A General and Intuitive Envelope Theorem

We present an envelope theorem for establishing first-order conditions in decision problems involving continuous and discrete choices. Our theorem accommodates general dynamic programming problems, even with unbounded marginal utilities. And, unlike classical envelope theorems that focus only on differentiating value functions, we accommodate other endogenous functions such as default probabilities and interest rates. Our main technical ingredient is how we establish the differentiability of a function at a point: we sandwich the function between two differentiable functions from above and below. Our theory is widely applicable. In unsecured credit models, neither interest rates nor continuation values are globally differentiable. Nevertheless, we establish an Euler equation involving marginal prices and values. In adjustment cost models, we show that first-order conditions apply universally, even if optimal policies are not (S,s). Finally, we incorporate indivisible choices into a classic dynamic insurance analysis.

An axiomatization of difference-form contest success functions

This paper presents an axiomatic characterization of difference-form group contests, that is, contests fought among groups and where their probability of victory depends on the difference of their effective efforts. This axiomatization rests on the property of Equalizing Consistency, stating that the difference between winning probabilities in the grand contest and in the smaller contest should be identical across all participants in the smaller contest. This property overcomes some of the drawbacks of the widely-used ratio-form contest success functions. Our characterization shows that the criticisms commonly-held against difference-form contests success functions, such as lack of scale invariance and zero elasticity of augmentation, are unfounded.By clarifying the properties of this family of contest success functions, this axiomatization can help researchers to find the functional form better suited to their application of interest.

Decision analysis for the genotype designation in low-template-DNA profiles

What genotype should the scientist specify for conducting a database search to try to find the source of a low-template-DNA (lt-DNA) trace? When the scientist answers this question, he or she makes a decision. Here, we approach this decision problem from a normative point of view by defining a decision-theoretic framework for answering this question for one locus. This framework combines the probability distribution describing the uncertainty over the trace's donor's possible genotypes with a loss function describing the scientist's preferences concerning false exclusions and false inclusions that may result from the database search. According to this approach, the scientist should choose the genotype designation that minimizes the expected loss. To illustrate the results produced by this approach, we apply it to two hypothetical cases: (1) the case of observing one peak for allele xi on a single electropherogram, and (2) the case of observing one peak for allele xi on one replicate, and a pair of peaks for alleles xi and xj, i ≠ j, on a second replicate. Given that the probabilities of allele drop-out are defined as functions of the observed peak heights, the threshold values marking the turning points when the scientist should switch from one designation to another are derived in terms of the observed peak heights. For each case, sensitivity analyses show the impact of the model's parameters on these threshold values. The results support the conclusion that the procedure should not focus on a single threshold value for making this decision for all alleles, all loci and in all laboratories.

Parental education and family characteristics: educational opportunities across cohorts in Italy and Spain

Drawing on data contained in the 2005 EU-SILC, this paper investigates the disparities in educational opportunities in Italy and Spain. Its main objective is to analyse the predicted probabilities of successfully completing upper-secondary and tertiary education for individuals with different parental backgrounds, and the changes in these probabilities across birth cohorts extending from 1940 to 1980. The results suggest that the disparities in tertiary education opportunities in Italy tend to increase over time. By contrast, the gap in educational opportunity in Spain shows a marked decrease across the cohorts. Moreover, by using an intuitive decomposition strategy, the paper shows that a large part of the educational gap between individuals of different backgrounds is “composed” of the difference in the endowment of family characteristics. Specifically, it seems that more highly educated parents are more able to endow their children with a better composition of family characteristics, which accounts for a significant proportion of the disparities in educational opportunity.

DNA evidence, probabilistic evaluation and collaborative tests.

Forensic scientists working in 12 state or private laboratories participated in collaborative tests to improve the reliability of the presentation of DNA data at trial. These tests were motivated in response to the growing criticism of the power of DNA evidence. The experts' conclusions in the tests are presented and discussed in the context of the Bayesian approach to interpretation. The use of a Bayesian approach and subjective probabilities in trace evaluation permits, in an easy and intuitive manner, the integration into the decision procedure of any revision of the measure of uncertainty in the light of new information. Such an integration is especially useful with forensic evidence. Furthermore, we believe that this probabilistic model is a useful tool (a) to assist scientists in the assessment of the value of scientific evidence, (b) to help jurists in the interpretation of judicial facts and (c) to clarify the respective roles of scientists and of members of the court. Respondents to the survey were reluctant to apply this methodology in the assessment of DNA evidence.

