap talk . 2. . Data (un)availability . 3.
. Why not polls? . Lack of variation . 1. . Cheap talk . 2. . Data (un)availability . 3.
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When do campaign contributions take off or fall flat? . A measurement question . When do campaigns take off or fall flat? . . Tools: Bayesian nonparametric model for overdispersed count data.
. A measurement question . When do campaigns take off or fall flat? . . Tools: Bayesian nonparametric model for overdispersed count data. When do campaign contributions take off or fall flat?
. A measurement question . When do campaigns take off or fall flat? . . Tools: Bayesian nonparametric model for overdispersed count data. When do campaign contributions take off or fall flat?
. Why contributions? . Lots of variation . 1. . Costly participation . 2. . Data availability . 3.
. Why contributions? . Lots of variation . 1. . Costly participation . 2. . Data availability . 3.
. Why contributions? . Lots of variation . 1. . Costly participation . 2. . Data availability . 3.
. Why contributions? . Lots of variation . 1. . Costly participation . 2. . Data availability . 3.
. 0 . 2000 . 1500 . 1000 . 500 . . . 200 . 150 . 100 . 50 . 0 . Why changepoint models?
. The challenges . Modeling daily contribution counts . Choosing the number of changepoints
. The challenges . Modeling daily contribution counts . Choosing the number of changepoints
. 0 . 2500 . 2000 . 1500 . 1000 . 500 . . . Jan 12 . Oct 11 . Jul 11 . Apr 11 . Contributions . Number of . Overdispersion in campaign contributions
π π’ = exp (π π’ πΎ) . (link function) . [π§ π’ |πΎ, π, π] βΌ NegBin (π, π/(π + π π’ )) . (random effect) . [π π’ |π] βΌ Gamma (π, π) . . Bayesian model for overdispersed counts . (data) . [π§ π’ |π π’ , πΎ, π, π] βΌ Poisson (π π’ π π’ ) . For observations π’ in {1, β¦ , π} : . marginal distribution of π§ :
. (link function) . [π§ π’ |πΎ, π, π] βΌ NegBin (π, π/(π + π π’ )) . (random effect) . [π π’ |π] βΌ Gamma (π, π) . . Bayesian model for overdispersed counts . (data) . [π§ π’ |π π’ , πΎ, π, π] βΌ Poisson (π π’ π π’ ) . For observations π’ in {1, β¦ , π} : . marginal distribution of π§ : π π’ = exp (π π’ πΎ)
. (link function) . [π§ π’ |πΎ, π, π] βΌ NegBin (π, π/(π + π π’ )) . (random effect) . [π π’ |π] βΌ Gamma (π, π) . . Bayesian model for overdispersed counts . (data) . [π§ π’ |π π’ , πΎ, π, π] βΌ Poisson (π π’ π π’ ) . For observations π’ in {1, β¦ , π} : . marginal distribution of π§ : π π’ = exp (π π’ πΎ)
. (link function) . [π§ π’ |πΎ, π, π] βΌ NegBin (π, π/(π + π π’ )) . (random effect) . [π π’ |π] βΌ Gamma (π, π) . . Bayesian model for overdispersed counts . (data) . [π§ π’ |π π’ , πΎ, π, π] βΌ Poisson (π π’ π π’ ) . For observations π’ in {1, β¦ , π} : . marginal distribution of π§ : π π’ = exp (π π’ πΎ)
π π’ = exp (π π’ πΎ π ) π‘ π’ = π Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = π π Pr(π‘ π’+τ·‘ = π + 1 | π‘ π’ = π) = 1 β π π Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = 0 . . . . . . (random effect) . [π π’ |π, π‘ π’ ] βΌ Gamma (π π , π π ) . (link function) Generalize to a mixture model . (1, β¦ , πΏ) . regimes . . (data) . [π§ π’ |π‘ π’ , π π’ , πΎ, π, π] βΌ Poisson (π π’ π π’ ) . ( βπ β {π, π + 1} )
π π’ = exp (π π’ πΎ π ) Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = π π Pr(π‘ π’+τ·‘ = π + 1 | π‘ π’ = π) = 1 β π π Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = 0 . (link function) . . . . (random effect) . [π π’ |π, π‘ π’ ] βΌ Gamma (π π , π π ) . . Generalize to a mixture model . (1, β¦ , πΏ) . regimes . . (data) . [π§ π’ |π‘ π’ , π π’ , πΎ, π, π] βΌ Poisson (π π’ π π’ ) . ( βπ β {π, π + 1} ) π‘ π’ = π
Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = π π Pr(π‘ π’+τ·‘ = π + 1 | π‘ π’ = π) = 1 β π π Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = 0 . (link function) . . . . (random effect) . [π π’ |π, π‘ π’ ] βΌ Gamma (π π , π π ) . . Generalize to a mixture model . (1, β¦ , πΏ) . regimes . . (data) . [π§ π’ |π‘ π’ , π π’ , πΎ, π, π] βΌ Poisson (π π’ π π’ ) . ( βπ β {π, π + 1} ) π π’ = exp (π π’ πΎ π ) π‘ π’ = π
Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = π π Pr(π‘ π’+τ·‘ = π + 1 | π‘ π’ = π) = 1 β π π Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = 0 . (link function) . . . . (random effect) . [π π’ |π, π‘ π’ ] βΌ Gamma (π π , π π ) . . Generalize to a mixture model . (1, β¦ , πΏ) . regimes . . (data) . [π§ π’ |π‘ π’ , π π’ , πΎ, π, π] βΌ Poisson (π π’ π π’ ) . ( βπ β {π, π + 1} ) π π’ = exp (π π’ πΎ π ) π‘ π’ = π
Pr(π‘ π’+τ·‘ = π + 1 | π‘ π’ = π) = 1 β π π Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = 0 . Generalize to a mixture model . . . . (random effect) . [π π’ |π, π‘ π’ ] βΌ Gamma (π π , π π ) . (link function) . . (1, β¦ , πΏ) . regimes . . (data) . [π§ π’ |π‘ π’ , π π’ , πΎ, π, π] βΌ Poisson (π π’ π π’ ) . ( βπ β {π, π + 1} ) π π’ = exp (π π’ πΎ π ) π‘ π’ = π Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = π π
Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = 0 . Generalize to a mixture model . . . . (random effect) . [π π’ |π, π‘ π’ ] βΌ Gamma (π π , π π ) . (link function) . . (1, β¦ , πΏ) . regimes . . (data) . [π§ π’ |π‘ π’ , π π’ , πΎ, π, π] βΌ Poisson (π π’ π π’ ) . ( βπ β {π, π + 1} ) π π’ = exp (π π’ πΎ π ) π‘ π’ = π Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = π π Pr(π‘ π’+τ·‘ = π + 1 | π‘ π’ = π) = 1 β π π
. Generalize to a mixture model . . . . (random effect) . [π π’ |π, π‘ π’ ] βΌ Gamma (π π , π π ) . (link function) . . (1, β¦ , πΏ) . regimes . . (data) . [π§ π’ |π‘ π’ , π π’ , πΎ, π, π] βΌ Poisson (π π’ π π’ ) . ( βπ β {π, π + 1} ) π π’ = exp (π π’ πΎ π ) π‘ π’ = π Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = π π Pr(π‘ π’+τ·‘ = π + 1 | π‘ π’ = π) = 1 β π π Pr(π‘ π’+τ·‘ = π | π‘ π’ = π) = 0
. π τ·‘ . 1 . 2 . 3 . . . 1 β π τ·‘ . changepoint . β― . N . Units (πΎ τ·€ , π τ·€ ) Traditional changepoint models . . 1 . Regimes . 2 . 3 4 . . (πΎ τ·‘ , π τ·‘ ) . Regimes . (πΎ τ·’ , π τ·’ ) . (πΎ τ·£ , π τ·£ ) Must be in the last regime
. π τ·‘ . 1 . 2 . 3 . . . 1 β π τ·‘ . changepoint . β― . N . Units (πΎ τ·€ , π τ·€ ) Traditional changepoint models . . 1 . Regimes . 2 . 3 4 . . (πΎ τ·‘ , π τ·‘ ) . Regimes . (πΎ τ·’ , π τ·’ ) . (πΎ τ·£ , π τ·£ ) Must be in the last regime
. π τ·‘ . 1 . 2 . 3 . . . 1 β π τ·‘ . changepoint . β― . N . Units (πΎ τ·€ , π τ·€ ) Traditional changepoint models . . 1 . Regimes . 2 . 3 4 . . (πΎ τ·‘ , π τ·‘ ) . Regimes . (πΎ τ·’ , π τ·’ ) . (πΎ τ·£ , π τ·£ ) Must be in the last regime
. π τ·‘ . 1 . 2 . 3 . . . 1 β π τ·‘ . changepoint . β― . N . Units (πΎ τ·€ , π τ·€ ) Traditional changepoint models . . 1 . Regimes . 2 . 3 4 . . (πΎ τ·‘ , π τ·‘ ) . Regimes . (πΎ τ·’ , π τ·’ ) . (πΎ τ·£ , π τ·£ ) Must be in the last regime
. π τ·‘ . 1 . 2 . 3 . . . 1 β π τ·‘ . changepoint . β― . N . Units (πΎ τ·€ , π τ·€ ) Traditional changepoint models . . 1 . Regimes . 2 . 3 4 . . (πΎ τ·‘ , π τ·‘ ) . Regimes . (πΎ τ·’ , π τ·’ ) . (πΎ τ·£ , π τ·£ ) Must be in the last regime
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