Meyn & Tweedie is back! The bible on Markov chains in general state spaces has been brought up to date to reflect developments in the field since 1996 - many of them sparked by publication of the first edition. The pursuit of more efficient simulation algorithms for complex Markovian models, or algorithms for computation of optimal policies for controlled Markov models, has opened new directions for research on Markov chains. As a result, new applications have emerged across a wide range of topics including optimisation, statistics, and economics. New commentary and an epilogue by Sean Meyn summarise recent developments and references have been fully updated. This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.

Markov Chains and Stochastic Stability

Statistics for Spatial Data.

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Convergence of Probability Measures. By Patrick Billingsley. Pp. xii, 253. 117s. 1968. (John Wiley & Sons, Inc.)

Economic Control of Quality of Manufactured Product.

We consider the model where φ 1, φ 2 are real coefficients, not necessarily equal, and the at ,'s are a sequence of i.i.d. random variables with mean 0. Necessary and sufficient conditions on the φ 's are given for stationarity of the process. Least squares estimators of the φ 's are derived and, under mild regularity conditions, are shown to be consistent and asymptotically normal. An hypothesis test is given to differentiate between an AR(1) (the case φ 1 = φ 2) and this threshold model. The asymptotic behavior of the test statistic is derived. Small-sample behavior of the estimators and the hypothesis test are studied via simulated data.

A threshold AR(1) model

We consider the model Zt = φ (0, k)+ φ(1, k)Zt –1 + at (k) whenever r k−1<Z t−1≦r k , 1≦k≦l, with r 0 = –∞ and rl =∞. Here {φ (i, k); i = 0, 1; 1≦k≦l} is a sequence of real constants, not necessarily equal, and, for 1≦k≦l, {at (k), t≧1} is a sequence of i.i.d. random variables with mean 0 and with {at (k), t≧1} independent of {at (j), t≧1} for j ≠ k. Necessary and sufficient conditions on the constants {φ (i, k)} are given for the stationarity of the process. Least squares estimators of the model parameters are derived and, under mild regularity conditions, are shown to be strongly consistent and asymptotically normal.

https://rmgsc.cr.usgs.gov/outgoing/threshold_articles/Chanetal1985.pdf

A multiple-threshold AR(1) model

This paper describes and compares three clustering techniques: traditional clustering methods, Kohonen maps and latent class models. The paper also proposes some novel measures of the quality of a clustering. To the best of our knowledge, this is the first contribution in the literature to compare these three techniques in a context where the classes are not known in advance.

Identifying Groups: A Comparison of Methodologies

Understanding physician perspectives on the intersection of race and genomics in clinical decision making is critical as personalized medicine and genomics become more integrated in health care services. There is a paucity of literature in the United States of America (USA) and globally regarding how health care providers understand and use information about race, ethnicity and genetic variation in their clinical decision making. This paper describes the development of three scales related to addressing this gap in the literature: the Bonham and Sellers Genetic Variation Knowledge Assessment Index--GKAI, Health Professionals Beliefs about Race—HPBR, and Racial Attributes in Clinical Evaluation—RACE scales. A cross-sectional, web survey of a national random sample of general internists in the USA (N = 787) was conducted. Confirmatory factor analysis was used to assess the construct validity of the scales. Scale items were developed through focus groups, cognitive interviews, expert advisory panels, and exploratory factor analysis of pilot data. GKAI was measured as a count of correct answers (Mean = 3.28 SD = 1.17). HPBR yielded two domains: beliefs about race as a biological phenomenon (HPBR-BD, alpha = .69, 4 items) and beliefs about the clinical value of race and genetic variation for understanding risk for disease (HPBR-CD alpha = .61, 3 items). RACE yielded one factor (alpha = .86, 7 items). GKAI is a timely knowledge scale that can be used to assess health professional knowledge of race and human genetic variation. HPBR is a promising new tool for assessing health professionals’ beliefs about the role of race and its relationship with human genetic variation in clinical practice. RACE offers a valid and reliable tool for assessing explicit use of racial attributes in clinical decision making.

/pdf/physicians-knowledge-beliefs-and-use-of-race-and-human-135tq1rohf.pdf

Physicians’ knowledge, beliefs, and use of race and human genetic variation: new measures and insights

Expectations of results from genome sequencing by end users are influenced by perceptions of uncertainty. This study aimed to assess uncertainties about sequencing by developing, evaluating, and implementing a novel scale. The Perceptions of Uncertainties in Genome Sequencing (PUGS) scale comprised ten items to assess uncertainties within three domains: clinical, affective, and evaluative. Participants (n=535) from the ClinSeq® NIH sequencing study completed a baseline survey that included the PUGS; responses (mean = 3.4/5, SD=0.58) suggested modest perceptions of certainty. A confirmatory factor analysis identified factor loadings that led to elimination of two items. A revised eight-item PUGS scale was used to test correlations with perceived ambiguity (r = -0.303, p < 0.001), attitudinal ambivalence (r = -0.111, p = 0.011), and ambiguity aversion (r = -0.093, p = 0.033). Results support nomological validity. A correlation with the MICRA uncertainty subscale was found among 175 cohort participants who had received results (r = -0.335, p < 0.001). Convergent and discriminant validity were also satisfied in a second sample of 208 parents from the HudsonAlpha CSER Project who completed the PUGS (mean = 3.4/5, SD = 0.72), and configural invariance was supported across the two datasets. As such, the PUGS is a promising scale for evaluating perceived uncertainties in genome sequencing, which can inform interventions to help patients form realistic expectations of these uncertainties.

PUGS: A novel scale to assess perceptions of uncertainties in genome sequencing.

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