Nuova ricerca


Ricercatore Universitario presso: Dipartimento di Economia "Marco Biagi"

Home | Curriculum(pdf) | Didattica |


2020 - Tertiary education decisions of immigrants and non-immigrants in Italy: an empirical approach [Working paper]
Lalla, M.; Frederic, P.

Decisions regarding tertiary schooling are important for young people as it affects future opportunities for employment and social mobility. Tertiary schooling also plays a role in the social integration of immigrants. To determine differences in the choices of young Italian natives and immigrants concerning education, two datasets for 2009 were used: European Union Statistics on Income and Living Conditions (EU-SILC) and the Italian Survey on Income and Living Conditions of Families with Immigrants in Italy (IT-SILCFI). Analysing a sub-sample of young Italians and immigrants, between 20 and 29 years of age, the association of both individual and family explanatory variables in the choice of secondary schooling (yes/no) was assessed using logistic models. The results show that young immigrants tend to interrupt their schooling earlier than their Italian peers. However, differences disappear when family background and parental characteristics are taken into account.

2019 - Measurement errors and tax evasion in annual incomes: evidence from survey data matched with fiscal data [Working paper]
Lalla, M.; Mantovani, D.; Frederic, P.

Individual records, referred to personal interviews of a survey on income carried out in Modena during 2012 and tax year 2011, had been matched with their corresponding records in the Ministry of Finance databases containing the fiscal incomes of tax year 2011. The analysis of the resulting data set suggested that the fiscal income was generally more reliable than surveyed income, but in the literature the exact opposite is often assumed. Moreover, the obtained data set enables identification of the factors determining over- and under-reporting, as well as measurement error, through a comparison of the surveyed income with the fiscal income, only for suitable categories of interviewees: the taxpayers who are obliged to respect the law (the constrained sector), and taxpayers who have many possibilities to evade (the unconstrained sector). The percentage of under-reporters (67.3%) was higher than those of over-reporters (32.7%). Level of income, age, and education were the main regressors affecting the measurement errors and the behaviours of taxpayers. Estimations of tax evasion and the impacts of personal factors affecting it were carried out following different approaches. The average of individual propensity to tax evasion was 25.93% of the corresponding fiscal income. The potential total tax evaders were about 10%.

2018 - Probability of Mitochondrial Lineage Extinction in Female Offspring, Modern and Paleolithic: Branching Process Analysis [Articolo su rivista]
D’Amore, G.; Orru, A.; Frederic, P.; Di Bacco, M.

We evaluate the probability of extinction of the female offspring of two populations of women: the one Paleolithic, the other that of Italy today. In both cases it is assumed that possible extinction arises exclusively on account of limitations in the degree of fertility and/or an imbalance in the sex-ratio of the population. The value is obtained as the probability that a Branching Process describing the evolution of the offspring by a progenitor degenerates to a “Blank Generation,” that is, a generation without women. Mathematically, it derives from a solution between 0 and 1 of a linear equation whose coefficients are the probabilities that a single progenitor breeds various integer numbers of daughters. We evaluated such probabilities by consulting literature. The probability of branch extinction is also the probability of extinction of progenitor’s mitochondrial lineage.

2018 - Spatial diffusion of surnames by long transhumance routes between highland and lowland: A study in Sardinia [Articolo su rivista]
Orrù, A.; De Iasio, S.; Frederic, P.; Girotti, M.; Boano, R.; Sanna, E.

