State of nature

In this expression, p(H) is referred to as the prior probability of the hypothesis H. It is used to express any information we may have about the probability that the hypothesis H is true before we consider the new data D. p(D H) is the likelihood of the data given that the hypothesis H is true. It describes our view of how the data arise from whatever H says about the state of nature, including uncertainties in measurement and any physical theory we might have that relates the data to the hypothesis. p(D) is the marginal distribution of the data D, and because it is a constant with respect to the parameters it is frequently considered only as a normalization factor in Eq. (2), so that p(H D) x p(D H)p(H) up to a proportionality constant. If we have a set of hypotheses that are exclusive and exliaus-tive, i.e., one and only one must be true, then... 

In frequentist statistics, probability is instead a long-run relative occurrence of some event out of an infinite number of repeated trials, where the event is a possible outcome of the trial. A hypothesis or parameter that expresses a state of nature cannot have a probability in frequentist statistics, because after an infinite number of experiments there can be no uncertainty in the parameter left. A hypothesis or parameter value is either... 

In a Lockean world, mineral rights do not accompany surface rights in either original or transferred ownership. Minerals would not be owTicd until homesteaded by the acts of discovery and intent to possess. In the case of oil and gas, initial ownership would occur when the oil or gas entered the well bore and was legally claimed by the driller. The reservoir would then turn from a state of nature into owned property. The homesteader (discoverer) could be the property owner directly overhead, another land owner, or a lessee of either. 

Decision-making may be undertaken by an individual under assumptions of certainty, risk, or uncertainty (partial or complete ignorance) on the states of Nature. 

Options analysis is a technique that can deal with such contingencies. It is a form of decision analysis that includes chance variables, initially hidden, representing states of nature that can be uncovered, in whole or in part, through a decision to carry out research. Such research creates options—the ability to progress, or abandon, one of several courses of action. This research might be technical or market research, in applications of option analysis to R D planning. 

As geochemists, we frequently need to describe the chemical states of natural waters, including how dissolved mass is distributed among aqueous species, and to understand how such waters will react with minerals, gases, and fluids of the Earth s crust and hydrosphere. We can readily undertake such tasks when they involve simple chemical systems, in which the relatively few reactions likely to occur can be anticipated through experience and evaluated by hand calculation. As we encounter more complex problems, we must rely increasingly on quantitative models of solution chemistry and irreversible reaction to find solutions. 

In this chapter we develop a description of the equilibrium state of a geochemical system in terms of the fewest possible variables and show how the resulting equations can be applied to calculate the equilibrium states of natural waters. We reserve for the next two chapters discussion of how these equations can be solved by using numerical techniques. 

The equilibrium model, despite its limitations, in many ways provides a useful if occasionally abstract description of the chemical states of natural waters. However, if used to predict the state of redox reactions, especially at low temperature, the model is likely to fail. This shortcoming does not result from any error in formulating the thermodynamic model. Instead, it arises from the fact that redox reactions in natural waters proceed at such slow rates that they commonly remain far from equilibrium. 

A gas in which the pressure no longer depends on the temperature is said to be degenerate, an unfortunate term indeed, because the corresponding state borders on perfection. One might call it a state of perfect fullness, since no interstice is left vacant. Electrons occupy all possible energy states and total order prevails. Both the electrical conductivity and the fluidity also attain perfection. Objects made from this sublime form of matter are perfectly spherical. And yet, in quantum circles, this state of nature is obstinately referred to as degenerate ... 

The basic premise of the Bayesian approach is that observations change the state of knowledge of a system. Let us suppose for simplicity that the item of interest is some parameter, 0, describing a state of nature (as in the above example, where 0 was a property of the coin and the conditions under which it was tossed). Figure 5.1 indicates symbolically the development of knowledge. 

The term Bayesian comes from Thomas Bayes, an 18th-century Presbyterian minister, who wrote An Essay Towards Solving a Problem in the Doctrine of Chances. The meat of the essay was that given some prior knowledge of the state of nature, the probability with which a decision could be made in a particular set of circumstances would be different than if the prior knowledge were not available. 

