1,450 research outputs found
An effective likelihood-free approximate computing method with statistical inferential guarantees
Approximate Bayesian computing is a powerful likelihood-free method that has
grown increasingly popular since early applications in population genetics.
However, complications arise in the theoretical justification for Bayesian
inference conducted from this method with a non-sufficient summary statistic.
In this paper, we seek to re-frame approximate Bayesian computing within a
frequentist context and justify its performance by standards set on the
frequency coverage rate. In doing so, we develop a new computational technique
called approximate confidence distribution computing, yielding theoretical
support for the use of non-sufficient summary statistics in likelihood-free
methods. Furthermore, we demonstrate that approximate confidence distribution
computing extends the scope of approximate Bayesian computing to include
data-dependent priors without damaging the inferential integrity. This
data-dependent prior can be viewed as an initial `distribution estimate' of the
target parameter which is updated with the results of the approximate
confidence distribution computing method. A general strategy for constructing
an appropriate data-dependent prior is also discussed and is shown to often
increase the computing speed while maintaining statistical inferential
guarantees. We supplement the theory with simulation studies illustrating the
benefits of the proposed method, namely the potential for broader applications
and the increased computing speed compared to the standard approximate Bayesian
computing methods
Finite- and Large- Sample Inference for Model and Coefficients in High-dimensional Linear Regression with Repro Samples
In this paper, we present a new and effective simulation-based approach to
conduct both finite- and large-sample inference for high-dimensional linear
regression models. This approach is developed under the so-called repro samples
framework, in which we conduct statistical inference by creating and studying
the behavior of artificial samples that are obtained by mimicking the sampling
mechanism of the data. We obtain confidence sets for (a) the true model
corresponding to the nonzero coefficients, (b) a single or any collection of
regression coefficients, and (c) both the model and regression coefficients
jointly. We also extend our approaches to drawing inferences on functions of
the regression coefficients. The proposed approach fills in two major gaps in
the high-dimensional regression literature: (1) lack of effective approaches to
address model selection uncertainty and provide valid inference for the
underlying true model; (2) lack of effective inference approaches that
guarantee finite-sample performances. We provide both finite-sample and
asymptotic results to theoretically guarantee the performances of the proposed
methods. In addition, our numerical results demonstrate that the proposed
methods are valid and achieve better coverage with smaller confidence sets than
the existing state-of-art approaches, such as debiasing and bootstrap
approaches
A note on Dempster-Shafer recombination of confidence distributions
It is often the case that there are several studies measuring the same parameter. Naturally, it is of interest to provide a systematic way to combine the information from these studies. Examples of such situations include clinical trials, key comparison trials and other problems of practical importance. Singh et al. (2005) provide a compelling framework for combining information from multiple sources using the framework of confidence distributions. In this paper we investigate the feasibility of using the Dempster-Shafer recombination rule on this problem. We derive a practical combination rule and show that under assumption of asymptotic normality, the Dempster-Shafer combined confidence distribution is asymptotically equivalent to one of the method proposed in Singh et al. (2005). Numerical studies and comparisons for the common mean problem and the odds ratio in tables are included
A review on heterogeneous solid catalysts and related catalytic mechanisms for epoxidation of olefins with H2O2
The epoxidation reaction using heterogeneous solid catalysts with H2O2 as oxidants are environmentally friendly routes to produce extensively useful epoxides which are traditionally obtained from capital-intensive or environmentally polluted processes. In this paper, various types of solid catalysts for the epoxidation of olefins with H2O2 as oxidants are reviewed. The efficient catalysts reported include microporous and mesoporous molecular sieves, layered-type materials, inorganic oxides, supported catalysts, zeolite encapsulated metal complexes, polyoxometalates, and supported organometallic catalysts. The proposed reaction mechanisms over different solid catalysts are summarized. The problems and perspectives to further efficiently improve the catalytic performances of the concerned heterogeneous catalysts for epoxidation reaction are remarked
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