13,773 research outputs found
Bayesian Analysis of ODE's: solver optimal accuracy and Bayes factors
In most relevant cases in the Bayesian analysis of ODE inverse problems, a
numerical solver needs to be used. Therefore, we cannot work with the exact
theoretical posterior distribution but only with an approximate posterior
deriving from the error in the numerical solver. To compare a numerical and the
theoretical posterior distributions we propose to use Bayes Factors (BF),
considering both of them as models for the data at hand. We prove that the
theoretical vs a numerical posterior BF tends to 1, in the same order (of the
step size used) as the numerical forward map solver does. For higher order
solvers (eg. Runge-Kutta) the Bayes Factor is already nearly 1 for step sizes
that would take far less computational effort. Considerable CPU time may be
saved by using coarser solvers that nevertheless produce practically error free
posteriors. Two examples are presented where nearly 90% CPU time is saved while
all inference results are identical to using a solver with a much finer time
step.Comment: 28 pages, 6 figure
A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting
This paper explores and develops alternative statistical representations and
estimation approaches for dynamic mortality models. The framework we adopt is
to reinterpret popular mortality models such as the Lee-Carter class of models
in a general state-space modelling methodology, which allows modelling,
estimation and forecasting of mortality under a unified framework. Furthermore,
we propose an alternative class of model identification constraints which is
more suited to statistical inference in filtering and parameter estimation
settings based on maximization of the marginalized likelihood or in Bayesian
inference. We then develop a novel class of Bayesian state-space models which
incorporate apriori beliefs about the mortality model characteristics as well
as for more flexible and appropriate assumptions relating to heteroscedasticity
that present in observed mortality data. We show that multiple period and
cohort effect can be cast under a state-space structure. To study long term
mortality dynamics, we introduce stochastic volatility to the period effect.
The estimation of the resulting stochastic volatility model of mortality is
performed using a recent class of Monte Carlo procedure specifically designed
for state and parameter estimation in Bayesian state-space models, known as the
class of particle Markov chain Monte Carlo methods. We illustrate the framework
we have developed using Danish male mortality data, and show that incorporating
heteroscedasticity and stochastic volatility markedly improves model fit
despite an increase of model complexity. Forecasting properties of the enhanced
models are examined with long term and short term calibration periods on the
reconstruction of life tables.Comment: 46 page
A nonparametric Bayesian approach to the rare type match problem
The "rare type match problem" is the situation in which the suspect's DNA
profile, matching the DNA profile of the crime stain, is not in the database of
reference. The evaluation of this match in the light of the two competing
hypotheses (the crime stain has been left by the suspect or by another person)
is based on the calculation of the likelihood ratio and depends on the
population proportions of the DNA profiles, that are unknown. We propose a
Bayesian nonparametric method that uses a two-parameter Poisson Dirichlet
distribution as a prior over the ranked population proportions, and discards
the information about the names of the different DNA profiles. This fits very
well the data coming from European Y-STR DNA profiles, and the calculation of
the likelihood ratio becomes quite simple thanks to a justified Empirical Bayes
approach.Comment: arXiv admin note: text overlap with arXiv:1506.0844
Did smallpox reduce height?: stature and the standard of living in London, 1770-1873.
In this paper, we re-examine the effect of smallpox on the height attained by those who suffered from this disease. To this end, we analyse a dataset assembled by Floud, Wachter and Gregory on the height of recruits into the Marine Society, 1770-1873. Using both time series and cross-sectional analysis, we show that smallpox was indeed an important determinant of height: those who had suffered from smallpox were significantly shorter. This suggests that the increase in heights documented by Floud et al. may be explained not just by increased nutritional intake, but also by the eradication of smallpox.
Subsampling MCMC - An introduction for the survey statistician
The rapid development of computing power and efficient Markov Chain Monte
Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics,
making it a highly practical inference method in applied work. However, MCMC
algorithms tend to be computationally demanding, and are particularly slow for
large datasets. Data subsampling has recently been suggested as a way to make
MCMC methods scalable on massively large data, utilizing efficient sampling
schemes and estimators from the survey sampling literature. These developments
tend to be unknown by many survey statisticians who traditionally work with
non-Bayesian methods, and rarely use MCMC. Our article explains the idea of
data subsampling in MCMC by reviewing one strand of work, Subsampling MCMC, a
so called pseudo-marginal MCMC approach to speeding up MCMC through data
subsampling. The review is written for a survey statistician without previous
knowledge of MCMC methods since our aim is to motivate survey sampling experts
to contribute to the growing Subsampling MCMC literature.Comment: Accepted for publication in Sankhya A. Previous uploaded version
contained a bug in generating the figures and reference
Statistical Inference for Partially Observed Markov Processes via the R Package pomp
Partially observed Markov process (POMP) models, also known as hidden Markov
models or state space models, are ubiquitous tools for time series analysis.
The R package pomp provides a very flexible framework for Monte Carlo
statistical investigations using nonlinear, non-Gaussian POMP models. A range
of modern statistical methods for POMP models have been implemented in this
framework including sequential Monte Carlo, iterated filtering, particle Markov
chain Monte Carlo, approximate Bayesian computation, maximum synthetic
likelihood estimation, nonlinear forecasting, and trajectory matching. In this
paper, we demonstrate the application of these methodologies using some simple
toy problems. We also illustrate the specification of more complex POMP models,
using a nonlinear epidemiological model with a discrete population,
seasonality, and extra-demographic stochasticity. We discuss the specification
of user-defined models and the development of additional methods within the
programming environment provided by pomp.Comment: In press at the Journal of Statistical Software. A version of this
paper is provided at the pomp package website: http://kingaa.github.io/pom
How Structural Are Structural Parameters?
This paper studies how stable over time are the so-called "structural parameters" of dynamic stochastic general equilibrium (DSGE) models. To answer this question, we estimate a medium-scale DSGE model with real and nominal rigidities using U.S. data. In our model, we allow for parameter drifting and rational expectations of the agents with respect to this drift. We document that there is strong evidence that parameters change within our sample. We illustrate variations in the parameters describing the monetary policy reaction function and in the parameters characterizing the pricing behavior of firms and households. Moreover, we show how the movements in the pricing parameters are correlated with inflation. Thus, our results cast doubts on the empirical relevance of Calvo models.
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