We explored the relationships among Sardinian populations by means of a spatial analysis of surnames in five villages in the historical–geographical zone of Barbagia di Belvì, a mountainous area traditionally devoted to sheep-herding and the point of departure of transhumance toward lowland areas. We collected the surnames of 19th century Sardinian populations through the Status Animarum (parish censuses). The structures of past populations were compared with current structures based on surnames reported in telephone directories. The lowland villages studied have been the final destination of transhumance and have a different historical, cultural and economic background. The spread of surnames in Sardinia may have occurred also by means of transhumance which took place every year along precise routes from the pastoral mountain zones to the agricultural plains. The standardized index of Chen and Cavalli-Sforza was used to calculate relationships among the five villages of Barbagia di Belvì (Aritzo, Belvì, Desulo, Gadoni and Tonara). An application of non-metric multidimensional scaling to the isonymy matrices showed that the villages of Barbagia di Belvì form a group that have changed very little over time. Transhumance routes were studied by spatial autocorrelation (Moran’s I) applied to surnames. The results suggest that there has been an appreciable admixture between the Sardinian populations of the mountain villages of the central areas and the populations of southern lowland villages.

D Amor, G.; Frederic, P.; Di Bacco, M.

In this note we evaluate the probability of extinction (EP) of the female offspring of two women: the one of the Paleolithic, the other of Italy today. In both cases it is assumed that possible extinction arises exclusively for the degree of fertility and / or for casual sex-ratio imbalance. EP is obtained as the probability that the Branching Process describing the evolution of the offspring by a progenitor degenerates in a “Blank Generation”, i.e. in our case. a generation without women. EP is the solution between 0 and 1 of a linear equation whose coefficients are the probabilities that progenitor has 0, 1, 2, ... daughters. We evaluated such probabilities by consulting literature. Of course, EP is also the probability of extinction of progenitor’s mitochondrial lineage.

2015 - Institutions, culture and background: the school performance of immigrant students [Articolo su rivista]
Murat, Marina Giovanna; Frederic, Patrizio

Programme for International Student Assessment data from 29 countries was used to measure immigrant school gaps (differences in scores between immigrants and natives) in relation to various potentially correlated factors. Results show that negative gaps are concentrated in the European Union; in the South, they are mainly correlated with school types - academic, intermediate or vocational - and country of origin; and in the North, they remain negative in all model specifications. This suggests a lack of assimilation, in some cases reinforced by educational institutions. Gaps are generally small in English-speaking countries; in the USA and GBR they are influenced by background

2012 - Combining Experts’ Probabilities via the Product of Odds [Articolo su rivista]
Frederic, Patrizio; DI BACCO, Mario; Lad, Frank

We resolve a useful formulation of the question how a statistician can coherently incorporate the information in a consulted expert’s probability assessment for an event into his/her own posterior probability assertion. Using a framework that recognises the total information available as composed of units available only to each of them along with units available to both, we show that: a sufficient statistic for the all the information available to both the expert and the statistician is the product of their odds ratios in favour of the event; the geometric mean of their two probabilities specifies a contour of pairs of assertions in the unit-square that yield the same posterior probability; the information-combining function is parameterised by an unknown probability for the event conditioned only on the unspecified information that is common to both the statistician and the expert; and that an assessable mixing distribution over this unspecified probability allows an integrable mixture distribution to represent a computable posterior probability. The exact results allow the identification of the subclass of coherent probabilities that are externally Bayesian operators. This subclass is equivalent to that of probabilities that honour the principles of uniformity and compromise.

2012 - Immigrant Students and Educational Systems. Cross-Country Evidence from PISA 2006 [Working paper]
MURAT, Marina Giovanna; FERRARI, Davide; FREDERIC, Patrizio

Using data from PISA 2006 on 29 countries, this paper analyses immigrant school gaps (difference in scores between immigrants and natives) and focuses on tracking and comprehensive educational systems. Results show that the wider negative gaps are present where tracking is sharp and less frequently in countries with comprehensive schooling. In both cases, negative gaps are concentrated in continental Western Europe, where they are also often related to immigrants and natives attending different schools, or are significant within schools.

