Theory and Applications of Proper Scoring Rules

We give an overview of some uses of proper scoring rules in statistical inference, including frequentist estimation theory and Bayesian model selection with improper priors.Comment: 13 page

Rejoinder to "Bayesian Model Selection Based on Proper Scoring Rules"

We are deeply appreciative of the initiative of the editor, Marina Vanucci, in commissioning a discussion of our paper, and extremely grateful to all the discussants for their insightful and thought-provoking comments. We respond to the discussions in alphabetical order [arXiv:1409.5291].Comment: Published at http://dx.doi.org/10.1214/15-BA942REJ in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

Bayesian Model Selection Based on Proper Scoring Rules

Bayesian model selection with improper priors is not well-defined because of the dependence of the marginal likelihood on the arbitrary scaling constants of the within-model prior densities. We show how this problem can be evaded by replacing marginal log-likelihood by a homogeneous proper scoring rule, which is insensitive to the scaling constants. Suitably applied, this will typically enable consistent selection of the true model.Comment: Published at http://dx.doi.org/10.1214/15-BA942 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

A Note on Bayesian Model Selection for Discrete Data Using Proper Scoring Rules

We consider the problem of choosing between parametric models for a discrete observable, taking a Bayesian approach in which the within-model prior distributions are allowed to be improper. In order to avoid the ambiguity in the marginal likelihood function in such a case, we apply a homogeneous scoring rule. For the particular case of distinguishing between Poisson and Negative Binomial models, we conduct simulations that indicate that, applied prequentially, the method will consistently select the true model.Comment: 8 pages, 2 figure

Comparisons of Hyv\"arinen and pairwise estimators in two simple linear time series models

The aim of this paper is to compare numerically the performance of two estimators based on Hyv\"arinen's local homogeneous scoring rule with that of the full and the pairwise maximum likelihood estimators. In particular, two different model settings, for which both full and pairwise maximum likelihood estimators can be obtained, have been considered: the first order autoregressive model (AR(1)) and the moving average model (MA(1)). Simulation studies highlight very different behaviours for the Hyv\"arinen scoring rule estimators relative to the pairwise likelihood estimators in these two settings.Comment: 14 pages, 2 figure

Excess of weight: is it a modifiable predictive and prognostic factor in locally advanced rectal cancer?

To evaluate the relationship between body mass index (BMI) and rates of treatment tolerance and clinical outcomes in patients with locally advanced rectal cancer treated with a multimodality approach. PATIENTS AND METHODS: This study was conducted on 56 patients with histologically proven rectal adenocarcinoma, staged T3-4, and/or node-positive tumor, which underwent intensified radiochemotherapy (RT-CHT) treatment before surgery. We calculated adiposity indices and analyzed their influence on treatment tolerance and clinical outcomes. RESULTS: Distribution of the 56 patients according to BMI was BMI < 25 kg/m2 (n = 19; 33.9%), BMI 25-29 kg/m2 (n = 29; 51.8%) and BMI ≥ 30 kg/m2 (n = 8; 14.3%). BMI had no significant influence on neo-adjuvant treatment-related toxicity. With a median follow-up of 23 months (range 11-47), the 2-year survival was 85.7%. We did not observe any significant difference among the three BMI categories for any of the outcomes. CONCLUSIONS: This study suggested no evident links between overweight and survival in patients with locally advanced rectal carcinoma treated with neo-adjuvant RT-CHT. Overweight patients tolerate treatment as normal-weight patients

From statistical evidence to evidence of causality

While statisticians and quantitative social scientists typically study the "effects of causes" (EoC), Lawyers and the Courts are more concerned with understanding the "causes of effects" (CoE). EoC can be addressed using experimental design and statistical analysis, but it is less clear how to incorporate statistical or epidemiological evidence into CoE reasoning, as might be required for a case at Law. Some form of counterfactual reasoning, such as the "potential outcomes" approach championed by Rubin, appears unavoidable, but this typically yields "answers" that are sensitive to arbitrary and untestable assumptions. We must therefore recognise that a CoE question simply might not have a well-determined answer. It is nevertheless possible to use statistical data to set bounds within which any answer must lie. With less than perfect data these bounds will themselves be uncertain, leading to a compounding of different kinds of uncertainty. Still further care is required in the presence of possible confounding factors. In addition, even identifying the relevant "counterfactual contrast" may be a matter of Policy as much as of Science. Defining the question is as non-trivial a task as finding a route towards an answer. This paper develops some technical elaborations of these philosophical points from a personalist Bayesian perspective, and illustrates them with a Bayesian analysis of a case study in child protection

Ion channels and neuronal excitability in polyglutamine neurodegenerative diseases

Abstract Polyglutamine (polyQ) diseases are a family composed of nine neurodegenerative inherited disorders (NDDs) caused by pathological expansions of cytosine-adenine-guanine (CAG) trinucleotide repeats which encode a polyQ tract in the corresponding proteins. CAG polyQ repeat expansions produce neurodegeneration via multiple downstream mechanisms; among those the neuronal activity underlying the ion channels is affected directly by specific channelopathies or indirectly by secondary dysregulation. In both cases, the altered excitability underlies to gain- or loss-of-function pathological effects. Here we summarize the repertoire of ion channels in polyQ NDDs emphasizing the biophysical features of neuronal excitability and their pathogenic role. The aim of this review is to point out the value of a deeper understanding of those functional mechanisms and processes as crucial elements for the designing and targeting of novel therapeutic avenues