By Ron Brookmeyer, Mitchell H. Gail
AIDS has seemed in additional than a hundred thirty nations, and over 100,000 circumstances of AIDS were stated within the U.S. on my own. increasingly more, the general public could be reckoning on statisticians to supply solutions in regards to the destiny process this epidemic.
This finished paintings confronts the issues which are particular to AIDS examine and unites them lower than a unmarried conceptual framework. It specializes in equipment for the layout and research of epidemiologic stories, the ordinary background of AIDS and the transmission of HIV, equipment for monitoring and projecting the process the epidemic, and statistical concerns in healing trials. many of the tools of tracking and forecasting this ailment obtain complete therapy. those equipment comprise back-calculation, which the authors constructed; interpretation of survey info on HIV occurrence; mathematical versions for HIV transmission; and ways that mix types of epidemiological information. a lot of this fabric -- corresponding to a dialogue of tools for assessing safeguard of the blood offer, an review of survey methods, and strategies to undertaking pediatric AIDS occurrence -- isn't on hand in the other paintings.
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Additional info for AIDS Epidemiology: A Quantitative Approach (Monographs in Epidemiology and Biostatistics ; V 22)
T ; LT = αT 1 . That the number of operations involved is of order T m2 can be deduced thus. For each of the values of t in the loop, there are m elements of αt to be computed, and each of those elements is a sum of m products of three quantities: an element of αt−1 , a transition probability γij , and a state-dependent probability (or density) pj (xt ). e. if δ, the distribution of C1 , is the stationary distribution of the Markov chain) is α0 = δ; αt = αt−1 ΓP(xt ) for t = 1, 2, . . , T ; LT = αT 1 .
Let X be a random variable which is distributed as a δ1 , δ2 -mixture of two distributions with expectations μ1 , μ2 , and variances σ12 and σ22 , respectively, where δ1 + δ2 = 1. (a) Show that Var(X) = δ1 σ12 + δ2 σ22 + δ1 δ2 (μ1 − μ2 )2 . (b) Show that a (nontrivial) mixture X of two Poisson distributions with distinct means is overdispersed, that is Var(X) > E(X). (c) Generalize part (b) to a mixture of m ≥ 2 Poisson distributions. 2. A zero-inﬂated Poisson distribution is sometimes used as a model for unbounded counts displaying overdispersion relative to the Poisson.
Prove the Chapman–Kolmogorov equations. 10. 4). 11. Let the quantities ai be nonnegative, with i ai > 0. Using a Lam grange multiplier, maximize S = i=1 ai log δi over δi ≥ 0, subject to i δi = 1. ) 12. ) Consider the following sequence of 21 observations, assumed to arise from a two-state (homogeneous) Markov chain: 11101 10111 10110 11111 1. © 2009 by Walter Zucchini and Iain MacDonald 28 PRELIMINARIES: MIXTURES AND MARKOV CHAINS (a) Estimate the transition probability matrix by ML (maximum likelihood) conditional on the ﬁrst observation.
AIDS Epidemiology: A Quantitative Approach (Monographs in Epidemiology and Biostatistics ; V 22) by Ron Brookmeyer, Mitchell H. Gail