2012 - Unit nonresponse errors in income surveys: A case study [Articolo su rivista]
Lalla, Michele; Ferrari, Davide; Frederic, Patrizio

A survey on the economic and social conditions of households in the city of Modena was carried out in 2002 and in 2006 (two waves) by the CAPP (Centre for Analyses of Public Policies). In first wave of 2002, each designated sampling unit (i.e., the family) had three units as reserves. If the first refused to be interviewed, the interviewer contacted the three reserves, one after the other, until obtaining either one respondent or four non-participant units. At the end of the survey four categories of units were distinguished: interviewees, refusals, noncontacts, and unused reserves. All units were matched with their corresponding record in the databases of the Ministry of Finance of 2002 and the Census of 2001. The resulting data set permitted the analysis of unit or total nonresponses. The distribution of fiscal income showed different shapes for the four categories, implying a selective participation of the families. The interviewees yielded a positive bias of about 600€, holding constant other factors. The selection of the significant factors affecting nonresponse was performed via backward elimination in a logit model and with the lasso method. Participation increased as fiscal income and age increased and by education level (secondary school and university degree), while it decreased among entrepreneurs, independent workers, managers, and medium-to-low skilled workers.

2011 - Modeling skew-symmetric distributions using B-spline and penalties [Articolo su rivista]
Frederic, Patrizio

We propose a new flexible procedure for modeling Skew-Symmetric (SS) distributions via B-splines. To avoid over-fitting we follow a penalized likelihood estimation method. The structure of “B-splines SS with penalties” provides a flexible and smooth semi-parametric setting allowing estimates that capture many features of the target function such as asymmetry and multimodality. After outlining some theoretical results, we propose an effective computational strategy. Finally, we present some empirical results on both simulated and real data from chemical processing and banknote forgery data.

2011 - Students’ Evaluation of Teaching Effectiveness: Satisfaction and Related Factors [Capitolo/Saggio]
Lalla, Michele; Frederic, Patrizio; Ferrari, Davide

The relationship between students’ attitude towards teaching evaluation and the success of a teaching evaluation procedure has been frequently investigated in education sciences. Nevertheless, accurate studies of the factors driving the rating are relatively rare. The present paper deals with the determinants of students’ satisfaction and teachers’ evaluation. Students’ satisfaction and the clarity of lectures were analysed using a 15-item evaluation questionnaire based on a 4-point Likert scale, 9-dichotomous observations in addition to student, teacher, and course characteristics. The data were collected three weeks before the end of each term from all the classes in business and economics taught during the academic year 2006/2007 at the University of Modena and Reggio Emilia. The chosen collection method was an internet survey, i.e., the questionnaires were filled by students via internet on voluntary participation base. The study was carried out for students seeking a degree in economics. Note that such a degree represents an interesting case study due to the presence of a variety of subjects, including history, sociology, mathematics, statistics, economics, business, law, and foreign languages. Switching from the traditional in-class paper survey to the internet survey: (i) increased the number of evaluated courses and (ii) decreased the number of participating students. In order to reduce the sample size effect on the variables referred to teacher and class, we considered evaluations for classes with more than five responding students. The total sample size turned out to be of n=4111 responding students. Almost all evaluation items showed a positive impact on both student satisfaction and clarity of teacher’s presentation. Instructors teaching foreign languages proved to be clearer than those in other subjects. When clarity of teacher’s presentation was considered as a response, the hypothesis of the same-sex-preference appeared to be supported by data. The class size exhibited a nonlinear relationship with students’ satisfaction, where the medium size was found to be optimal. Schools and subjects impacted differently on the dependent variables.

2010 - Immigrants, schooling and background. Cross-country evidence from PISA 2006. [Working paper]
MURAT, Marina Giovanna; FERRARI, Davide; FREDERIC, Patrizio; PIRANI, Giulia

Using data from PISA 2006, we examine the performance of immigrant students indifferent international educational environments. Our results show smaller immigrant gaps –differences in scores with respect to natives - where educational systems are more flexible andstudents’ mobility between courses and school programs is higher. Unlike previous studies, ouranalysis reveals no direct relation between these gaps and education models, be they comprehensiveor tracking, adopted by countries.

