BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CERN//INDICO//EN BEGIN:VEVENT SUMMARY:Maximum likelihood estimation of multivariate regime switching Stu dent-t copula models DTSTART;VALUE=DATE-TIME:20230629T105000Z DTEND;VALUE=DATE-TIME:20230629T111000Z DTSTAMP;VALUE=DATE-TIME:20261017T053325Z UID:indico-contribution-207-1025@cern.ch DESCRIPTION:Speakers: Federico Cortese (Università degli studi di Milano- Bicocca)\nWe propose a novel estimation method for multivariate regime swi tching models based on a Student-t copula function. These models account f or the interdependencies between multiple variables by considering the cor relation strength controlled by specific parameters. Moreover\, they addre ss fat-tailed distributions through the number of degrees of freedom. Thes e parameters\, in turn\, are governed by a latent Markov process.\n\nWe co nsider a two-steps procedure carried out through the Expectation-Maximizat ion algorithm to estimate model parameters by maximum likelihood. The prim ary computational challenge lies in estimating both the matrix of dependen ce parameters and determining the number of degrees of freedom for the Stu dent t-copula. To address this\, we introduce a new approach that leverage s Lagrange multipliers\, simplifying the estimation process.\n\nThrough a comprehensive simulation study\, we demonstrate that our estimators posses s desirable properties in finite samples. Additionally\, the estimation pr ocedure shows good computational efficiency.\n\nWe apply our model to anal yze the log-returns of five different cryptocurrencies. The results enable us to identify distinct bull and bear market periods based on the intensi ty of correlations observed between the crypto assets. This finding highli ghts the model's efficacy in capturing and characterizing market dynamics within the cryptocurrency domain.\n\nKeywords: statistical models for fina ncial analysis\, cryptocurrencies\, time series\, Expectation-Maximization algorithm\, latent variable models\n\nhttps://indico.unina.it/event/67/co ntributions/1025/ LOCATION:Department of Political Sciences Aula Spinelli URL:https://indico.unina.it/event/67/contributions/1025/ END:VEVENT BEGIN:VEVENT SUMMARY:Capturing Correlated Clusters Using Mixtures of Latent Class Model s DTSTART;VALUE=DATE-TIME:20230629T113000Z DTEND;VALUE=DATE-TIME:20230629T115000Z DTSTAMP;VALUE=DATE-TIME:20261017T053325Z UID:indico-contribution-207-1020@cern.ch DESCRIPTION:Speakers: Gertraud Malsiner-Walli (Vienna University of Econo mics and Business)\nLatent class models rely on the conditional\n independ ence assumption\, i.e.\, it is assumed that the categorical\n variables ar e independent given the cluster memberships. \n Within the Bayesian framew ork\, we propose a suitable specification of\n priors for the latent class model to identify the clusters in\n multivariate categorical data where t he independence assumption is not\n fulfilled. Each cluster distribution is approximated by a latent\n class model\, leading overall to a mixture o f latent class models.\n The Bayesian approach allows to identify the clus ters and fit their\n cluster distributions using a one-step procedure. We provide suitable estimation and inference methods for the\n mixture of lat ent class models and illustrate the performance of this\n approach on arti ficial and real data.\n\nKeywords: Bayesian inference\, model-based cluste ring\, prior on the number of components\, telescoping sampler.\n\nFop\, M .\, K. M. Smart\, and T. B. Murphy (2017). Variable selection for latent\n class analysis with application to low back pain diagnosis. The Annals of\ nApplied Statistics 11 (4)\, 2080-2110.\n\nFruehwirth-Schnatter\, S.\, G. Malsiner-Walli\, and B. Gruen (2021). Generalized\nmixtures of finite mixt ures and telescoping sampling. Bayesian\nAnalysis 16 (4)\, 1279–1307.\n\ nMalsiner-Walli\, G.