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4. Best practices, errors, and perspectives of half a century of plant translocation in Italy

Author

D'Agostino, M, Cao Pinna, L, Carboni, M, Assini, S, Bacchetta, G, Bartolucci, F, Brancaleoni, L, Buldrini, F, Carta, A, Cerabolini, B, Ceriani, R, Clementi, U, Cogoni, D, Conti, F, Crosti, R, Cuena-Lombrana, A, De Vitis, M, Di Giustino, A, Fabrini, G, Farris, E, Fenu, G, Fiorentin, R, Foggi, B, Forte, L, Garfi, G, Gentili, R, Giusso Del Galdo, G, Martinelli, V, Medagli, P, Nonis, D, Orsenigo, S, Paoli, L, Pierce, S, Pinna, M, Rainini, F, Ravera, S, Rossi, G, Schettino, A, Schicchi, R, Troia, A, Varone, L, Zappa, E, Abeli, T, D'Agostino M., Cao Pinna L., Carboni M., Assini S., Bacchetta G., Bartolucci F., Brancaleoni L., Buldrini F., Carta A., Cerabolini B., Ceriani R. M., Clementi U., Cogoni D., Conti F., Crosti R., Cuena-Lombrana A., De Vitis M., Di Giustino A., Fabrini G., Farris E., Fenu G., Fiorentin R., Foggi B., Forte L., Garfi G., Gentili R., Giusso Del Galdo G. P., Martinelli V., Medagli P., Nonis D., Orsenigo S., Paoli L., Pierce S., Pinna M. S., Rainini F., Ravera S., Rossi G., Schettino A., Schicchi R., Troia A., Varone L., Zappa E., Abeli T., D'Agostino, M, Cao Pinna, L, Carboni, M, Assini, S, Bacchetta, G, Bartolucci, F, Brancaleoni, L, Buldrini, F, Carta, A, Cerabolini, B, Ceriani, R, Clementi, U, Cogoni, D, Conti, F, Crosti, R, Cuena-Lombrana, A, De Vitis, M, Di Giustino, A, Fabrini, G, Farris, E, Fenu, G, Fiorentin, R, Foggi, B, Forte, L, Garfi, G, Gentili, R, Giusso Del Galdo, G, Martinelli, V, Medagli, P, Nonis, D, Orsenigo, S, Paoli, L, Pierce, S, Pinna, M, Rainini, F, Ravera, S, Rossi, G, Schettino, A, Schicchi, R, Troia, A, Varone, L, Zappa, E, Abeli, T, D'Agostino M., Cao Pinna L., Carboni M., Assini S., Bacchetta G., Bartolucci F., Brancaleoni L., Buldrini F., Carta A., Cerabolini B., Ceriani R. M., Clementi U., Cogoni D., Conti F., Crosti R., Cuena-Lombrana A., De Vitis M., Di Giustino A., Fabrini G., Farris E., Fenu G., Fiorentin R., Foggi B., Forte L., Garfi G., Gentili R., Giusso Del Galdo G. P., Martinelli V., Medagli P., Nonis D., Orsenigo S., Paoli L., Pierce S., Pinna M. S., Rainini F., Ravera S., Rossi G., Schettino A., Schicchi R., Troia A., Varone L., Zappa E., and Abeli T.

Abstract

Conservation translocations are becoming common conservation practice, so there is an increasing need to understand the drivers of plant translocation performance through reviews of cases at global and regional levels. The establishment of the Italian Database of Plant Translocation (IDPlanT) provides the opportunity to review the techniques used in 186 plant translocation cases performed in the last 50 years in the heart of the Mediterranean Biodiversity Hotspot. We described techniques and information available in IDPlanT and used these data to identify drivers of translocation outcomes. We tested the effect of 15 variables on survival of translocated propagules as of the last monitoring date with binomial logistic mixed-effect models. Eleven variables significantly affected survival of transplants: life form, site protection, material source, number of source populations, propagation methods, propagule life stage, planting methods, habitat suitability assessment, site preparation, aftercare, and costs. The integration of vegetation studies in the selection of suitable planting sites significantly increased the success of translocation efforts. Although posttranslocation watering had a generally positive effect on translocation outcome, other aftercare techniques did not always increase transplant survival. Finally, we found that how funds were spent appeared to be more important than the actual amount spent. Plant translocations in Italy and in the Mediterranean area should account for the complexity of speciation, gene flow, and plant migrations that has led to local adaptations and has important implications for the choice and constitution of source material.

Published
2024

6. Maximum Likelihood Estimation of Multivariate Regime Switching Student-t Copula Models

Author

Cortese, F, Pennoni, F, Bartolucci, F, Cortese, F., Pennoni, F., Bartolucci, F., Cortese, F, Pennoni, F, Bartolucci, F, Cortese, F., Pennoni, F., and Bartolucci, F.

Abstract

We propose a multivariate regime switching model based on a Student- (Formula presented.) copula function with parameters controlling the strength of correlation between variables and that are governed by a latent Markov process. To estimate model parameters by maximum likelihood, we consider a two-step procedure carried out through the Expectation–Maximisation algorithm. To address the main computational burden related to the estimation of the matrix of dependence parameters and the number of degrees of freedom of the Student- (Formula presented.) copula, we show a novel use of the Lagrange multipliers, which simplifies the estimation process. The simulation study shows that the estimators have good finite sample properties and the estimation procedure is computationally efficient. An application concerning log-returns of five cryptocurrencies shows that the model permits identifying bull and bear market periods based on the intensity of the correlations between crypto assets.

Published
2024

7. Lectotypification and taxonomy of the Italian endemic Biscutella incana (Brassicaceae).

Author

Bartolucci, F. and Conti, F.

Subjects
*BOTANY, *BRASSICACEAE, *PHENOLOGY, *CHROMOSOMES, *TAXONOMY
Abstract

Biscutella incana is endemic to the southern Apennine Peninsula (Italy) and was first described by Michele Tenore in 1826 from Calabria. It belongs to B. ser. Levigatae, the most morphologically diversified and critical series within the genus. In order to fix the application of this name, a lectotype housed in NAP was designated here. An updated and detailed morphological description, distribution and information about habitat and phenology are provided. Furthermore, a chromosome count made on a new population discovered in Dolomiti Lucane (Basilicata, southern Italy), confirmed that B. incana is diploid (2n = 18). [ABSTRACT FROM AUTHOR]

Published
2024
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9. On the connection between uniqueness from samples and stability in Gabor phase retrieval

Author

Alaifari, Rima (author), Bartolucci, F. (author), Steinerberger, Stefan (author), Wellershoff, Matthias (author), Alaifari, Rima (author), Bartolucci, F. (author), Steinerberger, Stefan (author), and Wellershoff, Matthias (author)

Abstract

Gabor phase retrieval is the problem of reconstructing a signal from only the magnitudes of its Gabor transform. Previous findings suggest a possible link between unique solvability of the discrete problem (recovery from measurements on a lattice) and stability of the continuous problem (recovery from measurements on an open subset of R2). In this paper, we close this gap by proving that such a link cannot be made. More precisely, we establish the existence of functions which break uniqueness from samples without affecting stability of the continuous problem. Furthermore, we prove the novel result that counterexamples to unique recovery from samples are dense in L2(R) . Finally, we develop an intuitive argument on the connection between directions of instability in phase retrieval and certain Laplacian eigenfunctions associated to small eigenvalues., Analysis

Published
2024
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10. Maximum likelihood for discrete latent variable models via evolutionary algorithms

Author

Brusa, L, Pennoni, F, Bartolucci, F, Brusa, L, Pennoni, F, and Bartolucci, F

Abstract

We propose an evolutionary optimization method for maximum likelihood and approximate maximum likelihood estimation of discrete latent variable models. The proposal is based on modified versions of the expectation–maximization (EM) and variational EM (VEM) algorithms, which are based on the genetic approach and allow us to accurately explore the parameter space, reducing the chance to be trapped into one of the multiple local maxima of the log-likelihood function. Their performance is examined through an extensive Monte Carlo simulation study where they are employed to estimate latent class, hidden Markov, and stochastic block models and compared with the standard EM and VEM algorithms. We observe a significant increase in the chance to reach global maximum of the target function and a high accuracy of the estimated parameters for each model. Applications focused on the analysis of cross-sectional, longitudinal, and network data are proposed to illustrate and compare the algorithms.

Published
2024

11. Variable selection for hidden Markov models with continuous variables and missing data

Author

Pennoni, F, Bartolucci, F, Pandolfi, S, Pennoni, F, Bartolucci, F, and Pandolfi, S

Abstract

We propose a variable selection method for multivariate hidden Markov models with continuous responses that are partially or completely missing at a given time occasion. Through this procedure, we achieve a dimensionality reduction by selecting the subset of the most informative responses for clustering individuals and simultaneously choosing the optimal number of these clusters corresponding to latent states. The approach is based on comparing different model specifications in terms of the subset of responses assumed to be dependent on the latent states, and it relies on a greedy search algorithm based on the Bayesian information criterion seen as an approximation of the Bayes factor. A suitable expectation-maximization algorithm is employed to obtain maximum likelihood estimates of the model parameters under the missing-at-random assumption. The proposal is illustrated via Monte Carlo simulation and an application where development indicators collected over eighteen years are selected, and countries are clustered into groups to evaluate their growth over time.