2008 - Two Moments of the Logitnormal Distribution [Articolo su rivista]
Frederic, Patrizio; F., Lad

We display the first two moment functions of the Logitnormal family of distributions, conveniently described in terms of the Normal mean, m, and the Normal signal-to-noiseratio, m/s, parameters that generate the family. Long neglected on account of the numerical integrations required to compute them, awareness of these moment functions should aid the sensible interpretation of logistic regression statistics and the specification of 'diffuse' prior distributions in hierarchical models, which can be deceiving. We also use numerical integration to compare the correlation between bivariate Logitnormal variables with the correlation between the bivariate Normal variables from which they are transformed.

2008 - Weibull regression of unemployment duration measured with error via the EM algorithm [Relazione in Atti di Convegno]
Ferrari, Davide; Frederic, Patrizio; Lalla, Michele

Several models aim to measure how demographic, professional, and labour market factors influence unemployment duration, which has a compelling social and economic interest. Nevertheless, this quest still appear challenging in both interpretations and solutions, due to various difficulties. Among others, a relevant issue is the accurate measurement of unemployment, which is often biased by the presence of unknown errors. In this paper, we consider the measurement error as a latent variable and derive an Expectation-Maximization (EM) algorithm in the context of aWeibull regression model. The proposed methodology allows to estimate at the same time: (i) the effect of the covariates of interest on unemployment duration and (ii) the measurement error.

2007 - Additive modeling for location, scale, and shape parameters of the skew normal distribution [Relazione in Atti di Convegno]
Frederic, Patrizio; Paterlini, Sandra

In questo lavoro, si propone di modellare additivamente i parametri di locazione, scala e simmetria della normale asimmetrica (Azzalini (2005)), estendendo l’approcciodi Rigby and Stasinopoulos (2005) a tale classe di distribuzioni. Il comportamento del modello ´e stato dapprima testato empiricamente mediante simulazioni Monte Carlo, verificando la robustezza dell’algoritmo di ottimizzazione utilizzato (differentialevolution) e la stabilit´a nella stima dei parametri. Infine, tale modello `e stato utilizzato per analizzare dati relativi all’evoluzione temporale della capacit`a cranica umana.

2007 - Aggregazioni di Probabilità [Capitolo/Saggio]
DI BACCO, M; Frederic, Patrizio

We develop a new outlook on the use of experts' probabilities for inference, distinguishing the information content available to them from their probability assertions based on that information. It allows a statistician to specify a flexible function that represents a posterior probability of interest conditioned on all the information available to any of the experts. We work here in the restricted case of one expert, but the results are extendible in a variety of ways. The combining function is computed from statistics provided by the expert personal probability assertions which are based on the data. Considered as functions of the data through the individual expert assessing functions, they thus provide a statistic. Given some assumptions this assertion is shown to be sufficient for the direct computation of thedesired posterior probability. We develop a mixture distribution structure that allows integration in one dimension to yield the complete computation.

2007 - Unusual morphological features in a presumably Neolithic individual from Riparo della Rossa, Serra San Quirico (Ancona, Italy) [Articolo su rivista]

The present study describes human skeletal remains from Riparo della Rossa, a rock shelter in the Marche region (Central Italy). The remains consist of a cranial vault and a few nonarticulatedpostcranial bones, possibly belonging to the same adult individual. As the cranial vault showed some morphological features that are unusual for a modern human (marked prominence of the supraorbital region, very prominent nasal bones and rather high thickness of the vault), an accurate anthropological analysis and quantification of the antiquity of thebones were required. The remains were dated with two different absolute dating methods, AMS 14C and 235U–231Pa non-destructive gamma-ray spectrometry (NDGRS), whichproduced discordant results: the uncalibrated 14C dating produced 5690780 BP for the cranial vault and 6110780 BP for the clavicle; the NDGRS dating produced 10,00073000 BPfor the cranial vault. The sex discriminant morphological characters on the skull are not unequivocal, though the masculine ones appear more evident. The aims of the present paper are: to provide a morphological and metric description of the remains; to interpret their unusual morphological features; to attempt to attribute them to male or female sex and to one of the possible prehistoric cultural groups, according to dating results (Upper Palaeolithic, Mesolithic or Neolithic). The attribution was obtained by a Bayesian procedure taking into account the reliability of the combined information of morphological/metric features and absolute dating results. The results suggest that the Riparo della Rossa remains are best attributed to a male individual of the Neolithic age.

