A Bayesian analysis of suicide data

The identification of change points in a sequence of suicide rates is one of the fundamental aspects of Durkheim’s theory. The specification of a statistical standard suitable for this purpose is the main condition for making inferences about the causes of suicide with distinctive trends of persistency and variability just as Durkheim theorized. At present, the statistical ‘strategy’ employed by the French social scientist is too ‘rudimentary’. A hundred years later, I take the opportunity to test Durkheim’s theory through modern methodological instruments, specifically the Bayesian change-point analysis. First of all, I analyzed the same suicide data which Durkheim took into consideration. Change-point analysis corroborates the Durkheimian analysis revealing the same change-points identified by the author. Secondly, I analyzed Italian suicide rates from 1864 to 2005. The change-point analysis was very useful. Durkheim’s theory ‘works’ until 1961: suicides rates increased as industrial development increased. However, after 1961 and the economic boom, they declined, and when they began increasing again, after 1984, they did not reach the same level as before. This finding obliges us to ‘adjust’ the Durkheim’s theory giving space to Halbwach’s convergence law. Therefore, as high economic and social development levels are attained, suicide rates tend to level-off: People adapt to the stress of modernization associated to low social integration levels. Although we are more ‘egoist’, individualism does not destroy identity and the sense of life as Durkheim had maintained.     

Some results on the existence of utility functions on path connected spaces

This paper concerns the existence of utility representations for preferences defined on a path connected space X. This includes any convex set. A classical result of Eilenberg (1941) proves the existence of utility representations when the consumption set is connected and separable. In an infinite dimensional space the above result may not be useful, because we lack, in general, the separability of the space. The non-separable spaces L^∞ and ca(K) are typical examples in mathematical economics. In this paper we show that a continuous preference relation ≽, on X has a continuous utility representation if and only if it is countably bounded, i.e., there is some countable subset F of X such that for all x in X there exist y and z in F with y≽x≽z. An easy corollary states that any continuous preference which has a best and a worst point has a continuous representation. We also obtain a convex continuous preference on a Banach lattice that has not a utility representation, because it is not countably bounded.     

Economies with a mean demand function

The present paper shows one way to look at G. Debreu and W. Hildenbrand's conjecture that certain atomless economies have mean demand functions. We conclude within the continuity framework that an economy gives rise ‘in general’ to a continuous mean demand function, and that the class of all atomless economies is ‘big’ in the space of all economies with a continuous mean demand function. The same problems are reconsidered within the framework of a space of differentiable preferences at the end.     

Continuous representation of a preference relation on a connected topological space

Necessary and sufficient conditions are given for the existence of two continuous real valued functions u and v on a connected topological space X endowed with a preference relation ≺ (i.e., an asymmetric binary relation) such that y is preferred to x if and only if v(y)>u(x). It is shown that these conditions - a slight generalization of the usual ones encountered in classical utility theory - entail the existence of such a continuous representation u, v with u and v continuous utility functions for two complete preorders intimately connected with the preference relation ≺.     

Simple axioms for countably additive subjective probability

This paper refines Savage’s theory of subjective probability for the case of countably additive beliefs. First, I replace his continuity axioms P6 and P7 with a simple modification of Arrow’s (1970) Monotone Continuity. Second, I relax Savage’s primitives: in my framework, the class of events need not be a σ-algebra, and acts need not have finite or bounded range. By varying the domains of acts and events, I obtain a unique extension of preference that parallels Caratheodory’s unique extension of probability measures. Aside from subjective expected utility, I characterize exponential time discounting in a setting with continuous time and an arbitrary consumption set.     

Rationalizability in continuous games

Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff function of each player is bounded and continuous. We prove that in this class of games the process of sequentially eliminating “never-best-reply” strategies terminates before or at the first uncountable ordinal, and this bound is tight. Also, we examine the connection between this process and common belief of rationality in the universal type space of Mertens and Zamir (1985).     

Nash implementation via simple stochastic mechanisms: strategy space reduction

Beno?t and Ok (Games Econ Behav 64:51–67, 2008) show that in a society with at least three agents any weakly unanimous social choice correspondence (SCC) is Maskin’s monotonic if and only if it is Nash-implementable via a simple stochastic mechanism (Beno?t-Ok’s Theorem). This paper fully identifies the class of weakly unanimous SCCs that are Nash-implementable via a simple stochastic mechanism endowed with Saijo’s message space specification (Saijo in Econometrica 56:693–700, 1988). It is shown that this class of SCCs is equivalent to the class of SCCs that are Nash-implementable via Beno?t-Ok’s Theorem.     

How risky is a random process?

The riskiness of random processes is compared by (a) employing a decision theoretic equivalence between processes and lotteries on path-spaces to identify the riskiness of the former with that of the latter, and (b) using the theory of comparative riskiness of lotteries over vector spaces to compare the riskiness of lotteries on a given path-space. We derive the equivalence used in step (a) and contribute a new criterion to the theory applied in step (b). The validity of the new criterion, which applies second order stochastic dominance to utility distributions, is established by showing its equivalence to the benchmark decision theoretic criterion when comparing the riskiness of lotteries over any vector space. We demonstrate the theory’s tractability via diverse economic applications.     

On the demand generated by a smooth and concavifiable preference ordering

It is shown that if a consumer's preference ordering is strictly convex and is representable by means of a concave, twice continuously differentiable utility function, then the partial derivative of a demanded commodity with respect to its price is bounded from above in a neighborhood of a price vector at which the demand fails to be differentiable. In the case of two commodities, if the demand does not possess finite derivatives with respect to prices at a certain point, then the partial ‘derivative’ of a commodity with respect to its price is equal to minus infinity. The same result holds for n commodities under ‘almost every’ choice of coordinates in the commodity space. If preferences are weakly convex but the same representation assumption holds, demand may not be single-valued but own-price difference quotients are still bounded from above.     