Published
2024

13. Maximum likelihood inference for hidden Markov models with parsimonious parametrizations of transition matrices

Author

Pandolfi, S, Bartolucci, F, Pennoni, F, Pandolfi, S., Bartolucci, F., Pennoni, F., Pandolfi, S, Bartolucci, F, Pennoni, F, Pandolfi, S., Bartolucci, F., and Pennoni, F.

Abstract

In longitudinal data analysis, hidden Markov (HM) models are fundamental tools, especially when the analysis is focused on transitions or the need to cluster individuals dynamically. When individual covariates are available in the dataset, a typical problem is how to parametrize the transition probabilities based on these covariates in a parsimonious way. In fact, standard multinomial parametrizations of these probabilities lead to models with many parameters, which are also difficult to interpret and, consequently, to unstable parameter estimates. To overcome the above problems, different parametrizations of the transition probabilities of HM models with covariates are introduced based on multinomial logit models formulated by two different choices of the reference state of each logit. These parametrizations rely on constraints having a straightforward interpretation, making the model much more parsimonious. Estimation based on the maximum likelihood (ML) approach is developed under different constraints based on the Expectation-Maximization algorithm. Steps of Newton-Raphson type are also included to improve the algorithm’s convergence speed

Published
2023

14. A causal hidden Markov model for assessing effects of multiple direct mail campaigns

Author

Pennoni, F, Paas, L, Bartolucci, F, Pennoni, F., Paas, L. J., Bartolucci, F., Pennoni, F, Paas, L, Bartolucci, F, Pennoni, F., Paas, L. J., and Bartolucci, F.

Abstract

We propose assessing the causal effects of a dynamic treatment in a longitudinal observational study, given observed confounders under suitable assumptions. The causal hidden Markov model is based on potential versions of discrete latent variables, and it accounts for the estimated propensity to be assigned to each treatment level over time using inverse probability weighting. Estimation of the model parameters is carried out through a weighted maximum log-likelihood approach. Standard errors for the parameter estimates are provided by nonparametric bootstrap. The proposal is validated through a simulation study aimed at comparing different model specifications. As an illustrative example, we consider a marketing campaign conducted by a large European bank over time on its customers. Findings provide straightforward managerial implications.

Published
2023

15. Causal inference in paired two-arm experimental studies under non-compliance with application to prognosis of myocardial infarction

Author

Bartolucci, F. and Farcomeni, A.

Subjects
Mathematics - Statistics Theory
Abstract

Motivated by a study about prompt coronary angiography in myocardial infarction, we propose a method to estimate the causal effect of a treatment in two-arm experimental studies with possible non-compliance in both treatment and control arms. The method is based on a causal model for repeated binary outcomes (before and after the treatment), which includes individual covariates and latent variables for the unobserved heterogeneity between subjects. Moreover, given the type of non-compliance, the model assumes the existence of three subpopulations of subjects: compliers, never-takers, and always-takers. The model is estimated by a two-step estimator: at the first step the probability that a subject belongs to one of the three subpopulations is estimated on the basis of the available covariates; at the second step the causal effects are estimated through a conditional logistic method, the implementation of which depends on the results from the first step. Standard errors for this estimator are computed on the basis of a sandwich formula. The application shows that prompt coronary angiography in patients with myocardial infarction may significantly decrease the risk of other events within the next two years, with a log-odds of about -2. Given that non-compliance is significant for patients being given the treatment because of high risk conditions, classical estimators fail to detect, or at least underestimate, this effect.

Published
2012

16. Nested hidden Markov chains for modeling dynamic unobserved heterogeneity in multilevel longitudinal data

Author

Bartolucci, F. and Lupparelli, M.

Subjects
Mathematics - Statistics Theory
Abstract

In the context of multilevel longitudinal data, where sample units are collected in clusters, an important aspect that should be accounted for is the unobserved heterogeneity between sample units and between clusters. For this aim we propose an approach based on nested hidden (latent) Markov chains, which are associated to every sample unit and to every cluster. The approach allows us to account for the mentioned forms of unobserved heterogeneity in a dynamic fashion; it also allows us to account for the correlation which may arise between the responses provided by the units belonging to the same cluster. Given the complexity in computing the manifest distribution of these response variables, we make inference on the proposed model through a composite likelihood function based on all the possible pairs of subjects within every cluster. The proposed approach is illustrated through an application to a dataset concerning a sample of Italian workers in which a binary response variable for the worker receiving an illness benefit was repeatedly observed.

Published
2012

17. A note on the application of the Oakes' identity to obtain the observed information matrix of hidden Markov models

Author

Bartolucci, F., Farcomeni, A., and Pennoni, F.

Subjects
Mathematics - Statistics Theory
Abstract

We derive the observed information matrix of hidden Markov models by the application of the Oakes (1999)'s identity. The method only requires the first derivative of the forward-backward recursions of Baum and Welch (1970), instead of the second derivative of the forward recursion, which is required within the approach of Lystig and Hughes (2002). The method is illustrated by an example based on the analysis of a longitudinal dataset which is well known in sociology.

Published
2012

18. A generalized Multiple-try Metropolis version of the Reversible Jump algorithm

Author

Pandolfi, S., Bartolucci, F., and Friel, N.

Subjects
Statistics - Methodology
Abstract

The Reversible Jump algorithm is one of the most widely used Markov chain Monte Carlo algorithms for Bayesian estimation and model selection. A generalized multiple-try version of this algorithm is proposed. The algorithm is based on drawing several proposals at each step and randomly choosing one of them on the basis of weights (selection probabilities) that may be arbitrary chosen. Among the possible choices, a method is employed which is based on selection probabilities depending on a quadratic approximation of the posterior distribution. Moreover, the implementation of the proposed algorithm for challenging model selection problems, in which the quadratic approximation is not feasible, is considered. The resulting algorithm leads to a gain in efficiency with respect to the Reversible Jump algorithm, and also in terms of computational effort. The performance of this approach is illustrated for real examples involving a logistic regression model and a latent class model.

Published
2010

19. An overview of latent Markov models for longitudinal categorical data

Author

Bartolucci, F., Farcomeni, A., and Pennoni, F.

Subjects
Mathematics - Statistics Theory
Abstract

We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. The main assumption behind these models is that the response variables are conditionally independent given a latent process which follows a first-order Markov chain. We first illustrate the basic LM model in which the conditional distribution of each response variable given the corresponding latent variable and the initial and transition probabilities of the latent process are unconstrained. For this model we also illustrate in detail maximum likelihood estimation through the Expectation-Maximization algorithm, which may be efficiently implemented by recursions known in the hidden Markov literature. We then illustrate several constrained versions of the basic LM model, which make the model more parsimonious and allow us to include and test hypotheses of interest. These constraints may be put on the conditional distribution of the response variables given the latent process (measurement model) or on the distribution of the latent process (latent model). We also deal with extensions of LM model for the inclusion of individual covariates and to multilevel data. Covariates may affect the measurement or the latent model; we discuss the implications of these two different approaches according to the context of application. Finally, we outline methods for obtaining standard errors for the parameter estimates, for selecting the number of states and for path prediction. Models and related inference are illustrated by the description of relevant socio-economic applications available in the literature.

Published
2010

20. A second update to the checklist of the vascular flora native to Italy.

Author

Bartolucci, F., Peruzzi, L., Galasso, G., Alessandrini, A., Ardenghi, N. M. G., Bacchetta, G., Banfi, E., Barberis, G., Bernardo, L., Bouvet, D., Bovio, M., Calvia, G., Castello, M., Cecchi, L., Del Guacchio, E., Domina, G., Fascetti, S., Gallo, L., Gottschlich, G., and Guarino, R.

Subjects
*BOTANY, *FERNS, *PTERIDOPHYTA, *SUBSPECIES, *PLANT diversity, *LYCOPHYTES
Abstract

Critical species inventories provide primary biodiversity data crucial for biogeographical, ecological, and conservation studies. After six years, a second update to the inventory of the vascular flora native to Italy is presented. It provides details on the occurrence at regional level and, for the first time, floristic data for San Marino. The checklist includes 8,241 species and subspecies, distributed in 1,111 genera and 153 families; 23 taxa are lycophytes, 108 ferns and fern allies, 30 gymnosperms, and 8,080 angiosperms. The species/subspecies endemic to Italy are 1,702, grouped in 71 families and 312 genera. The taxa currently occurring in Italy are 7,591, while 545 taxa have not been confirmed in recent times, 94 are doubtfully occurring in the country, 11 are data deficient, and 236 are reported by mistake and to be excluded at national level. Out of the 545 not confirmed taxa, 28 are considered extinct or possibly extinct. [ABSTRACT FROM AUTHOR]

Published
2024
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22. Analysis of Sacco Hospital longitudinal data by hidden Markov models

Author

Pennoni, F, Bartolucci, F, Spinelli, D, Vittadini, G, Pennoni, F, Bartolucci, F, Spinelli, D, and Vittadini, G

Subjects
SECS-S/01 - STATISTICA, chance of recovering, Expectation-Maximization algorithm, multivariate binary longitudinal categorical responses, post-.covid symptoms
Published
2023

