The paper demonstrates that minute‐to‐minute metabolic response to meals with different macronutrient content can be measured and discerned in the whole‐body indirect calorimeter. The ability to discriminate between high‐carbohydrate and high‐fat meals is achieved by applying a modified regularization technique with additional constraints imposed on oxygen consumption rate. These additional constraints reduce the differences in accuracy between the oxygen and carbon dioxide analyzers. The modified technique was applied to 63 calorimeter sessions that were each 24 h long. The data were collected from 16 healthy volunteers (eight males, eight females, aged 22–35 years). Each volunteer performed four 24‐h long calorimeter sessions. At each session, they received one of four treatment combinations involving exercise (high or low intensity) and diet (a high‐fat or high‐carbohydrate shake for lunch). One volunteer did not complete all four assignments, which brought the total number of sessions to 63 instead of 64. During the 24‐h stay in the calorimeter, subjects wore a continuous glucose monitoring system, which was used as a benchmark for subject's postprandial glycemic response. The minute‐by‐minute respiratory exchange ratio (RER) data showed excellent agreement with concurrent subcutaneous glucose concentrations in postprandial state. The averaged minute‐to‐minute RER response to the high‐carbohydrate shake was significantly different from the response to high‐fat shake. Also, postprandial RER slopes were significantly different for two dietary treatments. The results show that whole‐body respiration calorimeters can be utilized as tools to study short‐term kinetics of substrate oxidation in humans.

We propose an information complexity-based regularization parameter selection method for solution of ill conditioned inverse problems. The regularization parameter is selected to be the minimizer of the Kullback–Leibler (KL) distance between the unknown data-generating distribution and the fitted distribution. The KL distance is approximated by an information complexity criterion developed by Bozdogan. The method is not limited to the white Gaussian noise case. It can be extended to correlated and non-Gaussian noise. It can also account for possible model misspecification. We demonstrate the performance of the proposed method on a test problem from Hansen's regularization tools.

Specification of prior distribution is one of the most important methodological as well practical problems in Bayesian inference. Although a number of approaches have been proposed, none of them is completely satisfactory from both theoretical and practical points of view. We propose a new method to infer prior distribution from a priori information which may be available from observations. The method consists of specifying a predictive distribution of the value of interest and then working backwards towards the prior distribution on the parameters. The method requires the solution of the Fredholm integral equation of the first kind, which can be effectively approximated using Tikhonov regularization. Numerical examples for two cases of Bayesian inference are presented.