Updating Probabilities with Data and Moments

We use the method of Maximum (relative) Entropy to process information in the form of observed data and moment constraints. The generic "canonical" form of the posterior distribution for the problem of simultaneous updating with data and moments is obtained. We discuss the general problem of non-commuting constraints, when they should be processed sequentially and when simultaneously. As an illustration, the multinomial example of die tosses is solved in detail for two superficially similar but actually very different problems.Comment: Presented at the 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Saratoga Springs, NY, July 8-13, 2007. 10 pages, 1 figure V2 has a small typo in the end of the appendix that was fixed. aj=mj+1 is now aj=m(k-j)+

Extended parametric representation of compressor fans and turbines. Volume 1: CMGEN user's manual

A modeling technique for fans, boosters, and compressors has been developed which will enable the user to obtain consistent and rapid off-design performance from design point input. The fans and compressors are assumed to be multi-stage machines incorporating front variable stators. The boosters are assumed to be fixed geometry machines. The modeling technique has been incorporated into time sharing program to facilitate its use. Because this report contains a description of the input output data, values of typical inputs, and examples cases, it is suitable as a user's manual. This report is the first of a three volume set describing the parametric representation of compressors, fans, and turbines. The titles of the three volumes are as follows: (1) Volume 1 CMGEN USER's Manual (Parametric Compressor Generator); (2) Volume 2 PART USER's Manual (parametric Turbine); (3) Volume 3 MODFAN USER's Manual (Parametric Modulating Flow Fan)

Mass spectrometer with magnetic pole pieces providing the magnetic fields for both the magnetic sector and an ion-type vacuum pump

A mass spectrometer (MS) with unique magnetic pole pieces which provide a homogenous magnetic field across the gap of the MS magnetic sector as well as the magnetic field across an ion-type vacuum pump is disclosed. The pole pieces form the top and bottom sides of a housing. The housing is positioned so that portions of the pole pieces form part of the magnetic sector with the space between them defining the gap region of the magnetic sector, through which an ion beam passes. The pole pieces extend beyond the magnetic sector with the space between them being large enough to accommodate the electrical parts of an ion-type vacuum pump. The pole pieces which provide the magnetic field for the pump, together with the housing form the vacuum pump enclosure or housing

The effects of feeding two sources of protein with and without hay on the performance of beef heifers and steers

There are two major objectives in this study: (1) to compare a natural protein source, cottonseed meal, with urea, and (2) to determine the effect of adding limited quantities of hay to a high concentrate finishing ration. Both heifers and steers were used so a sex comparison was also made. One hundred and seventy medium grade heifers were involved in a three-year study at the Greeneville Tobacco Experiment Station. The heifers were pregnancy checked, implanted with DBS, weighed, and alloted. There were two general phases of feeding each year. During the first phase, the heifers were given corn silage ad libitum with five pounds of ground ear corn and one pound of protein supplement for an average of 112 days. Following the high silage phase was a concentrate phase, during which each heifer consumed a maximum amount of ground ear corn and either one pound of urea supplement or 1.25 pounds of cottonseed meal (1967, 1 pound of cottonseed meal). The concentrate phases lasted an average of 58 days. The heifers receiving cottonseed meal as a protein source gained significantly faster than the heifers receiving a high urea supplement during the first 28 days of the forage phases (P ≤ .05). However, when both the total forage and concentrate feeing periods were considered, no differences between urea and cottonseed meal were observed. The ADG obtained in the total forage and total concentrate feeding periods were higher for the cottonseed meal supplement but these differences were not significant (P ≤ .05). Heifers receiving hay gained significantly faster than heifers receiving no hay during the first 28 days of the forage and concentrate phases (P ≤ .05). One hundred and sixty medium to good grade steers were utilized in the study. The steers were weighed, implanted with DES, and lotted to treatments. The feeding period consisted of only a concentrate phase for the steers which averaged 92 days. The feeding program was the same as for the heifers in the concentrate phase. The steers receiving cottonseed meal gained significantly faster during the initial 28 days feeding and during the entire 92 days than the steers receiving urea (P ≤ .05). Steers receiving hay gained at a significantly faster rate than the steers receiving no hay during the total concentrate phase (P ≤ .001). When both the heifers and steers were marketed at similar visual condition grades, the final weight for the heifers was from 150 to 200 pounds less than the steers. The ADG of the steers for the feeding period was also slightly higher than for the heifers

