London : H. Renshaw, 1885.

Edinburgh : Young J. Pentland, 1886.

London : H.K. Lewis, 1903.

London : James Epps & Co., Limited, 1894.

London : J. Churchill, [1868]

London : Cassell, 1898.

London : Cassell, 1902.

London : Smith, Elder, 1881.

Edinburgh : W.P. Nimmo, [1867]

[London?] : [publisher not identified], [1850]

Edinburgh : Young J. Pentland, 1895.

Wiesbaden : J.F. Bergmann, 1914.

London : Taylor and Walton, 1841.

London : H.K. Lewis, 1883.

London : Philadelphia, 1890.

London : J. Churchill, 1861.

London : H. Renshaw, 1849.

Representatives from school districts, state education agencies, and institutions of higher education in Idaho convene to discuss teacher recruitment and retention.

London : Longmans, Green, Reader and Dyer, 1870.

London : [Published not identified], 1871.

London : [Published not identified], 1872.

London : [Published not identified], 1873.

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London : [Published not identified], 1875.

London : [Published not identified], 1876.

[London] : [Published not identified], [1877]

New York ; London : W.W. Norton, 2008.

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Rockville, Maryland : National Institute on Drug Abuse, 1984.

Rockville, Maryland : National Institute on Drug Abuse, 1988.

Rockville, Maryland : National Institute on Drug Abuse, 1988.

Rockville, Maryland : National Institute on Drug Abuse, 1995.

Rockville, Maryland : National Institute on Drug Abuse, 1984.

Rockville, Maryland : National Institute on Drug Abuse, 1986.

Rockville, Maryland : National Institute on Drug Abuse, 1981.

Rockville, Maryland : National Institute on Drug Abuse, 1985.

Rockville, Maryland : National Institute on Drug Abuse, 1985.

Rockville, Maryland : National Institute on Drug Abuse, 1978.

Rockville, Maryland : National Institute on Drug Abuse, 1979.

Rockville, Maryland : National Institute on Drug Abuse, 1978.

Rockville, Maryland : National Institute on Drug Abuse, 1978.

Rockville, Maryland : National Institute on Drug Abuse, 1977.

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Washington, D.C. : Wynne Associates, [1974]

London : London Research Centre, 1991.

Uttam Bandyopadhyay, Shirsendu Mukherjee, Atanu Biswas.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 291--303.

Abstract:
In adaptive crossover design, our goal is to allocate more patients to a promising treatment sequence. The present work contains a very simple three period crossover design for two competing treatments where the allocation in period 3 is done on the basis of the data obtained from the first two periods. Assuming normality of response variables we use a reliability functional for the choice between two treatments. We calculate the allocation proportions and their standard errors corresponding to the possible treatment combinations. We also derive some asymptotic results and provide solutions on related inferential problems. Moreover, the proposed procedure is compared with a possible competitor. Finally, we use a data set to illustrate the applicability of the proposed design.

Kushal K. Dey, Sourabh Bhattacharya.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 2, 222--266.

Abstract:
Transformation based Markov Chain Monte Carlo (TMCMC) was proposed by Dutta and Bhattacharya ( Statistical Methodology 16 (2014) 100–116) as an efficient alternative to the Metropolis–Hastings algorithm, especially in high dimensions. The main advantage of this algorithm is that it simultaneously updates all components of a high dimensional parameter using appropriate move types defined by deterministic transformation of a single random variable. This results in reduction in time complexity at each step of the chain and enhances the acceptance rate. In this paper, we first provide a brief review of the optimal scaling theory for various existing MCMC approaches, comparing and contrasting them with the corresponding TMCMC approaches.The optimal scaling of the simplest form of TMCMC, namely additive TMCMC , has been studied extensively for the Gaussian proposal density in Dey and Bhattacharya (2017a). Here, we discuss diffusion-based optimal scaling behavior of additive TMCMC for non-Gaussian proposal densities—in particular, uniform, Student’s $t$ and Cauchy proposals. Although we could not formally prove our diffusion result for the Cauchy proposal, simulation based results lead us to conjecture that at least the recipe for obtaining general optimal scaling and optimal acceptance rate holds for the Cauchy case as well. We also consider diffusion based optimal scaling of TMCMC when the target density is discontinuous. Such non-regular situations have been studied in the case of Random Walk Metropolis Hastings (RWMH) algorithm by Neal and Roberts ( Methodology and Computing in Applied Probability 13 (2011) 583–601) using expected squared jumping distance (ESJD), but the diffusion theory based scaling has not been considered. We compare our diffusion based optimally scaled TMCMC approach with the ESJD based optimally scaled RWM with simulation studies involving several target distributions and proposal distributions including the challenging Cauchy proposal case, showing that additive TMCMC outperforms RWMH in almost all cases considered.

Clément Marteau, Theofanis Sapatinas.

Source: Statistics Surveys, Volume 9, 253--297.

Abstract:
We are concerned with minimax signal detection. In this setting, we discuss non-asymptotic and asymptotic approaches through a unified treatment. In particular, we consider a Gaussian sequence model that contains classical models as special cases, such as, direct, well-posed inverse and ill-posed inverse problems. Working with certain ellipsoids in the space of squared-summable sequences of real numbers, with a ball of positive radius removed, we compare the construction of lower and upper bounds for the minimax separation radius (non-asymptotic approach) and the minimax separation rate (asymptotic approach) that have been proposed in the literature. Some additional contributions, bringing to light links between non-asymptotic and asymptotic approaches to minimax signal, are also presented. An example of a mildly ill-posed inverse problem is used for illustrative purposes. In particular, it is shown that tools used to derive ‘asymptotic’ results can be exploited to draw ‘non-asymptotic’ conclusions, and vice-versa. In order to enhance our understanding of these two minimax signal detection paradigms, we bring into light hitherto unknown similarities and links between non-asymptotic and asymptotic approaches.

A. Philip Dawid, Vanessa Didelez

Source: Statist. Surv., Volume 4, 184--231.

Abstract:
We consider the problem of learning about and comparing the consequences of dynamic treatment strategies on the basis of observational data. We formulate this within a probabilistic decision-theoretic framework. Our approach is compared with related work by Robins and others: in particular, we show how Robins’s ‘ G -computation’ algorithm arises naturally from this decision-theoretic perspective. Careful attention is paid to the mathematical and substantive conditions required to justify the use of this formula. These conditions revolve around a property we term stability , which relates the probabilistic behaviours of observational and interventional regimes. We show how an assumption of ‘sequential randomization’ (or ‘no unmeasured confounders’), or an alternative assumption of ‘sequential irrelevance’, can be used to infer stability. Probabilistic influence diagrams are used to simplify manipulations, and their power and limitations are discussed. We compare our approach with alternative formulations based on causal DAGs or potential response models. We aim to show that formulating the problem of assessing dynamic treatment strategies as a problem of decision analysis brings clarity, simplicity and generality.

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