23. Notulae to the Italian alien vascular flora: 14

Author

Galasso, G, Domina, G, Andreatta, S, Argenti, C, Astuti, G, Bacaro, G, Bacchetta, G, Bagella, S, Banfi, E, Barberis, D, Bartolucci, F, Bernardo, L, Bonari, G, Brundu, G, Buccomino, G, Calvia, G, Cancellieri, L, Capuano, A, Celesti-Grapow, L, Conti, F, Cuena-Lombraña, A, D’Amico, F, De Fine, G, de Simone, L, Guacchio, E, Emili, F, Fanfarillo, E, Fascetti, S, Fiaschi, T, Fois, M, Fortini, P, Gentili, R, Giardini, M, Hussain, A, Iamonico, D, Laface, V, Lallai, A, Lazzaro, L, Lecis, A, Ligato, E, Loi, G, Lonati, M, Lozano, V, Maccherini, S, Mainetti, A, Mascia, F, Mei, G, Menini, F, Merli, M, Montesano, A, Mugnai, M, Musarella, C, Nota, G, Olivieri, N, Passalacqua, N, Pinzani, L, Pisano, A, Pittarello, M, Podda, L, Posillipo, G, Potenza, G, Probo, M, Prosser, F, Quaglini, L, Enri, S, Rivieccio, G, Roma-Marzio, F, Rosati, L, Selvaggi, A, Soldano, A, Stinca, A, Tasinazzo, S, Tassone, S, Terzi, M, Vallariello, R, Vangelisti, R, Verloove, F, Lastrucci, L, Galasso G., Domina G., Andreatta S., Argenti C., Astuti G., Bacaro G., Bacchetta G., Bagella S., Banfi E., Barberis D., Bartolucci F., Bernardo L., Bonari G., Brundu G., Buccomino G., Calvia G., Cancellieri L., Capuano A., Celesti-Grapow L., Conti F., Cuena-Lombraña A., D’Amico F. S., De Fine G., de Simone L., Guacchio E. D., Emili F., Fanfarillo E., Fascetti S., Fiaschi T., Fois M., Fortini P., Gentili R., Giardini M., Hussain A. N., Iamonico D., Laface V. L. A., Lallai A., Lazzaro L., Lecis A. P., Ligato E., Loi G., Lonati M., Lozano V., Maccherini S., Mainetti A., Mascia F., Mei G., Menini F., Merli M., Montesano A., Mugnai M., Musarella C. M., Nota G., Olivieri N., Passalacqua N. G., Pinzani L., Pisano A., Pittarello M., Podda L., Posillipo G., Potenza G., Probo M., Prosser F., Quaglini L. A., Enri S. R., Rivieccio G., Roma-Marzio F., Rosati L., Selvaggi A., Soldano A., Stinca A., Tasinazzo S., Tassone S., Terzi M., Vallariello R., Vangelisti R., Verloove F., Lastrucci L., Galasso, G, Domina, G, Andreatta, S, Argenti, C, Astuti, G, Bacaro, G, Bacchetta, G, Bagella, S, Banfi, E, Barberis, D, Bartolucci, F, Bernardo, L, Bonari, G, Brundu, G, Buccomino, G, Calvia, G, Cancellieri, L, Capuano, A, Celesti-Grapow, L, Conti, F, Cuena-Lombraña, A, D’Amico, F, De Fine, G, de Simone, L, Guacchio, E, Emili, F, Fanfarillo, E, Fascetti, S, Fiaschi, T, Fois, M, Fortini, P, Gentili, R, Giardini, M, Hussain, A, Iamonico, D, Laface, V, Lallai, A, Lazzaro, L, Lecis, A, Ligato, E, Loi, G, Lonati, M, Lozano, V, Maccherini, S, Mainetti, A, Mascia, F, Mei, G, Menini, F, Merli, M, Montesano, A, Mugnai, M, Musarella, C, Nota, G, Olivieri, N, Passalacqua, N, Pinzani, L, Pisano, A, Pittarello, M, Podda, L, Posillipo, G, Potenza, G, Probo, M, Prosser, F, Quaglini, L, Enri, S, Rivieccio, G, Roma-Marzio, F, Rosati, L, Selvaggi, A, Soldano, A, Stinca, A, Tasinazzo, S, Tassone, S, Terzi, M, Vallariello, R, Vangelisti, R, Verloove, F, Lastrucci, L, Galasso G., Domina G., Andreatta S., Argenti C., Astuti G., Bacaro G., Bacchetta G., Bagella S., Banfi E., Barberis D., Bartolucci F., Bernardo L., Bonari G., Brundu G., Buccomino G., Calvia G., Cancellieri L., Capuano A., Celesti-Grapow L., Conti F., Cuena-Lombraña A., D’Amico F. S., De Fine G., de Simone L., Guacchio E. D., Emili F., Fanfarillo E., Fascetti S., Fiaschi T., Fois M., Fortini P., Gentili R., Giardini M., Hussain A. N., Iamonico D., Laface V. L. A., Lallai A., Lazzaro L., Lecis A. P., Ligato E., Loi G., Lonati M., Lozano V., Maccherini S., Mainetti A., Mascia F., Mei G., Menini F., Merli M., Montesano A., Mugnai M., Musarella C. M., Nota G., Olivieri N., Passalacqua N. G., Pinzani L., Pisano A., Pittarello M., Podda L., Posillipo G., Potenza G., Probo M., Prosser F., Quaglini L. A., Enri S. R., Rivieccio G., Roma-Marzio F., Rosati L., Selvaggi A., Soldano A., Stinca A., Tasinazzo S., Tassone S., Terzi M., Vallariello R., Vangelisti R., Verloove F., and Lastrucci L.

Abstract

In this contribution, new data concerning the distribution of vascular flora alien to Italy are presented. It includes new records, confirmations, and status changes for Italy or for Italian administrative regions. Nomenclatural and distribution updates, published elsewhere, and corrections are provided as Suppl. material 1. © Gabriele Galasso et al. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Published
2022

24. Mispecification tests for hidden Markov models based on a new class of finite mixture models

Author

CLAD - Associação Portuguesa de Classificação e Análise de Dados, Brito, P, Bartolucci, F, Pandolfi, F, Pennoni, F, Bartolucci F, Pandolfi F, Pennoni F, CLAD - Associação Portuguesa de Classificação e Análise de Dados, Brito, P, Bartolucci, F, Pandolfi, F, Pennoni, F, Bartolucci F, Pandolfi F, and Pennoni F

Abstract

In the context of longitudinal data, we show that a general class of hidden Markov (HM, [1]) models may be equivalent to a class of finite mixture (FM, [3]) models based on an augmented set of components and suitable constraints on the conditional response probabilities, given these components. We formulate a misspecification test for the latent structure of an HM model comparing maximum likelihood values of the two models for the same data, and when the number of possible latent state sequences is excessive, we propose a multiple version of this test including the Bonferroni correction. The procedure is simple since it is based on the output of the Expectation-Maximization estimation algorithm [2]. The properties of this testing procedure are evaluated through a simulation study. An empirical application illustrates it through data from the National Longitudinal Survey of Youth, in which we jointly consider wages and years of experience after labour force entry. We show that the proposed testing procedure may also be used as an alternative model selection criterion for the number of latent states of an HM model to those usually employed.

Published
2022

25. Exploring the dependencies among main cryptocurrency log-returns: A hidden Markov model

Author

Pennoni, F, Bartolucci, F, Forte, G, Ametrano, F, Pennoni F., Bartolucci F., Forte G., Ametrano F., Pennoni, F, Bartolucci, F, Forte, G, Ametrano, F, Pennoni F., Bartolucci F., Forte G., and Ametrano F.

Abstract

A hidden Markov model is proposed for the analysis of time-series of daily log-returns of the last 4 years of Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash. These log-returns are assumed to have a multivariate Gaussian distribution conditionally on a latent Markov process having a finite number of regimes or states. The hidden regimes represent different market phases identified through distinct vectors of expected values and variance–covariance matrices of the log-returns, so that they also differ in terms of volatility. Maximum-likelihood estimation of the model parameters is carried out by the expectation–maximisation algorithm, and regimes are singularly predicted for every time occasion according to the maximum-a-posteriori rule. Results show three positive and three negative phases of the market. In the most recent period, an increasing tendency towards positive regimes is also predicted. A rather heterogeneous correlation structure is estimated, and evidence of structural medium term trend in the correlation of Bitcoin with the other cryptocurrencies is detected.

Published
2022

26. A Regime switching Student-t copula model for the analysis of cryptocurrencies data

Author

Marco Corazza, Cira Perna, Claudio Pizzi, Marilena Sibillo, Magni, G, Bimonte, G, Naimoli, A, Cortese, F, Bartolucci, F, Pennoni, F, Cortese, F., Bartolucci, F., Pennoni, F., Marco Corazza, Cira Perna, Claudio Pizzi, Marilena Sibillo, Magni, G, Bimonte, G, Naimoli, A, Cortese, F, Bartolucci, F, Pennoni, F, Cortese, F., Bartolucci, F., and Pennoni, F.