Multivariate contemporaneous-threshold autoregressive models

This paper proposes a contemporaneous-threshold multivariate smooth transition autoregressive (C-MSTAR) model in which the regime weights depend on the ex ante probabilities that latent regime-specific variables exceed certain threshold values. A key feature of the model is that the transition function depends on all the parameters of the model as well as on the data. Since the mixing weights are also a function of the regime-specific innovation covariance matrix, the model can account for contemporaneous regime-specific co-movements of the variables. The stability and distributional properties of the proposed model are discussed, as well as issues of estimation, testing and forecasting. The practical usefulness of the C-MSTAR model is illustrated by examining the relationship between US stock prices and interest rates.

The Role of model uncertainty and learning in the U.S. postwar policy response to oil prices

This paper studies optimal monetary policy in a framework that explicitly accounts for policymakers' uncertainty about the channels of transmission of oil prices into the economy. More specfically, I examine the robust response to the real price of oil that US monetary authorities would have been recommended to implement in the period 1970 2009; had they used the approach proposed by Cogley and Sargent (2005b) to incorporate model uncertainty and learning into policy decisions. In this context, I investigate the extent to which regulator' changing beliefs over different models of the economy play a role in the policy selection process. The main conclusion of this work is that, in the specific environment under analysis, one of the underlying models dominates the optimal interest rate response to oil prices. This result persists even when alternative assumptions on the model's priors change the pattern of the relative posterior probabilities, and can thus be attributed to the presence of model uncertainty itself.

Civil war and foreign influence

We study a symmetric information bargaining model of civil war where a third (foreign) party can affect the probabilities of winning the conflict and the size of the post conflict spoils. We show that the possible alliance with a third party makes peaceful agreements difficult to reach and might lead to new commitment problems that trigger war. Also, we argue that the foreign party is likely to induce persistent informational asymmetries which might explain long lasting civil wars. We explore both political and economic incentives for a third party to intervene. The explicit consideration of political incentives leads to two predictions that allow for identifying the influence of foreign intervention on civil war incidence. Both predictions are confirmed for the case of the U.S. as a potential intervening nation: (i) civil wars around the world are more likely under Republican governments and (ii) the probability of civil wars decreases with U.S. presidential approval rates.

Trade, firm selection, and innovation: the competition channel

The availability of rich firm-level data sets has recently led researchers to uncover new evidence on the effects of trade liberalization. First, trade openness forces the least productive firms to exit the market. Secondly, it induces surviving firms to increase their innovation efforts and thirdly, it increases the degree of product market competition. In this paper we propose a model aimed at providing a coherent interpretation of these findings. We introducing firm heterogeneity into an innovation-driven growth model, where incumbent firms operating in oligopolistic industries perform cost-reducing innovations. In this framework, trade liberalization leads to higher product market competition, lower markups and higher quantity produced. These changes in markups and quantities, in turn, promote innovation and productivity growth through a direct competition effect, based on the increase in the size of the market, and a selection effect, produced by the reallocation of resources towards more productive firms. Calibrated to match US aggregate and firm-level statistics, the model predicts that a 10 percent reduction in variable trade costs reduces markups by 1:15 percent, firm surviving probabilities by 1 percent, and induces an increase in productivity growth of about 13 percent. More than 90 percent of the trade-induced growth increase can be attributed to the selection effect.

Large multi-gene phylogenetic trees of the grasses (Poaceae): progress towards complete tribal and generic level sampling.

In this paper we included a very broad representation of grass family diversity (84% of tribes and 42% of genera). Phylogenetic inference was based on three plastid DNA regions rbcL, matK and trnL-F, using maximum parsimony and Bayesian methods. Our results resolved most of the subfamily relationships within the major clades (BEP and PACCMAD), which had previously been unclear, such as, among others the: (i) BEP and PACCMAD sister relationship, (ii) composition of clades and the sister-relationship of Ehrhartoideae and Bambusoideae + Pooideae, (iii) paraphyly of tribe Bambuseae, (iv) position of Gynerium as sister to Panicoideae, (v) phylogenetic position of Micrairoideae. With the presence of a relatively large amount of missing data, we were able to increase taxon sampling substantially in our analyses from 107 to 295 taxa. However, bootstrap support and to a lesser extent Bayesian inference posterior probabilities were generally lower in analyses involving missing data than those not including them. We produced a fully resolved phylogenetic summary tree for the grass family at subfamily level and indicated the most likely relationships of all included tribes in our analysis.

