Prior 2 definition

Prior 2 s ∼ N (5, σ2) Similarly to the unknown parameter θ, a weak normal prior with large variance can be assigned to the parameter s. Based on preliminary literatures and classical approaches, we know the number of stages in the carcinogenesis model is about 6 to 7 for most cancers. Since one less the number of stages is assigned to the power of age in the Armitage-Doll model, we can simplify the prior mean for the s as 5. The choice of σ2 can be either a fixed large number or hyperprior with Gamma distribution. Prior 3: s ∼ Gamma(α, β) We can then assume a Gamma prior distribution for s with parameter α and β, i.e., f (s| α, β) ∝ sα—1 e—θ/b where 0 < ϕ < 1. Since the mean of the Gamma distribution is αβ and variance is αβ2, we choose α = 1 and β = 10 in order to design the Gamma distribution with mean at 10 and variance at 100. Alternatively, we can define hyperpriors for the shape and scale parameters (α and β) in the Gamma distribution. By Bayes rule [▇▇▇▇▇▇ and ▇▇▇▇▇, 2009] we have the posterior density f (s, ϕ|y) ∝ f (y|s)f (s|ϕ)f (ϕ), then the marginal posterior distribution of s can be derived at f (s|y) = ∫ f (s, ϕ|y)dϕ ∝ ∫ f (y|s)f (s|ϕ)f (ϕ)dϕ where ϕ = (α, β). At this point there are several choices to be made on the hyperpriors with respect to the direction of inference, especially for the derivation of the marginal posterior, f (s|y). Since the Gamma distribution is a two-parameter exponential family, I set the hyperprior for shape parameter α to be the Exponential distribution with mean at 5 and the hyperprior for the scale parameter β as the Gamma distribution with the shape value 0.1 and scale value 10.
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Examples of Prior 2 in a sentence

  • Domestic Period (weeks) Volume Period (weeks) Volume ------ ------- -------- ------ ------- --------- 4Q96 140-152 9755 3Q96 127-139 9343 3Q96 127-139 9343 2Q96 114-126 9303 2Q96 114-126 9303 1Q96 101-113 9296 1Q96 101-113 9296 4Q95 ▇▇▇-▇▇▇ ▇▇▇▇ TTL Domestic Volume 37697 37232 Div by 52 weeks 725 716 Div by 6 service days 121 119 Current less Prior 2 Rounded/unit of 10 0 Increase or Decrease 0.00% Prior DDT Adj.

Related to Prior 2

  • Prior CDA has the meaning set forth in Section 9.4.

  • Prior Agreement has the meaning set forth in the Recitals.

  • Prior Agreements has the meaning set forth in the recitals.

  • Prior Claims means the Competing Claims to which the Authority’s right to the Building Aid is subordinated by the School Financing Act.

  • Prior Year means the year commencing 1 April immediately prior to the relevant Charging Year;