Abstract

Flexible statistical models have an important role in explaining the joint distribution of financial returns. In these analyses, it is necessary to consider abrupt switches in the market conditions, especially if the focus is on cryptoassets, the market of which is characterized by high instabilities. Regime switching (RS) copula models represent a powerful tool to formulate the joint distribution of time-series accurately: they are based on a copula distribution with parameters governed by a hidden Markov process of first-order so as to account for the correlation patterns between series. The hidden states represent different market regimes, each described by a state-specific vector of copula parameters. We propose RS copula models as a valuable instrument for describing the joint behavior of log- returns. We choose a Student-t copula function to consider extreme dependent values appropriately as they are often observed in financial returns. We split the modeling process into two steps: the first one consists in fitting the marginal distribution of each univariate time-series, while the second one deals with the estimation of the joint distribution of the log-returns described by a RS copula model. Maximum likelihood estimation of the model parameters is carried out by the expectation-maximization (EM) algorithm, which alternates two steps until convergence: at the E-step, we compute the expectation of the log-likelihood evaluated using the current values for the parameters and, at the M-step, parameters estimates are updated by maximizing the expected complete-data log-likelihood computed at the previous step. The main computational burdens deal with estimating the correlation matrix (R) and the number of degrees of freedom (v) of the Student t-copula. At this aim, we propose performing the M-step by computing R given v using a closed form solution obtained from a constrained optimization of the log-likelihood using Lagrange multipliers. Then, we numerically maxim

Published
2022

27. Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations

Author

Sherratt, K., Gruson, H., Grah, R., Johnson, H., Niehus, R., Prasse, B., Sandmann, F., Deuschel, J., Wolffram, D., Abbott, S., Ullrich, A., Gibson, G., Ray, E. L., Reich, N. G., Sheldon, D., Wang, Y., Wattanachit, N., Wang, L., Trnka, J., Obozinski, G., Sun, T., Thanou, D., Pottier, L., Krymova, E., Meinke, J. H., Barbarossa, M. V., Leithäuser, N., Mohring, J., Schneider, J., Wlazlo, J., Fuhrmann, J., Lange, B., Rodiah, I., Baccam, P., Gurung, H., Stage, S., Suchoski, B., Budzinski, J., Walraven, R., Villanueva, I., Tucek, V., Smíd, M., Zajícek, M., Pérez Alvarez, C., Reina, B., Bosse, N. I., Meakin, S., Castro, L., Fairchild, G., Michaud, I., Osthus, D., Alaimo Di Loro, P., Maruotti, A., Eclerová, V., Kraus, A., Kraus, D., Pribylova, L., Dimitris, B., Li, M. L., Saksham, S., Dehning, J., Mohr, S., Priesemann, V., Redlarski, G., Bejar, B., Ardenghi, G., Parolini, N., Ziarelli, G., Bock, Wolfgang, Heyder, S., Hotz, T., E. Singh, D., Guzman-Merino, M., Aznarte, J. L., Moriña, D., Alonso, S., Alvarez, E., López, D., Prats, C., Burgard, J. P., Rodloff, A., Zimmermann, T., Kuhlmann, A., Zibert, J., Pennoni, F., Divino, F., Català, M., Lovison, G., Giudici, P., Tarantino, B., Bartolucci, F., Jona Lasinio, G., Mingione, M., Farcomeni, A., Srivastava, A., Montero-Manso, P., Adiga, A., Hurt, B., Lewis, B., Marathe, M., Porebski, P., Venkatramanan, S., Bartczuk, R., Dreger, F., Gambin, A., Gogolewski, K., Gruziel-S?omka, M., Krupa, B., Moszynski, A., Niedzielewski, K., Nowosielski, J., Radwan, M., Rakowski, F., Semeniuk, M., Szczurek, E., Zieli?ski, J., Kisielewski, J., Pabjan, B., Kheifetz, Y., Kirsten, H., Scholz, M., Biecek, P., Bodych, M., Filinski, M., Idzikowski, R., Krueger, T., Ozanski, T., Bracher, J., Funk, S., Sherratt, K., Gruson, H., Grah, R., Johnson, H., Niehus, R., Prasse, B., Sandmann, F., Deuschel, J., Wolffram, D., Abbott, S., Ullrich, A., Gibson, G., Ray, E. L., Reich, N. G., Sheldon, D., Wang, Y., Wattanachit, N., Wang, L., Trnka, J., Obozinski, G., Sun, T., Thanou, D., Pottier, L., Krymova, E., Meinke, J. H., Barbarossa, M. V., Leithäuser, N., Mohring, J., Schneider, J., Wlazlo, J., Fuhrmann, J., Lange, B., Rodiah, I., Baccam, P., Gurung, H., Stage, S., Suchoski, B., Budzinski, J., Walraven, R., Villanueva, I., Tucek, V., Smíd, M., Zajícek, M., Pérez Alvarez, C., Reina, B., Bosse, N. I., Meakin, S., Castro, L., Fairchild, G., Michaud, I., Osthus, D., Alaimo Di Loro, P., Maruotti, A., Eclerová, V., Kraus, A., Kraus, D., Pribylova, L., Dimitris, B., Li, M. L., Saksham, S., Dehning, J., Mohr, S., Priesemann, V., Redlarski, G., Bejar, B., Ardenghi, G., Parolini, N., Ziarelli, G., Bock, Wolfgang, Heyder, S., Hotz, T., E. Singh, D., Guzman-Merino, M., Aznarte, J. L., Moriña, D., Alonso, S., Alvarez, E., López, D., Prats, C., Burgard, J. P., Rodloff, A., Zimmermann, T., Kuhlmann, A., Zibert, J., Pennoni, F., Divino, F., Català, M., Lovison, G., Giudici, P., Tarantino, B., Bartolucci, F., Jona Lasinio, G., Mingione, M., Farcomeni, A., Srivastava, A., Montero-Manso, P., Adiga, A., Hurt, B., Lewis, B., Marathe, M., Porebski, P., Venkatramanan, S., Bartczuk, R., Dreger, F., Gambin, A., Gogolewski, K., Gruziel-S?omka, M., Krupa, B., Moszynski, A., Niedzielewski, K., Nowosielski, J., Radwan, M., Rakowski, F., Semeniuk, M., Szczurek, E., Zieli?ski, J., Kisielewski, J., Pabjan, B., Kheifetz, Y., Kirsten, H., Scholz, M., Biecek, P., Bodych, M., Filinski, M., Idzikowski, R., Krueger, T., Ozanski, T., Bracher, J., and Funk, S.

Abstract

Methods: We used open-source tools to develop a public European COVID-19 Forecast Hub. We invited groups globally to contribute weekly forecasts for COVID-19 cases and deaths reported by a standardised source for 32 countries over the next 1–4 weeks. Teams submitted forecasts from March 2021 using standardised quantiles of the predictive distribution. Each week we created an ensemble forecast, where each predictive quantile was calculated as the equally-weighted average (initially the mean and then from 26th July the median) of all individual models’ predictive quantiles. We measured the performance of each model using the relative Weighted Interval Score (WIS), comparing models’ forecast accuracy relative to all other models. We retrospectively explored alternative methods for ensemble forecasts, including weighted averages based on models’ past predictive performance. Results: Over 52 weeks, we collected forecasts from 48 unique models. We evaluated 29 models’ forecast scores in comparison to the ensemble model. We found a weekly ensemble had a consistently strong performance across countries over time. Across all horizons and locations, the ensemble performed better on relative WIS than 83% of participating models’ forecasts of incident cases (with a total N=886 predictions from 23 unique models), and 91% of participating models’ forecasts of deaths (N=763 predictions from 20 models). Across a 1–4 week time horizon, ensemble performance declined with longer forecast periods when forecasting cases, but remained stable over 4 weeks for incident death forecasts. In every forecast across 32 countries, the ensemble outperformed most contributing models when forecasting either cases or deaths, frequently outperforming all of its individual component models. Among several choices of ensemble methods we found that the most influential and best choice was to use a median average of models instead of using the mean, regardless of methods of weighting component forecast mod

Published
2023
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28. When nonresponse makes estimates from a census a small area estimation problem: The case of the survey on graduates’ employment status in Italy

Author

Coretto, P, Giordano, G, La Rocca, M, Parrella, ML, Rampichini, C, Ranalli, G, Pennoni, F, Bartolucci, F, Mira, A, Coretto, P, Giordano, G, La Rocca, M, Parrella, ML, Rampichini, C, Ranalli, G, Pennoni, F, Bartolucci, F, and Mira, A

Abstract

In this paper we frame the problem of obtaining estimates from the sur- vey on the employment status of graduates in Italy as a Small Area Estimation problem because of unit nonresponse. We propose to use generalized linear mixed models and to include two variables that can be considered proxies of the response propensity among the set of covariates to make the MAR assumption more tenable. Estimates for degree programmes are obtained as (semi-parametric) empirical best predictions.

Published
2023

29. Discrete latent variable models: Recent and advances and perspectives

Author

Coretto, P, Giordano, G, La Rocca, M, Parrella, ML, Rampichini, C, Bartolucci, F, Greenacre, M, Pandolfi, S, Pennoni, F, Coretto, P, Giordano, G, La Rocca, M, Parrella, ML, Rampichini, C, Bartolucci, F, Greenacre, M, Pandolfi, S, and Pennoni, F

Abstract

After a review of the class of discrete latent variable models in terms of formulation and estimation methods, recent advances and perspectives regarding these models are illustrated. We consider in detail the stochastic block model for social networks and models for spatio-temporal data. Among these developments, we discuss, in particular, the analysis of longitudinal compositional data about expenditures of the Spanish regions over several decades.

