1,721,006 research outputs found
A Bayesian model averaging approach with non-informative priors for cost-effectiveness analyses in health economics
No full textWe consider the problem of assessing new and existing technologies for their cost-effectiveness in
the case where data on both costs and effects are available from a clinical trial, and we address it by
means of the cost-effectiveness acceptability curve. The main difficulty in these analyses is that cost
data usually exhibit highly skew and heavy-tailed distributions, so that it can be extremely difficult to
produce realistic probabilistic models for the underlying population distribution, and in particular to
model accurately the tail of the distribution, which is highly influential in estimating the population
mean. Here, in order to integrate the uncertainty about the model into the analysis of cost data
and into cost-effectiveness analyses, we consider an approach based on Bayesian model averaging in
the particular case of weak prior informations about the unknown parameters of the different models
involved in the procedure. The main consequence of this assumption is that the marginal densities
required by Bayesian model averaging are undetermined. However in accordance with the theory of
partial Bayes factors and in particular of fractional Bayes factors, we suggest replacing each marginal
density with a ratio of integrals, that can be efficiently computed via Path Sampling. The results in
terms of cost-effectiveness are compared with those obtained with a semi-parametric approach that
does not require any assumption about the distribution of costs
A Bayesian model averaging approach with non-informative priors for cost-effectiveness analyses
No full textWe consider the problem of assessing new and existing technologies for their cost-effectiveness in the case where data on both costs and effects are available from a clinical trial, and we address it by means of the cost-effectiveness acceptability curve. The main difficulty in these analyses is that cost data usually exhibit highly skew and heavy-tailed distributions, so that it can be extremely difficult to produce realistic probabilistic models for the underlying population distribution. Here, in order to integrate the uncertainty about the model into the analysis of cost data and into cost-effectiveness analyses, we consider an approach based on Bayesian model averaging in the particular case of weak prior informations about the unknown parameters of the different models involved in the procedure. The main consequence of this assumption is that the marginal densities required by Bayesian model averaging are undetermined. However, in accordance with the theory of partial Bayes factors and in particular of fractional Bayes factors, we suggest replacing each marginal density with a ratio of integrals, that can be efficiently computed via Path Sampling
Sensitivity of the fractional Bayes factor to prior distributions
No full textCalculation of a suitable Bayes factor is required for Bayesian model comparison. The fractional Bayes factor is one of several alternative Bayes factors that have been introduced in recent years to address the problem of sensitivity of the usual Bayes factor when prior information is weak. Sensitivity of the fractional Bayes factor with respect to prior distributions is easy to assess when these are proper. On the other hand, when the priors are improper, most methods lead to trivial answers. Also, earlier work on fractional Bayes factors has assumed that sensitivity will be reduced if the training fraction, b, is increased, but this has only been justified by appeal to heuristic reasoning and simple examples. In this paper we derive a measure of the sensitivity of the fractional Bayes factor with respect to improper priors, and prove that it is a decreasing function of b in a class of problems
An alternative bayes factor for testing for unit autoregressive roots
No full textIn this paper we deal with the identification of an autoregressive model for
an observed time series, and the detection of a unit root in its
characteristic polynomial. This is a big issue concerned with distinguishing
stationary time series from time series for which differencing is required to
induce stationarity. We consider a Bayesian approach, and particular attention
is devoted to the problem of the sensitivity of the standard Bayesian analysis
with respect to the choice of the prior distribution for the autoregressive coefficients
Fractional Bayes factors for the analysis of autoregressive models with possible unit roots
No full textIn this paper we
consider the problem of identifying an autoregressive model for an observed
time series and detecting a possible unit root in its characteristic
polynomial. This is a big issue concerned with distinguishing stationary
time series from time series for which differencing is required to induce
stationarity. We adopt the Bayes approach and assume that the prior
information about the parameters of the models is weak. For the comparison of the models in this setting we introduce a modified version of
the fractional Bayes factor
Comparing parametric and semi-parametric approaches for bayesian cost-effectiveness analyses in health economics
No full textWe consider the problem of assessing new and existing technologies for their
cost-effectiveness in the case where data on both costs and effects are available from a
clinical trial, and we address it by means of the cost-effectiveness acceptability curve. The
main difficulty in these analyses is that cost data usually exhibit highly skew and heavytailed
distributions, so that it can be extremely difficult to produce realistic probabilistic
models for the underlying population distribution, and in particular to model accurately the
tail of the distribution, which is highly influential in estimating the population mean. Here,
in order to integrate the uncertainty about the model into the analysis of cost data and into
cost-effectiveness analyses, we consider an approach based on Bayesian model averaging:
instead of choosing a single parametric model, we specify a set of plausible models for
costs and estimate the mean cost with its posterior expectation, that can be obtained as
a weighted mean of the posterior expectations under each model, with weights given by
the posterior model probabilities. The results are compared with those obtained with a
semi-parametric approach that does not require any assumption about the distribution of
costs
A note on Bayesian hypothesis testing for the scalar skew-normal distribution
No full textThe skew-normal distribution is a class of densities that preserves some
useful properties of the normal distribution while allowing a shape parameter to account
for skewness. It has various remarkable properties in terms of mathematical
tractability and turned out to be quite useful in modelling real data. However from
an inferential point of view its use gives raise to many difficulties, that are intrinsically
tied with the shape of the likelihood function. This fact suggests to solve the
problem by calibrating the likelihood with a weight function, and perhaps the most
intuitive calibration can be obtained in the Bayesian framework, where the prior distribution
plays naturally the role of the weight function. Here we consider in details
the problem of testing normality in the general skew-normal model, and solve it by
means of different tools for hypothesis testing in the Bayesian framework, namely
the Bayes factor and the Jeffreys divergence, pointing out benefits and problems of
both approaches
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