2007 - Which company would you like to fly with? [Articolo su rivista]
DI BACCO, M; Frederic, Patrizio

Abbiamo posto ad ascoltatori ingenui – vale a dire né studenti o docenti, né gente più o meno del mestiere – il quesito che qui riproporremo. Diciamo subito che quel nostro interrogare non era una ricerca sul campo per contribuire alla discussione se una teoria dell’inferenza statistica o delle decisioni in condizioni di incertezza debba essere anche descrittiva oltreché normativa. Volevamo soltanto appagare la nostra curiosità eccitata dalla lettura di alcuni dei contributi raccolti nell’interessante libro curato da Kahneman et al. (1982), in particolare quello di Kahneman e Tversky a p. 48 sgg. Del resto – come si vedrà – il nostro quesito era in effetti volutamente mal posto – descrivevamo incompletamente lo scenario – cosicché dall’interrogato c’era da attendersi non la scelta di una decisione, ma piuttosto un “non so” o meglio un “dipende”. Se qui la riproponiamo è perché ci sembra un modo didatticamente efficace per presentare l’essenziale della teoria classica delle decisioni in condizioni di incertezza (Di Bacco (1992)). E diciamo, “classica” perché – oggi come oggi – non solo si giudica “ottima” una decisione se e solo se essa è coerente con quella teoria, ma anche perché i ben notiarnesi dell’inferenza statistica – la “stima” e il “test” – sono detti “ottimi” se possono essere interpretati come decisioni “ottime” Piccinato (1996).

2006 - The effect of unbalanced demographic structure on marriage and feritlity patterns in isolated populations: the case of Viking settlements in Greenland. [Articolo su rivista]
M., DI BACCO; L., DEL PANTA; Frederic, Patrizio; G., Damore; N., Lynnerup

Can the decline of a small and isolated population occur as a consequence of a random imbalance in the sex ratio at birth and/or in the male/female mortality rates in subsequent age groups? We should stress here the use of the term “random”. Indeed, the imbalance we refer to is what occurs in a small population as the ultimate result of pure chance. This hypothesis (of the imbalance of the sex ratio) was studied in particular by the Italian statistician Corrado Gini (1957), although it had previously been put forward by other authors (Livi 1941, 1944). More specifically, Gini explained the extinction of the medieval settlements in Greenland using this hypothesis.The recent publication of Lynnerup’s book (1998) concerning the demography of these settlements, based on the archaeological evidence of skeletal remains, prompted us to re-evaluate Gini’s treatise. We wanted to give a statistical contribution – using a Bayesian inference – to evaluate Gini’s hypothesis of that extinction. The extinction of the settlements in Greenland is widely regarded as “almost an enigma hinting at some inexplicable and dramatic event veiled by the passage of time” (Lynnerup1998, p. 8).The aim of this paper is therefore to check Gini’s hypothesis from a Bayesian point of view. In this scheme, the prior distribution is the probability of an imbalance in the sex ratio occurring in the history of a small and closed population as a result of random and unfavourable alterations of the sex-ratio at birth and at death. In order to evaluate such a probability, a Monte Carlo technique that uses historical, demographic and biometric constants (Livi Bacci 1998) will be outlined. The posterior probability is then updated in the light of some archaeological data.

