2,458 research outputs found
Environmental Noise Variability in Population Dynamics Matrix Models
The impact of environmental variability on population size growth rate in
dynamic models is a recurrent issue in the theoretical ecology literature. In
the scalar case, R. Lande pointed out that results are ambiguous depending on
whether the noise is added at arithmetic or logarithmic scale, while the matrix
case has been investigated by S. Tuljapurkar. Our contribution consists first
in introducing another notion of variability than the widely used variance or
coefficient of variation, namely the so-called convex orders. Second, in
population dynamics matrix models, we focus on how matrix components depend
functionaly on uncertain environmental factors. In the log-convex case, we show
that, in a sense, environmental variability increases both mean population size
and mean log-population size and makes them more variable. Our main result is
that specific analytical dependence coupled with appropriate notion of
variability lead to wide generic results, valid for all times and not only
asymptotically, and requiring no assumptions of stationarity, of normality, of
independency, etc. Though the approach is different, our conclusions are
consistent with previous results in the literature. However, they make it clear
that the analytical dependence on environmental factors cannot be overlooked
when trying to tackle the influence of variability.Comment: 9 page
Rationally Biased Learning
Are human perception and decision biases grounded in a form of rationality?
You return to your camp after hunting or gathering. You see the grass moving.
You do not know the probability that a snake is in the grass. Should you cross
the grass - at the risk of being bitten by a snake - or make a long, hence
costly, detour? Based on this storyline, we consider a rational decision maker
maximizing expected discounted utility with learning. We show that his optimal
behavior displays three biases: status quo, salience, overestimation of small
probabilities. Biases can be the product of rational behavior
Preferences Yielding the "Precautionary Effect"
Consider an agent taking two successive decisions to maximize his expected
utility under uncertainty. After his first decision, a signal is revealed that
provides information about the state of nature. The observation of the signal
allows the decision-maker to revise his prior and the second decision is taken
accordingly. Assuming that the first decision is a scalar representing
consumption, the \emph{precautionary effect} holds when initial consumption is
less in the prospect of future information than without (no signal).
\citeauthor{Epstein1980:decision} in \citep*{Epstein1980:decision} has provided
the most operative tool to exhibit the precautionary effect. Epstein's Theorem
holds true when the difference of two convex functions is either convex or
concave, which is not a straightforward property, and which is difficult to
connect to the primitives of the economic model. Our main contribution consists
in giving a geometric characterization of when the difference of two convex
functions is convex, then in relating this to the primitive utility model. With
this tool, we are able to study and unite a large body of the literature on the
precautionary effect
Preferences Yielding the ``Precautionary Effect''
Consider an agent taking two successive decisions to maximize his expected utility under uncertainty. After his first decision, a signal is revealed that provides information about the state of nature. The observation of the signal allows the decision-maker to revise his prior and the second decision is taken accordingly. Assuming that the first decision is a scalar representing consumption, the \emph{precautionary effect} holds when initial consumption is less in the prospect of future information than without (no signal). \citeauthor{Epstein1980:decision} in \citep*{Epstein1980:decision} has provided the most operative tool to exhibit the precautionary effect. Epstein's Theorem holds true when the difference of two convex functions is either convex or concave, which is not a straightforward property, and which is difficult to connect to the primitives of the economic model. Our main contribution consists in giving a geometric characterization of when the difference of two convex functions is convex, then in relating this to the primitive utility model. With this tool, we are able to study and unite a large body of the literature on the precautionary effect.value of information; uncertainty; learning; precautionary effect; support function
Precautionary Effect and Variations of the Value of Information
For a sequential, two-period decision problem with uncertainty and under broad conditions (non-finite sample set, endogenous risk, active learning and stochastic dynamics), a general sufficient condition is provided to compare the optimal initial decisions with or without information arrival in the second period. More generally the condition enables the comparison of optimal decisions related to different information structures. It also ties together and clarifies many conditions for the so-called irreversibility effect that are scattered in the environmental economics literature. A numerical illustration with an integrated assessment model of climate-change economics is provided.Value of Information, Uncertainty, Irreversibility effect, Climate change
Risk Assessment Algorithms Based On Recursive Neural Networks
The assessment of highly-risky situations at road intersections have been
recently revealed as an important research topic within the context of the
automotive industry. In this paper we shall introduce a novel approach to
compute risk functions by using a combination of a highly non-linear processing
model in conjunction with a powerful information encoding procedure.
