LIKELIHOOD Sample Clauses

LIKELIHOOD. XX XXXXX --------------------------------------------------------------
LIKELIHOOD. Cancer death counts yiap at area i, age a and period p are modelled as Poisson distribution with parameters rate λiap and population size Niap, i.e., yiap ~ Poisson(Niapλiap), where λiap is the relative risk for the αth age group and the pth calendar period in the ith area, and can be modeled as log(λiap) = νi + µi + θa + γp + δc + ϕip + ϕic. Therefore, we can write the likelihood as , P (y|λ) ∝ Qi,a,p eNiapλiap (Niapλiap)yiap ∝ Qi,a,p eλiap (λiap)yiap where λ = (λiap) includes all i, a, and p and represents all the parameters which need to have prior distributions. Niap is a known quantity which can be ignored here. Priors The joint prior distribution can be written as P (λ) = P (ν, µ, θ, γ, δ, ϕ1, ϕ2), where ν is the joint spatial unstructured effect, µ is the joint spatial structured effect, θ is the age effect, γ is the period effect, δ is the cohort effect, ϕ1 and ϕ2 are the joint spatial- period and spatial-cohort interactions, respectively. Age effects As we introduced before, we apply the carcinogenesis model into the AAPC model by replacing the age effects with hazard functions derived from the carcinogenesis model. For example, the age effect θa at age group a is given a noninformative prior as below: θa ∼ N (θ¯a, τa) where θ¯a = log(h(ta)), and τa ∼ Gamma(0.001, 0.001). Armitage and Doll [1954] assumed multiple transformations happened in stages for a cell to grow into a cancerous tumor. In the Armitage-Doll model, h(t) = cts—1 where s is the number of stages, ta is the age and c is constant. Therefore, we have the following age effects in a nonlinear function of age, θ¯a = c + (s — 1) ∗ log(ta). Hyperpriors are given to c and s at c ∼ N (0, τc) s ∼ N (5, τs) where Gamma hyperpriors are given to two precision terms as below: τc ∼ Gamma(0.001, 0.001) and τs ∼ Gamma(0.001, 0.001). The hazard function derived from the TSCE model is introduced to the AAPC model as well. In contrast to the simple format of the hazard function in the Armitage-Doll model, the hazard function from the TSCE model is more difficult. Four derived parameters will be summarized in the TSCE model, the rate of initiation, ν, the rate of division, α, and death, β, of initial cells, and the rate of malignant conversion, µ. The hazard function in the TSCE model is given by Xxxxxxxxxx [1979, 1981, 1990, 2009] as h(t) = ν e—qt e—pt pq , — α qe—pt — pe—qt where p and q are the roots of a quadratic equation, with p + q = —(α— β — µ) and pq = αµ. Three estimated parameters p, q, and r...

Related to LIKELIHOOD

  • Impact direct impact on people does not necessarily require direct contact, for example, environmental health, trading standards and similar officers may have a direct impact on people, through the implementation or enforcement of regulations, without necessarily having direct contact with those who benefit.

  • Impossibility Neither party shall be in default of this Charter, if the performance of any or all of this Charter is prevented, delayed, hindered or otherwise made impracticable or impossible by reason of any strike, flood, hurricane, riot, fire, explosion, war, act of God, sabotage or any other casualty or cause beyond either party’s control, and which cannot be overcome by reasonable diligence and without unusual expense.

  • No Material Adverse Change or Ratings Agency Change For the period from and after the date of this Agreement and prior to the Closing Date:

  • No Change in Facts or Circumstances Borrower warrants that (a) all information in the application for the loan submitted to Lender (the "Loan Application") and in all financial statements, rent schedules, reports, certificates and other documents submitted in connection with the Loan Application are complete and accurate in all material respects; and (b) there has been no material adverse change in any fact or circumstance that would make any such information incomplete or inaccurate.

  • No Adverse Change Since August 2, 2008, there has occurred no event which has had or could reasonably be expected to have a Materially Adverse Effect.

  • No Change in Facts or Circumstances; Disclosure All information submitted by Borrower to Lender and in all financial statements, rent rolls, reports, certificates and other documents submitted in connection with the Loan or in satisfaction of the terms thereof and all statements of fact made by Borrower in this Agreement or in any other Loan Document, are accurate, complete and correct in all material respects, provided, however, that if such information was provided to Borrower by non-affiliated third parties, Borrower represents that such information is, to the best of its knowledge after due inquiry, accurate, complete and correct in all material respects. There has been no material adverse change in any condition, fact, circumstance or event that would make any such information inaccurate, incomplete or otherwise misleading in any material respect or that otherwise materially and adversely affects or might materially and adversely affect the Property or the business operations or the financial condition of Borrower. Borrower has disclosed to Lender all material facts and has not failed to disclose any material fact that could cause any representation or warranty made herein to be materially misleading.

  • No Material Adverse Change in Business Except as otherwise stated therein, since the respective dates as of which information is given in the Registration Statement, the General Disclosure Package or the Prospectus, (A) there has been no material adverse change in the condition, financial or otherwise, or in the earnings, business affairs or business prospects of the Company and its subsidiaries considered as one enterprise, whether or not arising in the ordinary course of business (a “Material Adverse Effect”), (B) there have been no transactions entered into by the Company or any of its subsidiaries, other than those in the ordinary course of business, which are material with respect to the Company and its subsidiaries considered as one enterprise, and (C) there has been no dividend or distribution of any kind declared, paid or made by the Company on any class of its capital stock.

  • No Adverse Changes Except as contemplated in the Prospectus, subsequent to the respective dates as of which information is given in the Prospectus, neither the Company nor any of its subsidiaries shall have incurred any material liabilities or obligations, direct or contingent, or entered into any material transactions, or declared or paid any dividends or made any distribution of any kind with respect to its capital stock; and there shall not have been any change in the capital stock (other than a change in the number of outstanding Common Stock due to the issuance of shares upon the exercise of outstanding options or warrants), or any material change in the short-term or long-term debt of the Company, or any issuance of options, warrants, convertible securities or other rights to purchase the capital stock of the Company or any of its subsidiaries, or any development involving a prospective Material Adverse Effect (whether or not arising in the ordinary course of business), or any loss by strike, fire, flood, earthquake, accident or other calamity, whether or not covered by insurance, incurred by the Company or any subsidiary, the effect of which, in any such case described above, in the Agent’s judgment, makes it impractical or inadvisable to offer or deliver the Shares on the terms and in the manner contemplated in the Prospectus.

  • Adverse Circumstances No condition, circumstance, event, agreement, document, instrument, restriction, litigation or proceeding (or, to Grantor's knowledge, threatened litigation or proceeding or basis therefor) exists which (a) would have a Material Adverse Effect upon Grantor, or (b) would constitute an Event of Default or an Unmatured Event of Default.