210,101 research outputs found
Multivariate Bernoulli distribution
In this paper, we consider the multivariate Bernoulli distribution as a model
to estimate the structure of graphs with binary nodes. This distribution is
discussed in the framework of the exponential family, and its statistical
properties regarding independence of the nodes are demonstrated. Importantly
the model can estimate not only the main effects and pairwise interactions
among the nodes but also is capable of modeling higher order interactions,
allowing for the existence of complex clique effects. We compare the
multivariate Bernoulli model with existing graphical inference models - the
Ising model and the multivariate Gaussian model, where only the pairwise
interactions are considered. On the other hand, the multivariate Bernoulli
distribution has an interesting property in that independence and
uncorrelatedness of the component random variables are equivalent. Both the
marginal and conditional distributions of a subset of variables in the
multivariate Bernoulli distribution still follow the multivariate Bernoulli
distribution. Furthermore, the multivariate Bernoulli logistic model is
developed under generalized linear model theory by utilizing the canonical link
function in order to include covariate information on the nodes, edges and
cliques. We also consider variable selection techniques such as LASSO in the
logistic model to impose sparsity structure on the graph. Finally, we discuss
extending the smoothing spline ANOVA approach to the multivariate Bernoulli
logistic model to enable estimation of non-linear effects of the predictor
variables.Comment: Published in at http://dx.doi.org/10.3150/12-BEJSP10 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Modelling heterogeneity in response behaviour towards a sequence of discrete choice questions: a latent class approach
There is a growing body of evidence in the non-market valuation literature suggesting that responses to a sequence of discrete choice questions tend to violate the assumptions typically made by analysts regarding independence of responses and stability of preferences. Heuristics such as value learning and strategic misrepresentation have been offered as explanations for these results. While a few studies have tested these heuristics as competing hypotheses, none have investigated the possibility that each explains the response behaviour of a subgroup of the population. In this paper, we make a contribution towards addressing this research gap by presenting an equality-constrained latent class model designed to estimate the proportion of respondents employing each of the proposed heuristics. We demonstrate the model on binary and multinomial choice data sources and find three distinct types of response behaviour. The results suggest that accounting for heterogeneity in response behaviour may be a better way forward than attempting to identify a single heuristic to explain the behaviour of all respondents
Partially-commutative context-free languages
The paper is about a class of languages that extends context-free languages
(CFL) and is stable under shuffle. Specifically, we investigate the class of
partially-commutative context-free languages (PCCFL), where non-terminal
symbols are commutative according to a binary independence relation, very much
like in trace theory. The class has been recently proposed as a robust class
subsuming CFL and commutative CFL. This paper surveys properties of PCCFL. We
identify a natural corresponding automaton model: stateless multi-pushdown
automata. We show stability of the class under natural operations, including
homomorphic images and shuffle. Finally, we relate expressiveness of PCCFL to
two other relevant classes: CFL extended with shuffle and trace-closures of
CFL. Among technical contributions of the paper are pumping lemmas, as an
elegant completion of known pumping properties of regular languages, CFL and
commutative CFL.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244
Binary Independent Component Analysis with OR Mixtures
Independent component analysis (ICA) is a computational method for separating
a multivariate signal into subcomponents assuming the mutual statistical
independence of the non-Gaussian source signals. The classical Independent
Components Analysis (ICA) framework usually assumes linear combinations of
independent sources over the field of realvalued numbers R. In this paper, we
investigate binary ICA for OR mixtures (bICA), which can find applications in
many domains including medical diagnosis, multi-cluster assignment, Internet
tomography and network resource management. We prove that bICA is uniquely
identifiable under the disjunctive generation model, and propose a
deterministic iterative algorithm to determine the distribution of the latent
random variables and the mixing matrix. The inverse problem concerning
inferring the values of latent variables are also considered along with noisy
measurements. We conduct an extensive simulation study to verify the
effectiveness of the propose algorithm and present examples of real-world
applications where bICA can be applied.Comment: Manuscript submitted to IEEE Transactions on Signal Processin
Modelling heterogeneity in response behaviour towards a sequence of discrete choice questions: a probabilistic decision process model
There is a growing body of evidence in the non-market valuation literature suggesting that responses to a sequence of discrete choice questions tend to violate the assumptions typically made by analysts regarding independence of responses and stability of preferences. Decision processes (or heuristics) such as value learning and strategic misrepresentation have been offered as explanations for these results. While a few studies have tested these heuristics as competing hypotheses, none has investigated the possibility that each explains the response behaviour of a subgroup of the population. In this paper, we make a contribution towards addressing this research gap by presenting a probabilistic decision process model designed to estimate the proportion of respondents employing defined heuristics. We demonstrate the model on binary and multinomial choice data sources and find three distinct types of response behaviour. The results suggest that accounting for heterogeneity in response behaviour may be a better way forward than attempting to identify a single heuristic to explain the behaviour of all respondents.Choice experiment, decision process, ordering effects, strategic response, willingness to pay, Research Methods/ Statistical Methods, C25, L94, Q51,
Modelling heterogeneity in response behaviour towards a sequence of discrete choice questions: a latent class approach
There is a growing body of evidence in the non-market valuation literature suggesting that responses to a sequence of discrete choice questions tend to violate the assumptions typically made by analysts regarding independence of responses and stability of preferences. Heuristics such as value learning and strategic misrepresentation have been offered as explanations for these results. While a few studies have tested these heuristics as competing hypotheses, none have investigated the possibility that each explains the response behaviour of a subgroup of the population. In this paper, we make a contribution towards addressing this research gap by presenting an equality-constrained latent class model designed to estimate the proportion of respondents employing each of the proposed heuristics. We demonstrate the model on binary and multinomial choice data sources and find three distinct types of response behaviour. The results suggest that accounting for heterogeneity in response behaviour may be a better way forward than attempting to identify a single heuristic to explain the behaviour of all respondents.Choice experiment; latent class; ordering effects; strategic response; willingness-to-pay
Parameters estimation for asymmetric bifurcating autoregressive processes with missing data
We estimate the unknown parameters of an asymmetric bifurcating
autoregressive process (BAR) when some of the data are missing. In this aim, we
model the observed data by a two-type Galton-Watson process consistent with the
binary tree structure of the data. Under independence between the process
leading to the missing data and the BAR process and suitable assumptions on the
driven noise, we establish the strong consistency of our estimators on the set
of non-extinction of the Galton-Watson, via a martingale approach. We also
prove a quadratic strong law and the asymptotic normality
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