\, S. Fruehwirth-Schnatter\, and B. Gruen (2017). Iden tifying\nmixtures of mixtures using Bayesian estimation. Journal of Comput ational\nand Graphical Statistics 26 (2)\, 285–295.\n\nhttps://indico.un ina.it/event/67/contributions/1020/ LOCATION:Department of Political Sciences Aula Spinelli URL:https://indico.unina.it/event/67/contributions/1020/ END:VEVENT BEGIN:VEVENT SUMMARY:Latent Feeling and Uncertainty of Perception and Expectations of P rice levels over time: A Change Point Analysis DTSTART;VALUE=DATE-TIME:20230629T111000Z DTEND;VALUE=DATE-TIME:20230629T113000Z DTSTAMP;VALUE=DATE-TIME:20261017T053325Z UID:indico-contribution-207-1011@cern.ch DESCRIPTION:Speakers: Carmela Cappelli (University of Naples Federico II) \nFor the analysis of ordered categorical data\, CUB modelling approach en tails the estimation of two main structural latent components of the ratin g process: feeling and uncertainty\, parameterized within a two-component mixture of Binomial and uniform distributions: see Piccolo and Simone 2019 for an overview. Featuring parameters can be possibly linked to subject c ovariates to determine twofold response patterns and they can be promptly estimated using the EM algorithm (as implemented in the R package ‘CUB ’ available on CRAN).\nThe contribution aims at presenting how change po int detection of temporal series of estimated feeling and uncertainty can be pursued to identify if and to what extent Italian people modified their perception and judgments of price levels from 1994 to 2019. To this goal\ , we resort to the framework of Atheoretical Regression Trees (ART\, Cappe lli et al. 2008) considering the series of monthly response distributions to questions:\n1-(Judgments): How do you think the price level changed ove r the previous 12 months? \n2-(Expectations): How do you think the price l evel will change over the next 12 months?\nissued by the Italian National Statistical Institute (ISTAT) within the consumers’ confidence survey. R esponses are collected over a scale with m=5 categories (1 =`fall '\, 2 = `stay about the same'\, 3 = `rise slightly'\, 4 = `rise moderately'\, 5 = `rise a lot').\nPreliminary results indicate that ART is effective in part itioning the series into sub-intervals characterized by different levels o f the estimated model parameters\, allowing to study and compare over time \, the change points of both feeling and uncertainty. It’s worth noticin g that the model parameters refer to two different aspects of the responde nts’ perception and judgment of price level\, thus the study of their ch ange points may reveal that they show different number and location of bre ak dates providing a further and valuable insight into the two components of respondents’ answers.\nPerformances of ART are also discussed compa ratively with those of other techniques for structural change point detect ion\, in particular with respect to Bai and Perron’s procedure as ART mi mics this procedure.\nKeywords: price expectation\; price judgment\; Atheo retical Regression Trees\; CUB model\; change point detection\n\nReference s:\nC. Cappelli\, R. N. Penny\, W. S. Rea\, M. Reale (2008). Detecting mul tiple mean breaks at unknown points in official time series\, MATHEMATICS AND COMPUTERS IN SIMULATION\, Volume 78\, Issues 2–3\, Pages 351-356\, I SSN 0378-4754.\nD. Piccolo\, R. Simone (2019). The class of CUB models: st atistical foundations\, inferential issues and empirical evidence. STATIST ICAL METHOD AND APPLICATIONS\, Volume 28\, pages 389-435.