Archive for Italia

ABC for copula estimation

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags , , , , , , , on March 23, 2015 by xi'an

Roma from Piazzale Napoleone I, Villa Borghese, Feb. 29, 2012Clara Grazian and Brunero Liseo (di Roma) have just arXived a note on a method merging copulas, ABC, and empirical likelihood. The approach is rather hybrid and thus not completely Bayesian, but this must be seen as a consequence of an ill-posed problem. Indeed, as in many econometric models, the model there is not fully defined: the marginals of iid observations are represented as being from well-known parametric families (and are thus well-estimated by Bayesian tools), while the joint distribution remains uncertain and hence so does the associated copula. The approach in the paper is to proceed stepwise, i.e., to estimate correctly each marginal, well correctly enough to transform the data by an estimated cdf, and then only to estimate the copula or some aspect of it based on this transformed data. Like Spearman’s ρ. For which an empirical likelihood is computed and aggregated to a prior to make a BCel weight. (If this sounds unclear, each BEel evaluation is based on a random draw from the posterior samples, which transfers some uncertainty in the parameter evaluation into the copula domain. Thanks to Brunero and Clara for clarifying this point for me!)

At this stage of the note, there are two illustrations revolving around Spearman’s ρ. One on simulated data, with better performances than a nonparametric frequentist solution. And another one on a Garch (1,1) model for two financial time-series.

I am quite glad to see an application of our BCel approach in another domain although I feel a tiny bit uncertain about the degree of arbitrariness in the approach, from the estimated cdf transforms of the marginals to the choice of the moment equations identifying the parameter of interest like Spearman’s ρ. Especially if one uses a parametric copula which moments are equally well-known. While I see the practical gain in analysing each component separately, the object created by the estimated cdf transforms may have a very different correlation structure from the true cdf transforms. Maybe there exist consistency conditions on the estimated cdfs… Maybe other notions of orthogonality or independence could be brought into the picture to validate further the two-step solution…

Frescobaldi Castello di Nipozzano Montesodi

Posted in Wines with tags , , , , , , on December 20, 2014 by xi'an

montesodi

Gagliotto, Sangiovese di Romagna (superiore!)

Posted in pictures, Wines with tags , , , on September 20, 2014 by xi'an

Gagliotto

a partial review of BISP8 [guest post]

Posted in Statistics, Travel, University life with tags , , , , , , , on June 17, 2013 by xi'an

Chris Drovandi (QUT) sent me his impression on BISP8 that just took place in Milano, Italia (BISP stands for Bayesian inference in stochastic processes):

Here is a review of some of the talks at BISP8. For the other talks I do not have sufficient background to give the talks the justice that they deserve. It was a very enjoyable small workshop with many talks in my areas of interest.

In the first session Vanja Dukic presented bayesian inference of SEIR epidemic DE models and state space models of google flu trends data. In the case of the state space models a particle learning algorithm was developed. The author considered both fixed and random effects for the data in each US state. In the second session, Murali Haran presented a likelihood-free approach for inferring the parameters of a spatio-temporal epidemic model. The speaker used a Gaussian process emulator of the model based on model simulations from a regulator grid of parameter values. The emulator approach is suggested to be less intensive in terms of the number of model simulations compared with abc but is only suitable for low dimensional inference problems (even less so than abc).

In the first session of day 2 Ana Palacios combined the gompertz model with Markov processes to create flexible and realistic stochastic growth models. The resulting model has a difficult likelihood and inference was performed by completing the likelihood creating simple Gibbs moves and by ABC.

There were 3 talks in a row on inference for SDEs. The first, by Simon Särkkä, avoids evaluating an intractable transition density by proposing from another diffusion model and computing importance weights using the girsanov theorem. Next, Samuel Kou used a population MCMC type approach where each chain had a different Euler discretisation. This helps improve mixing for the chain with the finest grid. Moves between chains are complicated by the different dimension for each chain. The author used a filling approach to overcome this. A very interesting aspect of the talk was using information from all chains to extrapolate various posterior quantiles to delta_t is 0 (no discretisation implying the correct posterior). I assume the extrapolation may not work as well for the extreme quantiles. The third talk, by Andrew Golightly, proposed an auxiliary approach to improve PMCMC for these models. This talk was the most technical (for me) so need more time to digest. Following my talk (based on some work here.  And some current work.) was an applied talk using smc2 methodology.

On the final day Alexandros Beskos investigated the use of SMC for Bayesian inference for a high dimensional (static) parameter. SMC is advocated here due to the ease of adaptation relative to MCMC when there is no structure in the model. The base of the approach I believe was that of Chopin (2002).

Padova murals

Posted in Kids, pictures, Running, Travel with tags , , on March 31, 2013 by xi'an

piazza del castello, Padova, March 21, 2013mural on via Roma, Padova, March 22, 2013via Cesare Battisti, Padova, March 21, 2013

alba in Padova (due)

Posted in pictures, Running, Travel with tags , , , on March 28, 2013 by xi'an

fiume Bacchiglione, Padova, March 22, 2013

Basilica del Santo, Padova

Posted in pictures, Travel with tags , , , on March 27, 2013 by xi'an

Basilica di sant'Antonio, Padova, March 22, 2023

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