Statistical Inference and the Plethora of Probability Paradigms: A Principled Pluralism

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability

The Decomposition of Hydrazine in the Gas Phase and over an Iridium Catalyst

Hydrazine is an important rocket fuel, used as both a monopropellant and a bipropellant. This paper presents theoretical results to complement the extensive experimental studies of the gas phase and Ir catalyzed decompositions involved in the monopropellant applications of hydrazine. Gas phase electronic structure theory calculations that include electron correlation predict that numerous molecular and free radical reactions occur within the same energy range as the basic free radical pathways: NN bond breaking around 65 kcal/mol and NH bond breaking around 81 kcal/mol. The data suggest that a revision to existing kinetics modeling is desirable, based on the energetics and the new elementary steps reported herein. A supported Ir6 octahedron model for the Shell 405 Iridium catalyst used in thrusters was developed. Self-Consistent Field and electron correlation calculations (with core potentials and associated basis sets) find a rich chemistry for hydrazine on this catalyst model. The model catalyst provides dramatically lower NN and NH bond cleavage energies and an even smaller barrier to breaking the NH bond by NH2 abstractions. Thus, the low temperature decomposition over the catalyst is interpreted in terms of consecutive NH2 abstractions to produce ammonia and nitrogen. The higher temperature channel, which has hydrogen and nitrogen products, may be due to a mixture of two mechanisms. These two mechanisms are successive NH cleavages with surface H + H recombinations, and the same type of assisted H2 eliminations found to occur in the gas phase part of this study

Quasi-Degenerate Second-Order Perturbation Theory for Occupation Restricted Multiple Active Space Self-Consistent Field Reference Functions

A multi-configuration quasi-degenerate second-order perturbation method based on the occupation restricted multiple active space (ORMAS-PT/ORMAS) reference wavefunction is presented. ORMAS gives one the ability to approximate a complete active space self-consistent field (CASSCF) wavefunction using only a subset of the configurations from the CASSCF space. The essential idea behind ORMAS-PT is to use the multi-reference Møller-Plesset formalism to correct the ORMAS reference energy. A computational scheme employing direct CI methodology is presented. Several tests are presented to demonstrate the performance of the ORMAS-PT method