Published
2023

33. Latent potential outcomes: An analysis of the effects of programs aimed at improving student's non-cognitive skills

Author

Bucci, A, Cartone, A, Evangelista, A, Marletta, A, Pennoni, F, Bartolucci, F, Vittadini, G, Vittadini, G., Bucci, A, Cartone, A, Evangelista, A, Marletta, A, Pennoni, F, Bartolucci, F, Vittadini, G, and Vittadini, G.

Abstract

We illustrate a causal latent transition model to evaluate the effects of educational programs administered to pupils in the 6th and 7th grades during their middle school period. The programs are conducted in an Italian region and focus on improving non-cognitive abilities. The interest is in evaluating the effects on the skills acquired in the 8th grade in Italian and Mathematics. The model can be cast in the hidden Markov literature and is formulated as an extension of Rubin's causal model based on potential versions of discrete time-varying latent variables.

Published
2023

34. Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations

Author

Sherratt, K, Gruson, H, Grah, R, Johnson, H, Niehus, R, Prasse, B, Sandmann, F, Deuschel, J, Wolffram, D, Abbott, S, Ullrich, A, Gibson, G, L Ray, E, G Reich, N, Sheldon, D, Wang, Y, Wattanachit, N, Wang, L, Trnka, J, Obozinski, G, Sun, T, Thanou, D, Pottier, L, Krymova, E, H Meinke, J, Vittoria Barbarossa, M, Leithäuser, N, Mohring, J, Schneider, J, Włazło, J, Fuhrmann, J, Lange, B, Rodiah, I, Baccam, P, Gurung, H, Stage, S, Suchoski, B, Budzinski, J, Walraven, R, Villanueva, I, Tucek, V, Smid, M, Zajíček, M, Pérez Álvarez, C, Reina, B, I Bosse, N, R Meakin, S, Castro, L, Fairchild, G, Michaud, I, Osthus, D, Alaimo Di Loro, P, Maruotti, A, Eclerová, V, Kraus, A, Kraus, D, Pribylova, L, Dimitris, B, Lingzhi Li, M, Saksham, S, Dehning, J, Mohr, S, Priesemann, V, Redlarski, G, Bejar, B, Ardenghi, G, Parolini, N, Ziarelli, G, Bock, W, Heyder, S, Hotz, T, E Singh, D, Guzman-Merino, M, L Aznarte, J, Moriña, D, Alonso, S, Álvarez, E, López, D, Prats, C, Pablo Burgard, J, Rodloff, A, Zimmermann, T, Kuhlmann, A, Zibert, J, Pennoni, F, Divino, F, Català, M, Lovison, G, Giudici, P, Tarantino, B, Bartolucci, F, Jona Lasinio, G, Mingione, M, Farcomeni, A, Srivastava, A, Montero-Manso, P, Adiga, A, Hurt, B, Lewis, B, Marathe, M, Porebski, P, Venkatramanan, S, P Bartczuk, R, Dreger, F, Gambin, A, Gogolewski, K, Gruziel-Słomka, M, Krupa, B, Moszyński, A, Niedzielewski, K, Nowosielski, J, Radwan, M, Rakowski, F, Semeniuk, M, Szczurek, E, Zieliński, J, Kisielewski, J, Pabjan, B, Kirsten, H, Kheifetz, Y, Scholz, M, Biecek, P, Bodych, M, Filinski, M, Idzikowski, R, Krueger, T, Ozanski, T, Bracher, J, Funk, S, Katharine Sherratt, Hugo Gruson, Rok Grah, Helen Johnson, Rene Niehus, Bastian Prasse, Frank Sandmann, Jannik Deuschel, Daniel Wolffram, Sam Abbott, Alexander Ullrich, Graham Gibson, Evan L Ray, Nicholas G Reich, Daniel Sheldon, Yijin Wang, Nutcha Wattanachit, Lijing Wang, Jan Trnka, Guillaume Obozinski, Tao Sun, Dorina Thanou, Loic Pottier, Ekaterina Krymova, Jan H Meinke, Maria Vittoria Barbarossa, Neele Leithäuser, Jan Mohring, Johanna Schneider, Jaroslaw Włazło, Jan Fuhrmann, Berit Lange, Isti Rodiah, Prasith Baccam, Heidi Gurung, Steven Stage, Bradley Suchoski, Jozef Budzinski, Robert Walraven, Inmaculada Villanueva, Vit Tucek, Martin Smid, Milan Zajíček, Cesar Pérez Álvarez, Borja Reina, Nikos I Bosse, Sophie R Meakin, Lauren Castro, Geoffrey Fairchild, Isaac Michaud, Dave Osthus, Pierfrancesco Alaimo Di Loro, Antonello Maruotti, Veronika Eclerová, Andrea Kraus, David Kraus, Lenka Pribylova, Bertsimas Dimitris, Michael Lingzhi Li, Soni Saksham, Jonas Dehning, Sebastian Mohr, Viola Priesemann, Grzegorz Redlarski, Benjamin Bejar, Giovanni Ardenghi, Nicola Parolini, Giovanni Ziarelli, Wolfgang Bock, Stefan Heyder, Thomas Hotz, David E Singh, Miguel Guzman-Merino, Jose L Aznarte, David Moriña, Sergio Alonso, Enric Álvarez, Daniel López, Clara Prats, Jan Pablo Burgard, Arne Rodloff, Tom Zimmermann, Alexander Kuhlmann, Janez Zibert, Fulvia Pennoni, Fabio Divino, Marti Català, Gianfranco Lovison, Paolo Giudici, Barbara Tarantino, Francesco Bartolucci, Giovanna Jona Lasinio, Marco Mingione, Alessio Farcomeni, Ajitesh Srivastava, Pablo Montero-Manso, Aniruddha Adiga, Benjamin Hurt, Bryan Lewis, Madhav Marathe, Przemyslaw Porebski, Srinivasan Venkatramanan, Rafal P Bartczuk, Filip Dreger, Anna Gambin, Krzysztof Gogolewski, Magdalena Gruziel-Słomka, Bartosz Krupa, Antoni Moszyński, Karol Niedzielewski, Jedrzej Nowosielski, Maciej Radwan, Franciszek Rakowski, Marcin Semeniuk, Ewa Szczurek, Jakub Zieliński, Jan Kisielewski, Barbara Pabjan, Holger Kirsten, Yuri Kheifetz, Markus Scholz, Przemyslaw Biecek, Marcin Bodych, Maciej Filinski, Radoslaw Idzikowski, Tyll Krueger, Tomasz Ozanski, Johannes Bracher, Sebastian Funk, Sherratt, K, Gruson, H, Grah, R, Johnson, H, Niehus, R, Prasse, B, Sandmann, F, Deuschel, J, Wolffram, D, Abbott, S, Ullrich, A, Gibson, G, L Ray, E, G Reich, N, Sheldon, D, Wang, Y, Wattanachit, N, Wang, L, Trnka, J, Obozinski, G, Sun, T, Thanou, D, Pottier, L, Krymova, E, H Meinke, J, Vittoria Barbarossa, M, Leithäuser, N, Mohring, J, Schneider, J, Włazło, J, Fuhrmann, J, Lange, B, Rodiah, I, Baccam, P, Gurung, H, Stage, S, Suchoski, B, Budzinski, J, Walraven, R, Villanueva, I, Tucek, V, Smid, M, Zajíček, M, Pérez Álvarez, C, Reina, B, I Bosse, N, R Meakin, S, Castro, L, Fairchild, G, Michaud, I, Osthus, D, Alaimo Di Loro, P, Maruotti, A, Eclerová, V, Kraus, A, Kraus, D, Pribylova, L, Dimitris, B, Lingzhi Li, M, Saksham, S, Dehning, J, Mohr, S, Priesemann, V, Redlarski, G, Bejar, B, Ardenghi, G, Parolini, N, Ziarelli, G, Bock, W, Heyder, S, Hotz, T, E Singh, D, Guzman-Merino, M, L Aznarte, J, Moriña, D, Alonso, S, Álvarez, E, López, D, Prats, C, Pablo Burgard, J, Rodloff, A, Zimmermann, T, Kuhlmann, A, Zibert, J, Pennoni, F, Divino, F, Català, M, Lovison, G, Giudici, P, Tarantino, B, Bartolucci, F, Jona Lasinio, G, Mingione, M, Farcomeni, A, Srivastava, A, Montero-Manso, P, Adiga, A, Hurt, B, Lewis, B, Marathe, M, Porebski, P, Venkatramanan, S, P Bartczuk, R, Dreger, F, Gambin, A, Gogolewski, K, Gruziel-Słomka, M, Krupa, B, Moszyński, A, Niedzielewski, K, Nowosielski, J, Radwan, M, Rakowski, F, Semeniuk, M, Szczurek, E, Zieliński, J, Kisielewski, J, Pabjan, B, Kirsten, H, Kheifetz, Y, Scholz, M, Biecek, P, Bodych, M, Filinski, M, Idzikowski, R, Krueger, T, Ozanski, T, Bracher, J, Funk, S, Katharine Sherratt, Hugo Gruson, Rok Grah, Helen Johnson, Rene Niehus, Bastian Prasse, Frank Sandmann, Jannik Deuschel, Daniel Wolffram, Sam Abbott, Alexander Ullrich, Graham Gibson, Evan L Ray, Nicholas G Reich, Daniel Sheldon, Yijin Wang, Nutcha Wattanachit, Lijing Wang, Jan Trnka, Guillaume Obozinski, Tao Sun, Dorina Thanou, Loic Pottier, Ekaterina Krymova, Jan H Meinke, Maria Vittoria Barbarossa, Neele Leithäuser, Jan Mohring, Johanna Schneider, Jaroslaw Włazło, Jan Fuhrmann, Berit Lange, Isti Rodiah, Prasith Baccam, Heidi Gurung, Steven Stage, Bradley Suchoski, Jozef Budzinski, Robert Walraven, Inmaculada Villanueva, Vit Tucek, Martin Smid, Milan Zajíček, Cesar Pérez Álvarez, Borja Reina, Nikos I Bosse, Sophie R Meakin, Lauren Castro, Geoffrey Fairchild, Isaac Michaud, Dave Osthus, Pierfrancesco Alaimo Di Loro, Antonello Maruotti, Veronika Eclerová, Andrea Kraus, David Kraus, Lenka Pribylova, Bertsimas Dimitris, Michael Lingzhi Li, Soni Saksham, Jonas Dehning, Sebastian Mohr, Viola Priesemann, Grzegorz Redlarski, Benjamin Bejar, Giovanni Ardenghi, Nicola Parolini, Giovanni Ziarelli, Wolfgang Bock, Stefan Heyder, Thomas Hotz, David E Singh, Miguel Guzman-Merino, Jose L Aznarte, David Moriña, Sergio Alonso, Enric Álvarez, Daniel López, Clara Prats, Jan Pablo Burgard, Arne Rodloff, Tom Zimmermann, Alexander Kuhlmann, Janez Zibert, Fulvia Pennoni, Fabio Divino, Marti Català, Gianfranco Lovison, Paolo Giudici, Barbara Tarantino, Francesco Bartolucci, Giovanna Jona Lasinio, Marco Mingione, Alessio Farcomeni, Ajitesh Srivastava, Pablo Montero-Manso, Aniruddha Adiga, Benjamin Hurt, Bryan Lewis, Madhav Marathe, Przemyslaw Porebski, Srinivasan Venkatramanan, Rafal P Bartczuk, Filip Dreger, Anna Gambin, Krzysztof Gogolewski, Magdalena Gruziel-Słomka, Bartosz Krupa, Antoni Moszyński, Karol Niedzielewski, Jedrzej Nowosielski, Maciej Radwan, Franciszek Rakowski, Marcin Semeniuk, Ewa Szczurek, Jakub Zieliński, Jan Kisielewski, Barbara Pabjan, Holger Kirsten, Yuri Kheifetz, Markus Scholz, Przemyslaw Biecek, Marcin Bodych, Maciej Filinski, Radoslaw Idzikowski, Tyll Krueger, Tomasz Ozanski, Johannes Bracher, and Sebastian Funk