Perhaps there is a rather tenuous connection between this simple example and experimentation without data. The basic concept is that the presence of the existing knowledge of the state of nature (in this case the distribution of the black and white balls) helps to make a better decision than if we were forced to assume, for lack of information, that each box contained one white and one black ball. 

Because the outcome of a decision often depends on past or future states of nature that cannot be known with certainty, it is reasonable for the decision-maker to weigh the possible outcomes of an action by the probability of the states on which they depend. In many situations, the relevant states of nature are independent of one s choice. Despite numerous anecdotes to the contrary, the probability of rain does not depend on whether one has decided to wash one s car. We shall use the conventional notation for conditional probabilities, P(S/A), to refer to the probability of a state, Sf given act, A. Thus, the state rain is independent of the act car wash in the sense that P SfA) P(S/notA) P(S), the marginal (i.e. pre-decisional) probability of rain. 

Ionic history - The pH history of the protein sample influences its state of naturation and its conformation. 

Political philosophers have traditionally conceived of justice as a relationship among people living within the same nation or state. Plato (1974), for example, held that a just state is rationally ordered. Hobbes (1982) held that principles of justice are rules that people adopt in order to attain the benefits of social cooperation and avoid the dangers of the state of nature. Conceptual problems arise when one extends this standard account of justice to the international domain, because people around the globe are not living in the same nation. The world s five billion people live in more than 150 nations. How can there be justice among people in different nations ... 

IN the state of nature - a fictitious state much discussed by phOosophers and somewhat reminiscent of the island in Wil liam Golding s Lard of the Flies - people live in the present and care only about themselves. As a result, their lives, in Hobbes s memorable phrase, are "solitary, poor, nasty, brutish, and short." No known societies are quite like that. The Ik of Uganda, as described by a social anthropologist who stayed with them for some time, are probably as close to the state of nature as any human group on record, but even they display minimal forms of self-restraint. A major task of the social sciences is to explain why we are not in the state of nature. Here I shall consider foresight - the ability to be motivated by long-term consequences of action - as a possible explanation of self-restraint. Other explanations are discussed later. ... 

This could mean two things. First, if we (or our animal ancestors) ever were in the state of nature, how did we get out of it Second, what prevents us from sliding into it (or back into it) The first question is briefly addressed in chapter VIII, but the main focus is on the second. 

Earlier I said that the social sciences have to explain why we are not in the state of nature. Another challenge is to explain why societies have a modicum of ar /er-why they do not offer "a tale told by an idiot, full of sound and fury, signifying nothing." This phrase from facbeth evokes a different kind of anarchy than that suggested by Hobbes s description of life in the state of nature, as "solitary, poor, nasty, brutish and short." It conveys a lack of coordination rather than a lack of cooperation, chaos rather than nastiness. In the preceding chapter we looked at some ways in which people s plans can be thwarted. But no society could work if everybody s plans were thwarted all the time. Universal frustration of plans would be chaos. 

Each problem - why we are not in the state of nature and why we are not in a state of chaos - could be resolved in two ways. On the one hand, cooperation and coordination may emerge by decentralized, uncoerced action. This is the topic of this chapter and the two following ones. On the other hand, cooperation and coordination may be centrally imposed by social institutions backed by force. This is the topic of chapter XV, where 1 also argue, however, that the distinction is less clear-cut than it might appear. 

DeVun, Leah. "John of Rupescissa and the States of Nature Science, Apocalypse, and Society in the Late Middle Ages." PhD diss., Columbia University, 2004. 

The decision problem is represented by the decision tree in Figure 5, in which open circles represent chance nodes, squares represent decision nodes, and the black circle is a value node. The first decision node is the selection of the sample size n used in the experiment, and c represents the cost per observation. The experiment will generate random data values y that have to be analyzed by an inference method a. The difference between the true state of nature, represented by the fold changes 6 = 9, 9g), and the inference will determine a loss L(-) that is a function of the two decisions n and a, the data, and the experimental costs. There are two choices in this decision problem the optimal sample size and the optimal inference. 

The Holy and Profane States Of Natural Fools Maxim I (p. 171)... 

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