2006 - The seasonal forecast of electricity demand: A hierarchical Bayesian model with climatological weather generator [Articolo su rivista]
S., Pezzulli; Frederic, Patrizio; S., Majithia; S., Sabbagh; E., Black; R., Sutton; D., Stephenson

In this paper we focus on the one year ahead prediction of the electricity peak-demand daily trajectory during the winter season in Central England and Wales. We define a Bayesian hierarchical model for predicting the winter trajectories and present results based on the past observed weather. Thanks to the flexibility of the Bayesian approach, we are able to produce the marginal posterior distributions of all the predictands of interest. This is a fundamental progress with respect to the classical methods. The results are encouraging in both skill and representation of uncertainty. Further extensions are straightforward at least in principle. The main two of those consist in conditioning the weather generator model with respect to additional information like the knowledge of the first part of the winter and/or the seasonal weather forecast. Copyright

2005 - analisi predittiva bayesiana di un indicatore di qualità in un processo chimico-industriale. [Articolo su rivista]
Frederic, Patrizio; DI BACCO, M; Catellani, M.

Da alcuni anni CIBA SC. effettua, nel suo stabilimento di Pontecchio Marconi in Bologna, il monitoraggio elettronico di alcune proprie linee di produzione. Nel presente lavoro – prosecuzione di precedenti collaborazioni (si veda Catellani e Frederic(2001) )– viene analizzato, da un punto di vista statistico, il processo di produzione di un intermedio prodotto da CIBA. Una volta analizzati i dati disponibili con tecniche esplorative viene implementato un modello additivo eteroschedastico di impostazione Bayesiana predittiva. Tale modello mette in evidenza interessanti relazioni tra alcune variabili presenti nel sistema e un indicatore di qualità del prodotto finito.

2004 - Attributing a Paleoanthropological specimen to a prehistoric population: Bayesian approach with multivariate B-spline functions. [Capitolo/Saggio]
Frederic, Patrizio; Damore, G; Pacciani, E.

Human bones were recovered in 1997 near Serra San Quirico in Ancona province (Marche, Central Italy) during archaeological excavations carried out by the Soprintendenza ai Beni Archeologici delle Marche. The site is located in a cave, 20 metres above the plane of the road, on the wall of a fluvial gorge called “Gola della Rossa”. The remains consist of a cranial vault and a few non-articulated postcranial bones, possibly belonging to the same individual. The sex diagnosis was made on the basis of morphological features of the preserved anatomical parts. According to some of these qualitative features (e.g. supraorbital region development, receding frontal profile, rounded upper orbital margin, vault thickness), the cranial vault seems to belong to a male individual; other features (e.g. frontal eminences), instead, are more typical of a female.With these data, the likelihoods were elicited by means of the Bayesian B-spline model.

2004 - Bayesian statistical analysis of an efficiency-quality index in a chemical industrial process: a predictive analysis [Relazione in Atti di Convegno]
Frederic, Patrizio; Catellani, M.

Proseguendo nella collaborazione di CIBA S.C. con il Dipartimento Statistica di Bologna `e stata analizzata, da un punto di vista statistico, una fase intermedia del processodi produzione di un additivo nello stabilimento CIBA sito in Pontecchio Marconi (BO). La ricerca `e stata articolata in due fasi. Una fase preliminare di analisi dei dati: si sono esplorati i legami di dipendenza tra le 70 variabili coinvolte che CIBA raccoglie elettronicamente sul proprio impianto. Una seconda fase costituita dalla costruzione di un indicatore di resa-qualit`a dell’impianto e dalla realizzazione di un modello logit-adittivoche esprime le variazioni dell’indicatore in funzione delle variazioni di alcune delle variabili del processo.

2003 - Bayesian Discriminant Analysis using Mixture of Multivariate B-spline for Metric Data [Relazione in Atti di Convegno]
Frederic, Patrizio

Verrà mostrato l’utilizzo di misture di prodotti tensoriali di funzioni B-spline per modellare verosimiglianze in problemi analisi discriminatoria in ottica Bayesiana. Tali funzioni consentono di impostare modelli parametrici estremamente flessibili. Poiché i parametri del modello sono esclusivamente i pesi della mistura verosimiglianze costruite in questo modo sono estremamente veloci da calcolare. Verrà discusso il caso con dati mancanti e mostrato un algoritmo per il calcolo della densità predittiva.