Abstract

Background: Short-term forecasts of infectious disease contribute to situational awareness and capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise forecasts’ predictive performance by combining independent models into an ensemble. Here we report the performance of ensemble predictions of COVID-19 cases and deaths across Europe from March 2021 to March 2022. Methods: We created the European COVID-19 Forecast Hub, an online open-access platform where modellers upload weekly forecasts for 32 countries with results publicly visualised and evaluated. We created a weekly ensemble forecast from the equally-weighted average across individual models’ predictive quantiles. We measured forecast accuracy using a baseline and relative Weighted Interval Score (rWIS). We retrospectively explored ensemble methods, including weighting by past performance. Results: We collected weekly forecasts from 48 models, of which we evaluated 29 models alongside the ensemble model. The ensemble had a consistently strong performance across countries over time, performing better on rWIS than 91% of forecasts for deaths (N=763 predictions from 20 models), and 83% forecasts for cases (N=886 predictions from 23 models). Performance remained stable over a 4-week horizon for death forecasts but declined with longer horizons for cases. Among ensemble methods, the most influential choice came from using a median average instead of the mean, regardless of weighting component models. Conclusions: Our results support combining independent models into an ensemble forecast to improve epidemiological predictions, and suggest that median averages yield better performance than methods based on means. We highlight that forecast consumers should place more weight on incident death forecasts than case forecasts at horizons greater than two weeks. Funding: European Commission, Ministerio de Ciencia, Innovación y Universidades, FEDER; Ag

Published
2023

35. A Causal Latent Transition Model With Multivariate Outcomes and Unobserved Heterogeneity: Application to Human Capital Development

Author

Bartolucci, F, Pennoni, F, Vittadini, G, Bartolucci, Francesco, Pennoni, Fulvia, Vittadini, Giorgio, Bartolucci, F, Pennoni, F, Vittadini, G, Bartolucci, Francesco, Pennoni, Fulvia, and Vittadini, Giorgio

Abstract

In order to evaluate the effect of a policy or treatment with pre- and post-treatment outcomes, we propose an approach based on a transition model, which may be applied with multivariate outcomes and accounts for unobserved heterogeneity. This model is based on potential versions of discrete latent variables representing the individual characteristic of interest and may be cast in the hidden (latent) Markov literature for panel data. Therefore, it can be estimated by maximum likelihood in a relatively simple way. The approach extends the difference-in-difference method as it is possible to deal with multivariate outcomes. Moreover, causal effects may be expressed with respect to transition probabilities. The proposal is validated through a simulation study, and it is applied to evaluate educational programs administered to pupils in the sixth and seventh grades during their middle school period. These programs are carried out in an Italian region to improve non-cognitive skills (CSs). We study if they impact also on students’ CSs in Italian and Mathematics in the eighth grade, exploiting the pretreatment test scores available in the fifth grade. The main conclusion is that the educational programs aimed to develop noncognitive abilities help the best students to maintain their higher cognitive abilities over time.

Published
2023

36. A hidden Markov model for continuous longitudinal data with missing responses and dropout

Author

Pandolfi, S, Bartolucci, F, Pennoni, F, Pandolfi, S, Bartolucci, F, and Pennoni, F

Abstract

We propose a hidden Markov model for multivariate continuous longitudinal responses with covariates that accounts for three different types of missing pattern: (I) partially missing outcomes at a given time occasion, (II) completely missing outcomes at a given time occasion (intermittent pattern), and (III) dropout before the end of the period of observation (monotone pattern). The missing-at-random (MAR) assumption is formulated to deal with the first two types of missingness, while to account for the informative dropout, we rely on an extra absorbing state. Estimation of the model parameters is based on the maximum likelihood method that is implemented by an expectation-maximization (EM) algorithm relying on suitable recursions. The proposal is illustrated by a Monte Carlo simulation study and an application based on historical data on primary biliary cholangitis.

Published
2023

37. Tempered expectation-maximization algorithm for the estimation of discrete latent variable models

Author

Brusa, L, Bartolucci, F, Pennoni, F, Brusa Luca, Bartolucci Francesco, Pennoni Fulvia, Brusa, L, Bartolucci, F, Pennoni, F, Brusa Luca, Bartolucci Francesco, and Pennoni Fulvia

Abstract

Maximum likelihood estimation of discrete latent variable (DLV) models is usually performed by the expectation-maximization (EM) algorithm. A well-known drawback is related to the multimodality of the log-likelihood function so that the estimation algorithm can converge to a local maximum, not corresponding to the global one. We propose a tempered EM algorithm to explore the parameter space adequately for two main classes of DLV models, namely latent class and hidden Markov. We compare the proposal with the standard EM algorithm by an extensive Monte Carlo simulation study, evaluating both the ability to reach the global maximum and the computational time. We show the results of the analysis of discrete and continuous cross-sectional and longitudinal data referring to some applications of interest. All the results provide supporting evidence that the proposal outperforms the standard EM algorithm, and it significantly improves the chance to reach the global maximum. The advantage is relevant even considering the overall computing time.

Published
2023

38. Uncovering the limits of uniqueness in sampled Gabor phase retrieval: A dense set of counterexamples in L2(ℝ)

Author

Alaifari, Rima (author), Bartolucci, F. (author), Wellershoff, Matthias (author), Alaifari, Rima (author), Bartolucci, F. (author), and Wellershoff, Matthias (author)

Abstract

Sampled Gabor phase retrieval — the problem of recovering a square-integrable signal from the magnitude of its Gabor transform sampled on a lattice — is a fundamental problem in signal processing, with important applications in areas such as imaging and audio processing. Recently, a classification of square-integrable signals which are not phase retrievable from Gabor measurements on parallel lines has been presented. This classification was used to exhibit a family of counterexamples to uniqueness in sampled Gabor phase retrieval. Here, we show that the set of counterexamples to uniqueness in sampled Gabor phase retrieval is dense in L2(ℝ), but is not equal to the whole of L2(ℝ) in general. Overall, our work contributes to a better understanding of the fundamental limits of sampled Gabor phase retrieval., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Analysis

Published
2023
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41. Tempered Expectation-Maximization algorithm for discrete latent variable models

Author

Brusa, L, Bartolucci, F, Pennoni, F, Yuichi Mori, Hiroshi Yadohisa, Tomokazu Fujino, Hidetoshi Murakami, Wataru Sakamoto, Fumitake Sakaori, Hirohito Sakurai, Yoshikazu Terada, Makoto Tomita, Kensuke Okada, Kosuke Okusa, Koji Yamamoto, Michio Yamamoto, Yoshiro Yamamoto, Yoshitomo Akimoto, Brusa, L, Bartolucci, F, and Pennoni, F