Utility theory based on rational probabilities

Classical utility theory assumes that a preference order is defined for all mixtures αa+(1?α)b of pure prospects a,b for all real numbers α between 0 and 1. If α is irrational such mixtures are hard to interpret intuitively. We show here how to modify the usual axiomatisations to deal with the case where α is restricted to rational values, or even further to values of the form m/2ⁿ corresponding to mixtures built up from even bets.     

On aggregation and welfare analysis

In this article, the beginnings of a new approach to the theory of aggregation are developed. The basic idea is that aggregation should involve two things: (a) data over which social preferences are defined should be mapped into a smaller-dimensional space, and (b) there should exist an ordering on that lower-dimensional space such that an improvement in this criterion implies an improvement for any of a class of social preference functions and of a class of individual preference relations defined over the original space. Results are developed which show that this conception of aggregation can yield meaningful results; particularly with respect to comparisons of ‘real national income’ in two situations, for a given economy.     

On continuous utility functions derived from demand functions

In the theory of revealed preference and in the approach to integrability theory of Hurwicz and Uzawa certain conditions are proposed implying the existence of a utility function generating the given demand function. This article presents a hypothesis which, under supposition of some well-known axioms of those models, is necessary and sufficient for the existence of a continuous utility function. This hypothesis implies the existence of a utility function u with the property that all of the boundary points of the set $\text{{x|u(x)≧α}}$ for every $\text{α?}\text{R}$ are lower boundary points, being fundamental for the continuity of the utility function.     

Causality in social theory via linguistic fuzzy logic

I present a new approach to the study of causality in social theory using linguistic fuzzy logic as a framework. This approach differs from conventional analysis of causality on two fronts. First, all variables are considered to possess two degrees of freedom (or variation): a linguistic nuance value, which corresponds to what we conventionally refer to as interval or categorical value, and a linguistic truth value, which measures our confidence level in this nuance value. Second, combining this double fuzzification of variables with linguistic fuzzy logic I propose new tools for studying fuzzy causality. The linguistic fuzzy logic approach is illustrated through a re-examination of Skocpol’s (1979, States and social revolutions: a comparative analysis of France, Russia, and China. Cambridge University Press, Cambridge) theory of social revolution.     

Characterizing lexicographic preferences

We characterize lexicographic preferences on product sets of finitely many coordinates. The main new axiom is a robustness property. It roughly requires this: Suppose $x$ is preferred to $y$; many of its coordinates indicate that the former is better and only a few indicate the opposite. Then the decision maker is allowed a change of mind turning one coordinate in favor of $x$ to an indifference: even if one less argument supports the preference, the fact that we started with many arguments in favor of $x$ suggests that such a small change is not enough to give rise to the opposite preference.     

Generic properties of simple Bergson-Samuelson welfare functions

Methods of transversality theory are introduced to determine the generic properties of a simple non-collegial preference function σ, whose domain is the class of ordinal utility profiles on a smooth manifold W of policy alternatives. When the dimension of W is sufficiently large, it is shown that (i) the set of local optima of σ is generically empty, and (ii) the local cycle set of σ is generically dense.     

The Monty Hall problem is not a probability puzzle* (It's a challenge in mathematical modelling)

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, ‘Do you want to pick door No. 2?’ Is it to your advantage to switch your choice? The answer is ‘yes’ but the literature offers many reasons why this is the correct answer. This article argues that the most common reasoning found in introductory statistics texts, depending on making a number of ‘obvious’ or ‘natural’ assumptions and then computing a conditional probability, is a classical example of solution driven science. The best reason to switch is to be found in von Neumann's minimax theorem from game theory, rather than in Bayes’ theorem.     

Revealed preference test and shortest path problem; graph theoretic structure of the rationalizability test

This paper presents some substantial relationships between the revealed preference test for a data set and the shortest path problem of a weighted graph. We give a unified perspective of several forms of rationalizability tests based on the shortest path problem and an additional graph theoretic structure, which we call the shortest path problem with weight adjustment. Furthermore, the proposed structure is used to extend the result of Quah (2014), which sharpened classical Afriat’s Theorem-type results.     

Enhancing capacity planning through forecasting: An integrated tool for maintenance of complex product systems

Despite the extensive amount of data generated and stored during the maintenance capacity planning process, Maintenance, Repair, and Overhaul (MRO) organizations have yet to explore their full potential in forecasting the required capacity to face future and unprecedented maintenance interventions. This paper explores the integration of time series forecasting capabilities in a tool for maintenance capacity planning of complex product systems (CoPS), intended to value data that is routinely generated and stored, but often disregarded by MROs. State space formulations with multiplicative errors for the simple exponential smoothing (SES), Holt’s linear method (HLM), additive Holt-Winters (AHW), and multiplicative Holt-Winters (MHW) are assessed using real data, comprised of 171 maintenance projects collected from a major Portuguese aircraft MRO. A state space formulation of the MHW, selected using the bias-corrected Akaike information criterion (AICc), is integrated in a Decision Support System (DSS) for capacity planning with probabilistic inference capabilities and used to forecast the workload probability distribution of a future and unprecedent maintenance intervention. The developed tool is validated by comparing forecasted values with workloads of a particular maintenance intervention and with a model simulating current forecasting practices employed by MROs.