Search results for " Probability"
showing 10 items of 2176 documents
Backwards Martingales and Exchangeability
2020
With many data acquisitions, such as telephone surveys, the order in which the data come does not matter. Mathematically, we say that a family of random variables is exchangeable if the joint distribution does not change under finite permutations. De Finetti’s structural theorem says that an infinite family of E-valued exchangeable random variables can be described by a two-stage experiment. At the first stage, a probability distribution Ξ on E is drawn at random. At the second stage, independent and identically distributed random variables with distribution Ξ are implemented.
Forward and backward diffusion approximations for haploid exchangeable population models
2001
Abstract The class of haploid population models with non-overlapping generations and fixed population size N is considered such that the family sizes ν1,…,νN within a generation are exchangeable random variables. A criterion for weak convergence in the Skorohod sense is established for a properly time- and space-scaled process counting the number of descendants forward in time. The generator A of the limit process X is constructed using the joint moments of the offspring variables ν1,…,νN. In particular, the Wright–Fisher diffusion with generator Af(x)= 1 2 x(1−x)f″(x) appears in the limit as the population size N tends to infinity if and only if the condition lim N→∞ E((ν 1 −1) 3 )/(N Var …
Bayesian forecasting of demand time-series data with zero values
2013
This paper describes the development of a Bayesian procedure to analyse and forecast positive demand time-series data with a proportion of zero values and a high level of variability for the non-zero data. The resulting forecasts play decisive roles in organisational planning, budgeting, and performance monitoring. Exponential smoothing methods are widely used as forecasting techniques in industry and business. However, they can be unsuitable for the analysis of non-negative demand time-series data with the aforementioned features. In this paper, an unconstrained latent demand underlying the observed demand is introduced into the linear heteroscedastic model associated with the Holt-Winters…
ISARIC-COVID-19 dataset: A Prospective, Standardized, Global Dataset of Patients Hospitalized with COVID-19
2022
The International Severe Acute Respiratory and Emerging Infection Consortium (ISARIC) COVID-19 dataset is one of the largest international databases of prospectively collected clinical data on people hospitalized with COVID-19. This dataset was compiled during the COVID-19 pandemic by a network of hospitals that collect data using the ISARIC-World Health Organization Clinical Characterization Protocol and data tools. The database includes data from more than 705,000 patients, collected in more than 60 countries and 1,500 centres worldwide. Patient data are available from acute hospital admissions with COVID-19 and outpatient follow-ups. The data include signs and symptoms, pre-existing como…
On the use of approximate Bayesian computation Markov chain Monte Carlo with inflated tolerance and post-correction
2020
Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often sensitive to the tolerance parameter: low tolerance leads to poor mixing and large tolerance entails excess bias. We consider an approach using a relatively large tolerance for the Markov chain Monte Carlo sampler to ensure its sufficient mixing, and post-processing the output leading to estimators for a range of finer tolerances. We introduce an approximate confidence interval for the related post-corrected estimators, and propose an adaptive approximate Bayesi…
Core of communities in bipartite networks
2017
We use the information present in a bipartite network to detect cores of communities of each set of the bipartite system. Cores of communities are found by investigating statistically validated projected networks obtained using information present in the bipartite network. Cores of communities are highly informative and robust with respect to the presence of errors or missing entries in the bipartite network. We assess the statistical robustness of cores by investigating an artificial benchmark network, the co-authorship network, and the actor-movie network. The accuracy and precision of the partition obtained with respect to the reference partition are measured in terms of the adjusted Ran…
Selectivity in Probabilistic Causality: Drawing Arrows from Inputs to Stochastic Outputs
2011
Given a set of several inputs into a system (e.g., independent variables characterizing stimuli) and a set of several stochastically non-independent outputs (e.g., random variables describing different aspects of responses), how can one determine, for each of the outputs, which of the inputs it is influenced by? The problem has applications ranging from modeling pairwise comparisons to reconstructing mental processing architectures to conjoint testing. A necessary and sufficient condition for a given pattern of selective influences is provided by the Joint Distribution Criterion, according to which the problem of "what influences what" is equivalent to that of the existence of a joint distr…
Probabilistic entailment in the setting of coherence: The role of quasi conjunction and inclusion relation
2013
In this paper, by adopting a coherence-based probabilistic approach to default reasoning, we focus the study on the logical operation of quasi conjunction and the Goodman-Nguyen inclusion relation for conditional events. We recall that quasi conjunction is a basic notion for defining consistency of conditional knowledge bases. By deepening some results given in a previous paper we show that, given any finite family of conditional events F and any nonempty subset S of F, the family F p-entails the quasi conjunction C(S); then, given any conditional event E|H, we analyze the equivalence between p-entailment of E|H from F and p-entailment of E|H from C(S), where S is some nonempty subset of F.…
Uncommon Suffix Tries
2011
Common assumptions on the source producing the words inserted in a suffix trie with $n$ leaves lead to a $\log n$ height and saturation level. We provide an example of a suffix trie whose height increases faster than a power of $n$ and another one whose saturation level is negligible with respect to $\log n$. Both are built from VLMC (Variable Length Markov Chain) probabilistic sources; they are easily extended to families of sources having the same properties. The first example corresponds to a ''logarithmic infinite comb'' and enjoys a non uniform polynomial mixing. The second one corresponds to a ''factorial infinite comb'' for which mixing is uniform and exponential.
Transitive reasoning with imprecise probabilities
2015
We study probabilistically informative (weak) versions of transitivity, by using suitable definitions of defaults and negated defaults, in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Finally, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving the p-entailment for the associated knowledge bases.