Specifically, the elements of information either static or dynamic that appear
in a road intersection scene are encoded by using directed positional acyclic
labeled graphs. The risk assessment problem is then reformulated in terms of an
inductive learning task carried out by a recursive neural network. Recursive
neural networks are connectionist models capable of solving supervised and
non-supervised learning problems represented by directed ordered acyclic
graphs. The potential of this novel approach is demonstrated through well
predefined scenarios. The major difference of our approach compared to others
is expressed by the fact of learning the structure of the risk. Furthermore,
the combination of a rich information encoding procedure with a generalized
model of dynamical recurrent networks permit us, as we shall demonstrate, a
sophisticated processing of information that we believe as being a first step
for building future advanced intersection safety system
Viable Control of an Epidemiological Model
In mathematical epidemiology, epidemic control often aims at driving the
number of infected individuals to zero, asymptotically. However , during the
transitory phase, the number of infected can peak at high values. In this
paper, we consider mosquito vector control in the Ross-Macdonald
epidemiological model, with the goal of capping the proportion of infected by
dengue at the peak. We formulate this problem as one of control of a dynamical
system under state constraint. We allow for time-dependent fumigation rates to
reduce the population of mosquito vector, in order to maintain the proportion
of infected individuals by dengue below a threshold for all times. The
so-called viability kernel is the set of initial states (mosquitoes and
infected individuals) for which such a fumigation control trajectory exists.
Depending on whether the cap on the proportion of infected is low, high or
medium, we provide different expressions of the viability kernel. We also
characterize so-called viable policies that produce, at each time, a fumigation
rate as a function of current proportions of infected humans and mosquitoes,
such that the proportion of infected humans remains below a threshold for all
times. We provide a numerical application in the case of control of a dengue
outbreak in 2013 in Cali, Colombia
Conditional Value-at-Risk Constraint and Loss Aversion Utility Functions
We provide an economic interpretation of the practice consisting in
incorporating risk measures as constraints in a classic expected return
maximization problem. For what we call the infimum of expectations class of
risk measures, we show that if the decision maker (DM) maximizes the
expectation of a random return under constraint that the risk measure is
bounded above, he then behaves as a ``generalized expected utility maximizer''
in the following sense. The DM exhibits ambiguity with respect to a family of
utility functions defined on a larger set of decisions than the original one;
he adopts pessimism and performs first a minimization of expected utility over
this family, then performs a maximization over a new decisions set. This
economic behaviour is called ``Maxmin under risk'' and studied by Maccheroni
(2002). This economic interpretation allows us to exhibit a loss aversion
factor when the risk measure is the Conditional Value-at-Risk
Conditional Value-at-Risk Constraint and Loss Aversion Utility Functions
We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in a classic expected return maximization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker (DM) maximizes the expectation of a random return under constraint that the risk measure is bounded above, he then behaves as a ``generalized expected utility maximizer'' in the following sense. The DM exhibits ambiguity with respect to a family of utility functions defined on a larger set of decisions than the original one; he adopts pessimism and performs first a minimization of expected utility over this family, then performs a maximization over a new decisions set. This economic behaviour is called ``Maxmin under risk'' and studied by Maccheroni (2002). This economic interpretation allows us to exhibit a loss aversion factor when the risk measure is the Conditional Value-at-Risk.Risk measures; Utility functions; Nonexpected utility theory; Maxmin; Conditional Value-at-Risk; Loss aversion
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