We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference in the absence of a likelihood function. The popular synthetic likelihood approach infers the parameters by modelling summary statistics of the data by a Gaussian probability distribution. In another popular approach called approximate Bayesian computation, the inference is performed by identifying parameter values for which the summary statistics of the simulated data are close to those of the observed data. Synthetic likelihood is easier to use as no measure of "closeness" is required but the Gaussianity assumption is often limiting. Moreover, both approaches require judiciously chosen summary statistics. We here present an alternative inference approach that is as easy to use as synthetic likelihood but not as restricted in its assumptions, and that, in a natural way, enables automatic selection of relevant summary statistic from a large set of candidates. The basic idea is to frame the problem of estimating the posterior as a problem of estimating the ratio between the data generating distribution and the marginal distribution. This problem can be solved by logistic regression, and including regularising penalty terms enables automatic selection of the summary statistics relevant to the inference task. We illustrate the general theory on canonical examples and employ it to perform inference for challenging stochastic nonlinear dynamical systems and high-dimensional summary statistics.
Broiler breeders display high levels of aggressive activity as a result of feed restriction. The objective of this study was to determine if aggressive activity in developing and mature broiler breeder males is influenced by increased dietary L-tryptophan (Trp). Broiler breeder males were raised using a skip-a-day feed restriction regimen. In Experiment 1, three levels of dietary Trp, .19 (control), .75, and 1.5%, were fed from the start of feed restriction at 4 wk of age and throughout development. All occurrences of aggressive behavior were recorded during three 20-min observation sessions per week on mornings on which feed was not delivered through Week 20. The Trp significantly decreased (P less than .05) aggressive pecking in birds fed supplemental Trp as compared to controls. No differences in threatening behavior were found. In the second part of Experiment 1, the effect of continued Trp supplementation on mature flocks of male broiler breeders and time-of-day effects on aggression were investigated. A depressing effect of supplemental Trp on pecking and threatening was observed. Maximum aggressive activity in all treatment groups occurred on mornings when feed was delivered. In Experiment 2, four levels of Trp, .19 (control), .38, .75, and 1.5%, were fed to developing birds as in Experiment 1. Birds fed supplemental Trp pecked less (P less than .05) than controls and .38% Trp was as effective in decreasing pecking as was 1.5%. It was concluded that increased levels of dietary Trp decrease aggression in both developing and mature, socially stable flocks of broiler breeder males.
The edible alga Spirulina platensis was uniformly labeled with 13C by growth in an atmosphere of pure 3C02. The labeled biomass was then incorporated into the diet of a laying hen for 27 days. The isotopic enrichment of individual amino acids in egg white and yolk proteins, as well as in various tissues of the hen at the end of the feeding period, was analyzed by negative chemical ionization gas chromatography/mass spectrometry. The amino acids of successive eggs showed one of two exclusive enrichment patterns: complete preservation of the intact carbon skeleton or extensive degradation and resynthesis. The same observation was made in tissue proteins. These patterns were cleanly divided according to known nutritional amino acid essentiality/nonessentiality but revealed differences in labeling among the nonessential amino acids: most notable was that proline accretion was derived entirely from the diet. Feeding uniformly 13C-labeled algal protein and recovering and analyzing de novo-synthesized protein provides a useful method to examine amino acid metabolism and determine conditional amino acid essentially in vivo.The use of stable isotopically labeled amino acids has been the key to many developments in our understanding of the protein metabolism of humans (1-4). Stable isotopically labeled amino acids have also been used to examine some important practical questions concerned with human nutrition. In a recent series ofreports, Young and coworkers (5-7) have reported the use of amino acids labeled with 13C on the carboxyl group to examine the essential amino acid requirements of adult men; the studies have provided invaluable information about the obligatory metabolic "needs" for these amino acids (3,8). This approach, however, does not directly address questions related to the efficiency with which different dietary proteins support metabolic requirements. Such information is necessary if biological needs are to be converted into dietary recommendations. Questions about the extent to which dietary proteins support metabolic requirements can best be answered by comparing the use of dietary protein with free amino acids administered i.v. This method would enable an estimate of the significance of protein digestibility and absorptive processes for overall requirements of dietary amino acids.In general, 13C-, 2H-, and '5N-isotopes are inserted into single amino acids via specific chemical reactions. This process limits the number of positions within a given molecule that can be labeled, which, in turn, limits the metabolic information that can be obtained from studies with commercially available amino acids.Apart from the extremely high sensitivity with which uniformly labeled substrates can be detected, they can be used to great benefit in studies of intermediary metabolism. For example, several recent reports describing hepatic glucose metabolism in vivo have depended on the use of [U-_3Clglucose (9-11) and have included a detailed analysis of the mass isotopomer labeling patterns in the circulating glu...
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