An Objective Approach to Prior Mass Functions for Discrete Parameter Spaces

Villa, Cristiano; Walker, Stephen G.

doi:10.1080/01621459.2014.946319

Cited by 19 publications

(31 citation statements)

References 16 publications

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“…We contribute to the area by deriving an objective prior distribution to detect change point locations, when the number of change points is known a priori. As a change point location can be interpreted as a discrete parameter, we apply recent results in the literature (Villa and Walker, 2015a) to make inference. The resulting prior distribution, which is the discrete uniform distribution, it is not new in the literature (Girón et al, 2007), and therefore can be considered as a validation of the proposed approach.…”

Section: Resultsmentioning

confidence: 99%

Bayesian loss-based approach to change point analysis

Hinoveanu

Leisen

Villa

2019

Computational Statistics & Data Analysis

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In this paper we present a loss-based approach to change point analysis. In particular, we look at the problem from two perspectives. The first focuses on the definition of a prior when the number of change points is known a priori. The second contribution aims to estimate the number of change points by using a loss-based approach recently introduced in the literature. The latter considers change point estimation as a model selection exercise. We show the performance of the proposed approach on simulated data and real data sets.

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Section: Resultsmentioning

confidence: 99%

Bayesian loss-based approach to change point analysis

Hinoveanu

Leisen

Villa

2019

Computational Statistics & Data Analysis

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“…For instance, this is a well known fact for the Student-t distribution. Villa and Walker (2015) introduced a method for specifying an objective prior for discrete parameters. Consider the general two-piece location scale distribution…”

Section: Loss-based Prior For Pmentioning

confidence: 99%

Loss-based approach to two-piece location-scale distributions with applications to dependent data

2019

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Two-piece location-scale models are used for modeling data presenting departures from symmetry. In this paper, we propose an objective Bayesian methodology for the tail parameter of two particular distributions of the above family: the skewed exponential power distribution and the skewed generalised logistic distribution. We apply the proposed objective approach to time series models and linear regression models where the error terms follow the distributions object of study. The performance of the proposed approach is illustrated through simulation experiments and real data analysis. The methodology yields improvements in density forecasts, as shown by the analysis we carry out on the electricity prices in Nordpool markets.MSC: 62F15, 62M10.In the literature, the asymmetric Laplace distribution (ALD) or the asymmetric Studentt distribution (AST) have gained importance in a wide range of disciplines, such as economics (Zhao et al., 2007;Leisen et al., 2017), financial analysis (Zhu and Galbraith, 2010;Kozubowski and Podgorski, 2001;Harvey and Lange, 2016) and microbiology (Rubio and Steel, 2011). However, the application of the SEPD and SGLD to represent the errors of time series and regression models, has received limited attention in the context of objective Bayesian analysis. The aim of this paper is to contribute to the above research area by introducing an information theoretical approach to address inference on the tail parameter of the two skewed distributions.As currently there is a growing interest in electricity prices (see Weron (2014) and Nowotarski and Weron (2018) for a review), we will contribute to the analysis of monthly electricity prices in the Nordpool market, in particular for Denmark and Finland through an autoregressive model with errors distributed as a SEPD. Compared to the standard frequentist autoregressive approach, which is the benchmark in the literature (see Conejo et al. (2005), Misiorek et al. (2006 and Maciejowska and Weron (2015)), we can show that our methodology improves the density forecasting. In addition, we consider a linear regression model where the residuals are SGLD with a loss-based prior on the tail parameter. We illustrate the above model by studying the Small Cell Cancer data set in Ying et al. (1995) and in Rubio and Yu (2017).The structure of this document is as follows. In Section 2 we introduce the general two-piece location-scale distribution and discuss special distributions further developed in the paper, such as the SEPD and the SGLD. Section 3 focuses on the derivation of the objective priors for the parameters of the models here considered. In Section 4 we analyse the frequentist properties of the proposed prior using data simulated from regression models and time series models. Section 5 deals with real data, in particular we model electricity prices and a cancer dataset. Final discussion points and conclusions are presented in Section 6.

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“…Once the worth has been determined, this will be linked to the prior probability by means of the self‐information loss function

- normal l o g π (θ)

. A detailed illustration of the idea can be found in , but here is an overview.…”

Section: The Prior Distributions For the Parameters Of The Asymmetricmentioning

confidence: 99%

“…The posterior distribution for is obtained by marginalising the full posterior ( , , , ) ∝ L( , , , |x) ( , , , ), where ( , , , ) is the prior defined in (4) and L( , , , |x) is the likelihood function defined in (2). As the posterior distribution is analytically intractable, we use Monte Carlo methods to obtain the marginal posterior distributions for each parameter.…”

Section: Simulation Studymentioning

confidence: 99%

Objective Bayesian modelling of insurance risks with the skewed Student‐t distribution

Leisen

Marín

Villa

2017

Appl Stoch Models Bus & Ind

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Insurance risks data typically exhibit skewed behaviour. In this paper, we propose a Bayesian approach to capture the main features of these data sets. This work extends a methodology recently introduced in the literature by considering an extra parameter that captures the skewness of the data. In particular, a skewed Student‐t distribution is considered. Two data sets are analysed: the Danish fire losses and the US indemnity loss. The analysis is carried with an objective Bayesian approach. For the discrete parameter representing the number of the degrees of freedom, we adopt a novel prior recently appeared in the literature. Copyright © 2017 John Wiley & Sons, Ltd.

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An Objective Approach to Prior Mass Functions for Discrete Parameter Spaces

Abstract: Proof. We prove the lemma by considering the sign of the difference between D KL (p R 0 ||p R 0 +1 ) and D KL (p R 0 ||p R 0 −1 ), which depends on the (relative) values of R 0 , N and n.

Cited by 19 publications

References 16 publications

Bayesian loss-based approach to change point analysis

Bayesian loss-based approach to change point analysis

Loss-based approach to two-piece location-scale distributions with applications to dependent data

Objective Bayesian modelling of insurance risks with the skewed Student‐t distribution

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