Subjects
SECS-S/01 - STATISTICA, Annealing, Global maximum, Hidden Markov model, Latent class model, Local maxima
Abstract

The Latent Class (LC) model is one of the most well-known latent variable models; it is very popular for the analysis of categorical response variables, and it is typically used to cluster subjects, by assuming the existence of individual-specific latent variables having a discrete distribution. A Hidden (or Latent) Markov (HM) model represents a generalization of the LC model to the case of longitudinal data. It assumes the existence of a discrete latent process generally following a first-order Markov chain, corresponding to subpopulations, usually referred to as latent states. As typically happens for discrete latent variable models, despite maximum likelihood estimation of both LC and HM model parameters can be rather simply performed using the Expectation-Maximization (EM) algorithm, a well-known drawback of this estimation method is related to the multimodality of the log-likelihood function. The consequence is that the estimation algorithm could converge to one of the local maxima, not corresponding to the global optimum. In order to face the multimodality problem described above, we propose a Tempered EM (T-EM) algorithm, which is able to explore the parameter space adequately. It consists in rescaling the objective function depending on a parameter known as the temperature, which controls global and local maxima prominence. High temperatures allow us to explore wide regions of the parameter space, avoiding the maximization algorithm being trapped in non-global maxima; low temperatures, instead, guarantee a sharp optimization in a local region of the parameter space. By properly tuning the sequence of temperature values, the target function is gradually attracted towards the global maximum, escaping local sub-optimal solutions. We rely on an accurate Monte Carlo simulation study to compare the proposal with the standard EM algorithm, evaluating both the ability to hit the global maximum and the computational time of the proposed algorithm. We also show the results for both LC and HM models, using the proposal on discrete and continuous cross-sectional and longitudinal data in connection with some applications of interest. We conclude that the proposal outperforms the standard EM algorithm, significantly improving the chance to reach the global maximum in the overwhelming majority of considered cases. The advantage is relevant even considering the overall computing time.

Published
2022

42. A Regime switching Student-t copula model for the analysis of cryptocurrencies data

Author

Cortese, F., Bartolucci, F., Pennoni, F., Marco Corazza, Cira Perna, Claudio Pizzi, Marilena Sibillo, Magni, G, Bimonte, G, Naimoli, A, Cortese, F, Bartolucci, F, and Pennoni, F

Subjects
copula models, cryptocurrencies, daily log-returns, Expectation-Maximization algorithm, latent variable models, SECS-S/01 - STATISTICA
Abstract

Flexible statistical models have an important role in explaining the joint distribution of financial returns. In these analyses, it is necessary to consider abrupt switches in the market conditions, especially if the focus is on cryptoassets, the market of which is characterized by high instabilities. Regime switching (RS) copula models represent a powerful tool to formulate the joint distribution of time-series accurately: they are based on a copula distribution with parameters governed by a hidden Markov process of first-order so as to account for the correlation patterns between series. The hidden states represent different market regimes, each described by a state-specific vector of copula parameters. We propose RS copula models as a valuable instrument for describing the joint behavior of log- returns. We choose a Student-t copula function to consider extreme dependent values appropriately as they are often observed in financial returns. We split the modeling process into two steps: the first one consists in fitting the marginal distribution of each univariate time-series, while the second one deals with the estimation of the joint distribution of the log-returns described by a RS copula model. Maximum likelihood estimation of the model parameters is carried out by the expectation-maximization (EM) algorithm, which alternates two steps until convergence: at the E-step, we compute the expectation of the log-likelihood evaluated using the current values for the parameters and, at the M-step, parameters estimates are updated by maximizing the expected complete-data log-likelihood computed at the previous step. The main computational burdens deal with estimating the correlation matrix (R) and the number of degrees of freedom (v) of the Student t-copula. At this aim, we propose performing the M-step by computing R given v using a closed form solution obtained from a constrained optimization of the log-likelihood using Lagrange multipliers. Then, we numerically maximize the log-likelihood with respect to v given the previous update of R. The proposal is validated through a simulation study showing that the estimators have good finite sample properties. We consider data on daily log-returns over four years of five cryptos Bitcoin, Bitcoin Cash, Ethereum, Litecoin, and Ripple as an application.

Published
2022

43. A multivariate statistical approach to predict COVID-19 count data with epidemiological interpretation and uncertainty quantification

Author

Pennoni, F, Bartolucci, F, Mira, A, Pennoni F., Bartolucci F., Mira A., Pennoni, F, Bartolucci, F, Mira, A, Pennoni F., Bartolucci F., and Mira A.

Abstract

We propose statistical autoregressive models to analyze the observed time series of count data referred to different categories. The main assumption is that observed frequencies correspond to margins of a sequence of unobserved contingency tables. Inference is based on a Bayesian approach and a suitable Markov chain Monte Carlo (MCMC) algorithm. We apply the proposal to Italian COVID-19 data (at national level and for Lombardy) considering different categories of patients further to susceptible individuals and deaths.

Published
2021

44. Hidden Markov and regime switching copula models for state allocation in multiple time-series

Author

Giovanni C Porzio, Carla Rampichini, Chiara Bocci, Bartolucci, F, Pennoni, F, Cortese, F, Bartolucci F., Pennoni F., Cortese F., Giovanni C Porzio, Carla Rampichini, Chiara Bocci, Bartolucci, F, Pennoni, F, Cortese, F, Bartolucci F., Pennoni F., and Cortese F.

Abstract

We consider hidden Markov and regime-switching copula models as approaches for state allocation in multiple time-series, where state allocation means the prediction of the latent state characterizing each time occasion based on the observed data. This dynamic clustering, performed under the two model specifications, takes the correlation structure of the time-series into account. Maximum likelihood estimation of the model parameters is carried out by the expectation-maximization algorithm. For illustration we use data on the market of cryptocurrencies characterized by periods of high turbulence in which interdependence among assets is marked.

Published
2021

45. IDPlanT: the Italian database of plant translocation

Author

Abeli, T, D'Agostino, M, Orsenigo, S, Bartolucci, F, Accogli, R, Albani Rocchetti, G, Alessandrelli, C, Amadori, A, Amato, F, Angiolini, C, Assini, S, Bacchetta, G, Banfi, E, Bonini, I, Bonito, A, Borettini, M, Brancaleoni, L, Brusa, G, Buldrini, F, Carruggio, F, Carta, A, Castagnini, P, Cerabolini, B, Ceriani, R, Ciaschetti, G, Citterio, S, Clementi, U, Cogoni, D, Congiu, A, Conti, F, Crescente, M, Crosti, R, Cuena, A, D'Antraccoli, M, Dallai, D, De Andreis, R, Deidda, A, Dessi, C, De Vitis, M, Di Cecco, V, Di Cecco, M, Di Giustino, A, Di Martino, L, Di Noto, G, Domina, G, Fabrini, G, Farris, E, Fiorentin, R, Foggi, B, Forte, L, Galasso, G, Garfi, G, Gentile, C, Gentili, R, Geraci, A, Gerdol, R, Gheza, G, Giusso del Galdo, G, Gratani, L, La Placa, G, Landi, M, Loi, T, Luzzaro, A, Alfredo, M, Magnani, C, Magrini, S, Mantino, F, Mariotti, M, Martinelli, V, Mastrullo, S, Medagli, P, Minuto, L, Nonis, D, Palumbo, M, Paoli, L, Pasta, S, Peruzzi, L, Pierce, S, Pinna, M, Rainini, F, Ravera, S, Rossi, G, Sanna, N, Santini, C, Sau, S, Schettino, A, Schicchi, R, Sciandrello, S, Sgarbi, E, Gristina, A, Troia, A, Varone, L, Villa, M, Zappa, E, Fenu, G, Abeli T., D'Agostino M., Orsenigo S., Bartolucci F., Accogli R., Albani Rocchetti G., Alessandrelli C., Amadori A., Amato F., Angiolini C., Assini S., Bacchetta G., Banfi E., Bonini I., Bonito A., Borettini M. L., Brancaleoni L., Brusa G., Buldrini F., Carruggio F., Carta A., Castagnini P., Cerabolini B. E. L., Ceriani R. M., Ciaschetti G., Citterio S., Clementi U., Cogoni D., Congiu A., Conti F., Crescente M. F., Crosti R., Cuena A., D'Antraccoli M., Dallai D., De Andreis R., Deidda A., Dessi C., De Vitis M., Di Cecco V., Di Cecco M., Di Giustino A., Di Martino L., Di Noto G., Domina G., Fabrini G., Farris E., Fiorentin R., Foggi B., Forte L., Galasso G., Garfi G., Gentile C., Gentili R., Geraci A., Gerdol R., Gheza G., Giusso del Galdo G., Gratani L., La Placa G., Landi M., Loi T., Luzzaro A., Alfredo M., Magnani C., Magrini S., Mantino F., Mariotti M. G., Martinelli V., Mastrullo S., Medagli P., Minuto L., Nonis D., Palumbo M. E., Paoli L., Pasta S., Peruzzi L., Pierce S., Pinna M. S., Rainini F., Ravera S., Rossi G., Sanna N., Santini C., Sau S., Schettino A., Schicchi R., Sciandrello S., Sgarbi E., Gristina A. S., Troia A., Varone L., Villa M., Zappa E., Fenu G., Abeli, T, D'Agostino, M, Orsenigo, S, Bartolucci, F, Accogli, R, Albani Rocchetti, G, Alessandrelli, C, Amadori, A, Amato, F, Angiolini, C, Assini, S, Bacchetta, G, Banfi, E, Bonini, I, Bonito, A, Borettini, M, Brancaleoni, L, Brusa, G, Buldrini, F, Carruggio, F, Carta, A, Castagnini, P, Cerabolini, B, Ceriani, R, Ciaschetti, G, Citterio, S, Clementi, U, Cogoni, D, Congiu, A, Conti, F, Crescente, M, Crosti, R, Cuena, A, D'Antraccoli, M, Dallai, D, De Andreis, R, Deidda, A, Dessi, C, De Vitis, M, Di Cecco, V, Di Cecco, M, Di Giustino, A, Di Martino, L, Di Noto, G, Domina, G, Fabrini, G, Farris, E, Fiorentin, R, Foggi, B, Forte, L, Galasso, G, Garfi, G, Gentile, C, Gentili, R, Geraci, A, Gerdol, R, Gheza, G, Giusso del Galdo, G, Gratani, L, La Placa, G, Landi, M, Loi, T, Luzzaro, A, Alfredo, M, Magnani, C, Magrini, S, Mantino, F, Mariotti, M, Martinelli, V, Mastrullo, S, Medagli, P, Minuto, L, Nonis, D, Palumbo, M, Paoli, L, Pasta, S, Peruzzi, L, Pierce, S, Pinna, M, Rainini, F, Ravera, S, Rossi, G, Sanna, N, Santini, C, Sau, S, Schettino, A, Schicchi, R, Sciandrello, S, Sgarbi, E, Gristina, A, Troia, A, Varone, L, Villa, M, Zappa, E, Fenu, G, Abeli T., D'Agostino M., Orsenigo S., Bartolucci F., Accogli R., Albani Rocchetti G., Alessandrelli C., Amadori A., Amato F., Angiolini C., Assini S., Bacchetta G., Banfi E., Bonini I., Bonito A., Borettini M. L., Brancaleoni L., Brusa G., Buldrini F., Carruggio F., Carta A., Castagnini P., Cerabolini B. E. L., Ceriani R. M., Ciaschetti G., Citterio S., Clementi U., Cogoni D., Congiu A., Conti F., Crescente M. F., Crosti R., Cuena A., D'Antraccoli M., Dallai D., De Andreis R., Deidda A., Dessi C., De Vitis M., Di Cecco V., Di Cecco M., Di Giustino A., Di Martino L., Di Noto G., Domina G., Fabrini G., Farris E., Fiorentin R., Foggi B., Forte L., Galasso G., Garfi G., Gentile C., Gentili R., Geraci A., Gerdol R., Gheza G., Giusso del Galdo G., Gratani L., La Placa G., Landi M., Loi T., Luzzaro A., Alfredo M., Magnani C., Magrini S., Mantino F., Mariotti M. G., Martinelli V., Mastrullo S., Medagli P., Minuto L., Nonis D., Palumbo M. E., Paoli L., Pasta S., Peruzzi L., Pierce S., Pinna M. S., Rainini F., Ravera S., Rossi G., Sanna N., Santini C., Sau S., Schettino A., Schicchi R., Sciandrello S., Sgarbi E., Gristina A. S., Troia A., Varone L., Villa M., Zappa E., and Fenu G.

