3,812 research outputs found

    An effective likelihood-free approximate computing method with statistical inferential guarantees

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    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

    Primordia initiation of mushroom (Agaricus bisporus) strains on axenic casing materials

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    The mushroom (Agaricus bisporus) has a requirement for a ‘‘casing layer’’ that has specific physical, chemical and microbiological properties which stimulate and promote the initiation of primordia. Some of these primordia then may develop further into sporophores, involving differentiation of tissue. Wild and commercial strains of A. bisporus were cultured in axenic and nonaxenic microcosms, using a rye grain substrate covered by a range of organic and inorganic casing materials. In axenic culture, A. bisporus (commercial strain A15) was capable of producing primordia and mature sporophores on charcoal (wood and activated), anthracite coal, lignite and zeolite, but not on bark, coir, peat, rockwool, silica or vermiculite. Of six strains tested, only the developmental variant mutant, B430, produced rudimentary primordia on axenic peat-based casing material. However, none of these rudimentary primordia developed differentiated tissues or beyond 4 mm diameter, either on axenic casing material in the microcosms or in larger-scale culture. In larger-scale, nonaxenic culture, strain B430 produced severely malformed but mature sporophores in similar numbers to those of other strains. Typically, 3–6% of primordia developed into mature sporophores, but significant differences in this proportion, as well as in the numbers of primordia produced, were recorded between 12 A. bisporus strains
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