Practicing ethical research to empower sexual assault survivors in higher education: An international perspective

Sexual violence is a major global health concern and sociocultural issue (World Health Organization, 2021), with around one-third of sexual assault survivors developing mental health issues (Carey et al., 2018). However, there is a dearth in research about sexual assault survivors in higher education. Therefore, this paper will explore how researchers can ethically empower sexual assault survivors through research processes in higher education. The questions guiding this study are: 1) What are the current strategies used by researchers to ethically empower sexual assault survivors in higher education? 2) How do researchers employ these strategies in practice

Information and Entropy

What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore it is the force that induces us to change our minds. This problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), which is designed for updating from arbitrary priors given information in the form of arbitrary constraints, includes as special cases both MaxEnt (which allows arbitrary constraints) and Bayes' rule (which allows arbitrary priors). Thus, ME unifies the two themes of these workshops -- the Maximum Entropy and the Bayesian methods -- into a single general inference scheme that allows us to handle problems that lie beyond the reach of either of the two methods separately. I conclude with a couple of simple illustrative examples.Comment: Presented at MaxEnt 2007, the 27th International Workshop on Bayesian Inference and Maximum Entropy Methods (July 8-13, 2007, Saratoga Springs, New York, USA

The marginalization paradox and the formal Bayes' law

It has recently been shown that the marginalization paradox (MP) can be resolved by interpreting improper inferences as probability limits. The key to the resolution is that probability limits need not satisfy the formal Bayes' law, which is used in the MP to deduce an inconsistency. In this paper, I explore the differences between probability limits and the more familiar pointwise limits, which do imply the formal Bayes' law, and show how these differences underlie some key differences in the interpretation of the MP.Comment: Presented at Maxent 2007, Saratoga Springs, NY, July 200

Origins of the Combinatorial Basis of Entropy

The combinatorial basis of entropy, given by Boltzmann, can be written $H = N^{-1} \ln \mathbb{W}$, where $H$ is the dimensionless entropy, $N$ is the number of entities and $\mathbb{W}$ is number of ways in which a given realization of a system can occur (its statistical weight). This can be broadened to give generalized combinatorial (or probabilistic) definitions of entropy and cross-entropy: $H=\kappa (\phi(\mathbb{W}) +C)$ and $D=-\kappa (\phi(\mathbb{P}) +C)$, where $\mathbb{P}$ is the probability of a given realization, $\phi$ is a convenient transformation function, $\kappa$ is a scaling parameter and $C$ an arbitrary constant. If $\mathbb{W}$ or $\mathbb{P}$ satisfy the multinomial weight or distribution, then using $\phi(\cdot)=\ln(\cdot)$ and $\kappa=N^{-1}$, $H$ and $D$ asymptotically converge to the Shannon and Kullback-Leibler functions. In general, however, $\mathbb{W}$ or $\mathbb{P}$ need not be multinomial, nor may they approach an asymptotic limit. In such cases, the entropy or cross-entropy function can be {\it defined} so that its extremization ("MaxEnt'' or "MinXEnt"), subject to the constraints, gives the ``most probable'' (``MaxProb'') realization of the system. This gives a probabilistic basis for MaxEnt and MinXEnt, independent of any information-theoretic justification. This work examines the origins of the governing distribution $\mathbb{P}$.... (truncated)Comment: MaxEnt07 manuscript, version 4 revise

From Information Geometry to Newtonian Dynamics

Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by a probability distribution. The corresponding configuration space is a statistical manifold the geometry of which is defined by the information metric. The trajectory follows from a principle of inference, the method of Maximum Entropy. No additional "physical" postulates such as an equation of motion, or an action principle, nor the concepts of momentum and of phase space, not even the notion of time, need to be postulated. The resulting entropic dynamics reproduces the Newtonian dynamics of any number of particles interacting among themselves and with external fields. Both the mass of the particles and their interactions are explained as a consequence of the underlying statistical manifold.Comment: Presented at MaxEnt 2007, the 27th International Workshop on Bayesian Inference and Maximum Entropy Methods (July 8-13, 2007, Saratoga Springs, New York, USA