Abstract

IDPlanT is the Italian Database of Plant Translocation, an initiative of the Nature Conservation Working Group of the Italian Botanical Society. IDPlanT currently includes 185 plant translocations. The establishment of a national database on plant translocation is a key step forward in data sharing and techniques improvement in this field of plant conservation. Supplemental data for this article is available online at https://doi.org/10.1080/11263504.2021.1985004.

Published
2021

47. Dimensionality of the Latent Structure and Item Selection via Latent Class Multidimensional IRT Models

Author

Bartolucci, F., Montanari, G. E., and Pandolfi, S.

Abstract

With reference to a questionnaire aimed at assessing the performance of Italian nursing homes on the basis of the health conditions of their patients, we investigate two relevant issues: dimensionality of the latent structure and discriminating power of the items composing the questionnaire. The approach is based on a multidimensional item response theory model, which assumes a two-parameter logistic parameterization for the response probabilities. This model represents the health status of a patient by latent variables having a discrete distribution and, therefore, it may be seen as a constrained version of the latent class model. On the basis of the adopted model, we implement a hierarchical clustering algorithm aimed at assessing the actual number of dimensions measured by the questionnaire. These dimensions correspond to disjoint groups of items. Once the number of dimensions is selected, we also study the discriminating power of every item, so that it is possible to select the subset of these items which is able to provide an amount of information close to that of the full set. We illustrate the proposed approach on the basis of the data collected on 1,051 elderly people hosted in a sample of Italian nursing homes. (Contains 10 tables and 1 figure.)

Published
2012
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48. Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations

Author

Sherratt, K., primary, Gruson, H., additional, Grah, R., additional, Johnson, H., additional, Niehus, R., additional, Prasse, B., additional, Sandman, F., additional, Deuschel, J., additional, Wolffram, D., additional, Abbott, S., additional, Ullrich, A., additional, Gibson, G., additional, Ray, EL., additional, Reich, NG., additional, Sheldon, D., additional, Wang, Y., additional, Wattanachit, N., additional, Wang, L., additional, Trnka, J., additional, Obozinski, G., additional, Sun, T., additional, Thanou, D., additional, Pottier, L., additional, Krymova, E., additional, Barbarossa, MV., additional, Leithäuser, N., additional, Mohring, J., additional, Schneider, J., additional, Wlazlo, J., additional, Fuhrmann, J., additional, Lange, B., additional, Rodiah, I., additional, Baccam, P., additional, Gurung, H., additional, Stage, S., additional, Suchoski, B., additional, Budzinski, J., additional, Walraven, R., additional, Villanueva, I., additional, Tucek, V., additional, Šmíd, M., additional, Zajícek, M., additional, Pérez Álvarez, C., additional, Reina, B., additional, Bosse, NI., additional, Meakin, S., additional, Di Loro, P. Alaimo, additional, Maruotti, A., additional, Eclerová, V., additional, Kraus, A., additional, Kraus, D., additional, Pribylova, L., additional, Dimitris, B., additional, Li, ML., additional, Saksham, S., additional, Dehning, J., additional, Mohr, S., additional, Priesemann, V., additional, Redlarski, G., additional, Bejar, B., additional, Ardenghi, G., additional, Parolini, N., additional, Ziarelli, G., additional, Bock, W., additional, Heyder, S., additional, Hotz, T., additional, E. Singh, D., additional, Guzman-Merino, M., additional, Aznarte, JL., additional, Moriña, D., additional, Alonso, S., additional, Álvarez, E., additional, López, D., additional, Prats, C., additional, Burgard, JP., additional, Rodloff, A., additional, Zimmermann, T., additional, Kuhlmann, A., additional, Zibert, J., additional, Pennoni, F., additional, Divino, F., additional, Català, M., additional, Lovison, G., additional, Giudici, P., additional, Tarantino, B., additional, Bartolucci, F., additional, Jona Lasinio, G., additional, Mingione, M., additional, Farcomeni, A., additional, Srivastava, A., additional, Montero-Manso, P., additional, Adiga, A., additional, Hurt, B., additional, Lewis, B., additional, Marathe, M., additional, Porebski, P., additional, Venkatramanan, S., additional, Bartczuk, R., additional, Dreger, F., additional, Gambin, A., additional, Gogolewski, K., additional, Gruziel-Slomka, M., additional, Krupa, B., additional, Moszynski, A., additional, Niedzielewski, K., additional, Nowosielski, J., additional, Radwan, M., additional, Rakowski, F., additional, Semeniuk, M., additional, Szczurek, E., additional, Zielinski, J., additional, Kisielewski, J., additional, Pabjan, B., additional, Holger, K., additional, Kheifetz, Y., additional, Scholz, M., additional, Bodych, M., additional, Filinski, M., additional, Idzikowski, R., additional, Krueger, T., additional, Ozanski, T., additional, Bracher, J., additional, and Funk, S., additional

Published
2022
Full Text
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50. Multivariate Hidden Markov model: An application to study correlations among cryptocurrency log-returns

Author

Pennoni, F, Bartolucci, F, Forte, G, Ametrano, F, Pennoni, F., Bartolucci, F., Forte, G., Ametrano, F., Pennoni, F, Bartolucci, F, Forte, G, Ametrano, F, Pennoni, F., Bartolucci, F., Forte, G., and Ametrano, F.

Abstract

We provide an analysis of the market data of the major cryptocurrencies by summing a multivariate hidden Markov process also known as the latent Markov process. We model jointly the daily log-returns of BTC, ETH, XRP, LTC, and BCH. The observed log-returns are assumed to be correlated according to a variance-covariance matrix conditionally on a latent Markov process of first-order having a discrete number of latent states. In order to compare states according to their volatility, we estimate the specific variance-covariance matrix of each state. Maximum likelihood estimation of the model parameters is carried out by the Expectation-Maximization algorithm. The latent states can be ordered according to expected average values of the log-returns and their estimated volatility. We consider different model specifications in terms of number of latent states, which are identified in terms of expected log-returns and level of volatility. Under each considered scenario we also predict the latent state by the maximum a posteriori rule.

Published
2020

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