\n\nhttps://indic o.unina.it/event/67/contributions/1011/ LOCATION:Department of Political Sciences Aula Spinelli URL:https://indico.unina.it/event/67/contributions/1011/ END:VEVENT BEGIN:VEVENT SUMMARY:Power Prior's Weight Parameter elicitation via Bayes Factor-Calibr ated p-values DTSTART;VALUE=DATE-TIME:20230629T103000Z DTEND;VALUE=DATE-TIME:20230629T105000Z DTSTAMP;VALUE=DATE-TIME:20261017T053325Z UID:indico-contribution-207-1017@cern.ch DESCRIPTION:Speakers: Roberto Macrì Demartino (University of Padova)\nIn recent times\, the integration of historical data in the design and analys is of new clinical trials has gained considerable attention\, owing to eth ical reasons and difficulties encountered in recruiting patients. In the B ayesian framework\, the process of informative prior elicitation is widely recognized as a complex and multifaceted undertaking\, requiring the care ful quantification and synthesis of prior information into an appropriate prior distribution. Hence\, there is a pressing need for developing techni ques and methods that can facilitate synthesizing and quantifying prior in formation more effectively and efficiently. Within this context\, the conc ept of *power priors* ([Chen and Ibrahim\, 2000][1]) has emerged as a popu lar approach for incorporating historical data into the prior distribution of a treatment effect\, in a flexible and controlled manner. \nThe power prior methodology heavily relies on the *weight parameter* $\\delta$\, ran ging between 0 and 1\, that is a crucial factor in determining the degree to which the historical data influences the prior distribution\, and for w hich multiple elicitation strategies are available. A modification of the power prior allows a hierarchical prior specification by taking $\\delta$ as a random quantity\n\n$\\hspace{4.5cm}\n\\pi\\left({\\theta}\, \\delta \ \mid D_0\\right) \\propto L\\left({\\theta} \\mid D_0\\right)^\\delta \\pi _0({\\theta}) \\pi_0(\\delta)\,\n$\n\nwhere $D_0$ is an historical dataset with corresponding likelihood $L(\\theta \\mid D_0)$\, $\\pi_0({\\theta}) $ and $\\pi_0(\\delta)$ are the initial priors for $\\theta$ and $\\delta$ \, respectively. Furthermore\, a significant benefit of incorporating a no rmalizing factor in the power prior methodology is its adherence to the li kelihood principle\, as demonstrated by the joint normalized power prior\n \n\n$\\hspace{4.5cm}\n \\pi\\left({\\theta}\, \\delta \\mid D_0\\right) = \\frac{L\\left({\\theta} \\mid D_0\\right)^\\delta \\pi_0({\\theta}) \\ pi_0(\\delta)}{\\int_{\\Theta} L\\left({\\theta} \\mid D_0\\right)^\\delta \\pi_0({\\theta}) d {\\theta}}.\n$\n\nConsequently\, in a fully Bayesian approach\, the ability to effectively elicit an appropriate initial prior distribution for the weight parameter $\\delta$ is a crucial step. As far as we know from reviewing the existing literature\, a comprehensive justif ication underlying the choice of a Beta distribution with fixed hyper-para meters\, that is an usual choice for this framework\, is pretty vague. \n\ nThe Bayes factor (BF) constitutes a valuable statistical tool for model c omparison\; however\, we explore the use of the Bayes Factor to discrimina te between competing models that incorporate distinct initial Beta prior d istributions for the weight parameter by exploiting some BF $p$-value cali bration techniques ([Garcia-Donato and Chen\, 2005][2]). \nThis would enab le the selection of candidate models based on a more accurate and reliable assessment of the available evidence\, thereby enhancing the validity and robustness of statistical inference.\n\n**Keywords:** Beta distribution\, Clinical trial\, Historical information\, Robust selection.\n\n\n**Refere nces**\n\n 1. Chen\, M.-H. and Ibrahim\, J. G. (2000). Power prior distrib utions for regression models. Statistical Science\, 15(1):46 – 60.\n\n 2 . Garcia-Donato\, G. and Chen\, M.-H. (2005). Calibrating Bayes factor\n under prior predictive distributions. Statistica Sinica\, 15(2):359–38 0.\n\n [1]: https://www.jstor.org/stable/2676676\n [2]: https://www.jsto r.org/stable/24307360\n\nhttps://indico.unina.it/event/67/contributions/10 17/ LOCATION:Department of Political Sciences Aula Spinelli URL:https://indico.unina.it/event/67/contributions/1017/ END:VEVENT END:VCALENDAR