2003 - Learning from the Probability Assertions of Experts [Working paper]
M., Di Bacco; Frederic, Patrizio; F., Lad

We develop a new outlook on the use of experts’ probabilities for inference, distinguishing the information content available to the experts from their probability assertions based on that information. Considered as functions of the data, the experts’ assessment functions provide statistics relevant to the event of interest. This allows us to specify a flexible combining function that represents a posterior probability of interest conditioned on all the information available to any of the experts; but it is computed as a function of their probability assertions. We work here in the restricted case of two experts, but the results areextendible in a variety of ways. Their probability assertions are shown to be almost sufficient for the direct specification of the desired posterior probability. A mixture distributionstructure that allows integration in one dimension is required to yield the complete computation, accounting for the insufficiency. One sidelight of this development is a display of themoment structure of the logitnormal family of distributions. Another is a generalisation of the factorisation property of probabilities for the product of independent events, allowinga parametric characterisation of distributions which orders degrees of dependency. Three numerical examples portray an interesting array of combining functions. The coherent posterior probability for the event conditioned on the experts’ two probabilities does not specify an externally Bayesian operator on their probabilities. However, we identify a natural condition under which the contours of asserted probability pairs supporting identical inferences are the same as the contours specified by EB operators. Our discussion provides motivation for the differing function values on the contours. The unanimity and compromise properties of these functions are characterised numerically and geometrically. The results are quite promising for representing a vast array of attitudes toward experts, and for empirical studies.

2003 - Statistical Analysis of an Industrial Distillation Process, [Articolo su rivista]
Frederic, Patrizio; Catellani, M.

This paper deals with the statistical analysis of a distillation process. The aim is to find statistical relations between the quality of final output and the variables measured during the process. Such relations cannot be analyzed with standard deterministic models because the presence of refluxes and recycled products tends to increase the complexity of the system. Since many variables are involved in the study, we implemented algorithms that can search for such functional relations automatically.

2001 - Introduzione al Calcolo delle Probabilità [Monografia/Trattato scientifico]
DI BACCO, M; Frederic, Patrizio

Il libro presenta una introduzione al calcolo delle probabilità con particolare attenzione all'apparato definitorio.

2001 - Process of encephalization in hominid evolution: preliminary results of biostatic analysis of brain size phylogenetic changes [Articolo su rivista]
G., Damore; Frederic, Patrizio; V., Vančata

In order to produce an evolutionary interpretation of the rate and mode of encephalization in hominid evolution, we present a new statistical approach which should be able to describe more precisely the individual phases of relative brain size evolution and to explore the possibility of different trends at a geographical or phylogenetic level. We start from the hypothesis that brain size evolution has not been linear, because indications exist that the evolution of the brain in the hominid lineage cannot be considered an allometric change. Therefore we need more advanced statistical procedures than the widely used linear regression methods. We have collected from literature endocranial capacity estimates pertaining to 166 fossil specimens dating from 3.3 million to about 10 thousand years ago. Sources of additional variation, such as the quality of fossil remains, the reliability of estimates of their brain size and of the sexual diagnosis of the specimens, have also been taken into account. We have performed a preliminary standardization of brain size estimates with estimates of body size, in order to study changes in encephalization instead of simply endocranial capacity alone. Once the sample has been divided in taxonomic groups an increment of encephalization between two groups index has been created. A kernel density estimation to evaluate the distribution of such an index has been performed. Finally a non parametric regression, such as smoothing spline regression, has been used to investigate on relationship between time and encephalization. The results indicate that brain size evolved at a different rate and velocity in individual phases of hominid evolution. Two stases seem to fit well with the fossil evidence: (1) in early Homo, and (2) in very late Homo erectus and archaic Homo sapiens (or Homo heidelbergensis). However, a geographical analysis provides an indication of a more gradualist trend. Our results suggest that the introduction of new statistical