56,949 research outputs found
The Prior Can Often Only Be Understood in the Context of the Likelihood
A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys’ priors, reference priors, maximum entropy priors, and weakly informative priors. These methods, however, often manifest a key conceptual tension in prior modeling: a model encoding true prior information should be chosen without reference to the model of the measurement process, but almost all common prior modeling techniques are implicitly motivated by a reference likelihood. In this paper we resolve this apparent paradox by placing the choice of prior into the context of the entire Bayesian analysis, from inference to prediction to model evaluation
LHC and dark matter phenomenology of the NUGHM
We present a Bayesian analysis of the NUGHM, a supersymmetric scenario with
non-universal gaugino masses and Higgs masses, including all the relevant
experimental observables and dark matter constraints. The main merit of the
NUGHM is that it essentially includes all the possibilities for dark matter
(DM) candidates within the MSSM, since the neutralino and chargino spectrum
-and composition- are as free as they can be in the general MSSM. We identify
the most probable regions in the NUHGM parameter space, and study the
associated phenomenology at the LHC and the prospects for DM direct detection.
Requiring that the neutralino makes all of the DM in the Universe, we identify
two preferred regions around ,
which correspond to the (almost) pure Higgsino and wino case. There exist other
marginal regions (e.g. Higgs-funnel), but with much less statistical weight.
The prospects for detection at the LHC in this case are quite pessimistic, but
future direct detection experiments like LUX and XENON1T, will be able to probe
this scenario. In contrast, when allowing other DM components, the prospects
for detection at the LHC become more encouraging -- the most promising signals
being, beside the production of gluinos and squarks, the production of the
heavier chargino and neutralino states, which lead to WZ and same-sign WW final
states -- and direct detection remains a complementary, and even more powerful,
way to probe the scenario.Comment: The Sommerfeld enhancement has been included in the computation of
the relic density and in the discussion of indirect-detection limits. Some
references have been adde
Entropy and inference, revisited
We study properties of popular near-uniform (Dirichlet) priors for learning
undersampled probability distributions on discrete nonmetric spaces and show
that they lead to disastrous results. However, an Occam-style phase space
argument expands the priors into their infinite mixture and resolves most of
the observed problems. This leads to a surprisingly good estimator of entropies
of discrete distributions.Comment: LaTex2e, 9 pages, 5 figures; references added, minor revisions
introduced, formatting errors correcte
Bayesian games with a continuum of states
We show that every Bayesian game with purely atomic
types has a measurable Bayesian equilibrium when the common knowl-
edge relation is smooth. Conversely, for any common knowledge rela-
tion that is not smooth, there exists a type space that yields this common
knowledge relation and payoffs such that the resulting Bayesian game
will not have any Bayesian equilibrium. We show that our smoothness
condition also rules out two paradoxes involving Bayesian games with
a continuum of types: the impossibility of having a common prior on
components when a common prior over the entire state space exists, and
the possibility of interim betting/trade even when no such trade can be
supported
ex ante
Learning without Recall: A Case for Log-Linear Learning
We analyze a model of learning and belief formation in networks in which
agents follow Bayes rule yet they do not recall their history of past
observations and cannot reason about how other agents' beliefs are formed. They
do so by making rational inferences about their observations which include a
sequence of independent and identically distributed private signals as well as
the beliefs of their neighboring agents at each time. Fully rational agents
would successively apply Bayes rule to the entire history of observations. This
leads to forebodingly complex inferences due to lack of knowledge about the
global network structure that causes those observations. To address these
complexities, we consider a Learning without Recall model, which in addition to
providing a tractable framework for analyzing the behavior of rational agents
in social networks, can also provide a behavioral foundation for the variety of
non-Bayesian update rules in the literature. We present the implications of
various choices for time-varying priors of such agents and how this choice
affects learning and its rate.Comment: in 5th IFAC Workshop on Distributed Estimation and Control in
Networked Systems, (NecSys 2015
Bayes and empirical Bayes: do they merge?
Bayesian inference is attractive for its coherence and good frequentist
properties. However, it is a common experience that eliciting a honest prior
may be difficult and, in practice, people often take an {\em empirical Bayes}
approach, plugging empirical estimates of the prior hyperparameters into the
posterior distribution. Even if not rigorously justified, the underlying idea
is that, when the sample size is large, empirical Bayes leads to "similar"
inferential answers. Yet, precise mathematical results seem to be missing. In
this work, we give a more rigorous justification in terms of merging of Bayes
and empirical Bayes posterior distributions. We consider two notions of
merging: Bayesian weak merging and frequentist merging in total variation.
Since weak merging is related to consistency, we provide sufficient conditions
for consistency of empirical Bayes posteriors. Also, we show that, under
regularity conditions, the empirical Bayes procedure asymptotically selects the
value of the hyperparameter for which the prior mostly favors the "truth".
Examples include empirical Bayes density estimation with Dirichlet process
mixtures.Comment: 27 page
Supersymmetry Without Prejudice
We begin an exploration of the physics associated with the general
CP-conserving MSSM with Minimal Flavor Violation, the pMSSM. The 19 soft SUSY
breaking parameters in this scenario are chosen so as to satisfy all existing
experimental and theoretical constraints assuming that the WIMP is a
conventional thermal relic, ie, the lightest neutralino. We scan this parameter
space twice using both flat and log priors for the soft SUSY breaking mass
parameters and compare the results which yield similar conclusions. Detailed
constraints from both LEP and the Tevatron searches play a particularly
important role in obtaining our final model samples. We find that the pMSSM
leads to a much broader set of predictions for the properties of the SUSY
partners as well as for a number of experimental observables than those found
in any of the conventional SUSY breaking scenarios such as mSUGRA. This set of
models can easily lead to atypical expectations for SUSY signals at the LHC.Comment: 61 pages, 24 figs. Refs., figs, and text added, typos fixed; This
version has reduced/bitmapped figs. For a version with better figs please go
to http://www.slac.stanford.edu/~rizz
MSSM Forecast for the LHC
We perform a forecast of the MSSM with universal soft terms (CMSSM) for the
LHC, based on an improved Bayesian analysis. We do not incorporate ad hoc
measures of the fine-tuning to penalize unnatural possibilities: such
penalization arises from the Bayesian analysis itself when the experimental
value of is considered. This allows to scan the whole parameter space,
allowing arbitrarily large soft terms. Still the low-energy region is
statistically favoured (even before including dark matter or g-2 constraints).
Contrary to other studies, the results are almost unaffected by changing the
upper limits taken for the soft terms. The results are also remarkable stable
when using flat or logarithmic priors, a fact that arises from the larger
statistical weight of the low-energy region in both cases. Then we incorporate
all the important experimental constrains to the analysis, obtaining a map of
the probability density of the MSSM parameter space, i.e. the forecast of the
MSSM. Since not all the experimental information is equally robust, we perform
separate analyses depending on the group of observables used. When only the
most robust ones are used, the favoured region of the parameter space contains
a significant portion outside the LHC reach. This effect gets reinforced if the
Higgs mass is not close to its present experimental limit and persits when dark
matter constraints are included. Only when the g-2 constraint (based on
data) is considered, the preferred region (for ) is well inside
the LHC scope. We also perform a Bayesian comparison of the positive- and
negative- possibilities.Comment: 42 pages: added figures and reference
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