Tenofovir use is associated with a reduction in calculated glomerular filtration rates in the Swiss HIV Cohort Study.

BACKGROUND: A growing number of case reports have described tenofovir (TDF)-related proximal renal tubulopathy and impaired calculated glomerular filtration rates (cGFR). We assessed TDF-associated changes in cGFR in a large observational HIV cohort. METHODS: We compared treatment-naive patients or patients with treatment interruptions > or = 12 months starting either a TDF-based combination antiretroviral therapy (cART) (n = 363) or a TDF-sparing regime (n = 715). The predefined primary endpoint was the time to a 10 ml/min reduction in cGFR, based on the Cockcroft-Gault equation, confirmed by a follow-up measurement at least 1 month later. In sensitivity analyses, secondary endpoints including calculations based on the modified diet in renal disease (MDRD) formula were considered. Endpoints were modelled using pre-specified covariates in a multiple Cox proportional hazards model. RESULTS: Two-year event-free probabilities were 0.65 (95% confidence interval [CI] 0.58-0.72) and 0.80 (95% CI 0.76-0.83) for patients starting TDF-containing or TDF-sparing cART, respectively. In the multiple Cox model, diabetes mellitus (hazard ratio [HR] = 2.34 [95% CI 1.24-4.42]), higher baseline cGFR (HR = 1.03 [95% CI 1.02-1.04] by 10 ml/min), TDF use (HR = 1.84 [95% CI 1.35-2.51]) and boosted protease inhibitor use (HR = 1.71 [95% CI 1.30-2.24]) significantly increased the risk for reaching the primary endpoint. Sensitivity analyses showed high consistency. CONCLUSION: There is consistent evidence for a significant reduction in cGFR associated with TDF use in HIV-infected patients. Our findings call for a strict monitoring of renal function in long-term TDF users with tests that distinguish between glomerular dysfunction and proximal renal tubulopathy, a known adverse effect of TDF.

The likelihood approach to compare populations : a study on DNA evidence and pitfalls of intuitions

The paper follows on from earlier work [Taroni F and Aitken CGG. Probabilistic reasoning in the law, Part 1: assessment of probabilities and explanation of the value of DNA evidence. Science & Justice 1998; 38: 165-177]. Different explanations of the value of DNA evidence were presented to students from two schools of forensic science and to members of fifteen laboratories all around the world. The responses were divided into two groups; those which came from a school or laboratory identified as Bayesian and those which came from a school or laboratory identified as non-Bayesian. The paper analyses these responses using a likelihood approach. This approach is more consistent with a Bayesian analysis than one based on a frequentist approach, as was reported by Taroni F and Aitken CGG. [Probabilistic reasoning in the law, Part 1: assessment of probabilities and explanation of the value of DNA evidence] in Science & Justice 1998.

Repeat Gamma Knife surgery for recurrent trigeminal neuralgia: long-term outcomes and systematic review.

Object The purpose of this study was to establish the safety and efficacy of repeat Gamma Knife surgery (GKS) for recurrent trigeminal neuralgia (TN). Methods Using the prospective database of TN patients treated with GKS in Timone University Hospital (Marseille, France), data were analyzed for 737 patients undergoing GKS for TN Type 1 from July 1992 to November 2010. Among the 497 patients with initial pain cessation, 34.4% (157/456 with ≥ 1-year follow-up) experienced at least 1 recurrence. Thirteen patients (1.8%) were considered for a second GKS, proposed only if the patients had good and prolonged initial pain cessation after the first GKS, with no other treatment alternative at the moment of recurrence. As for the first GKS, a single 4-mm isocenter was positioned in the cisternal portion of the trigeminal nerve at a median distance of 7.6 mm (range 4-14 mm) anterior to the emergence of the nerve (retrogasserian target). A median maximum dose of 90 Gy (range 70-90 Gy) was delivered. Data for 9 patients with at least 1-year followup were analyzed. A systematic review of literature was also performed, and results are compared with those of the Marseille study. Results The median time to retreatment in the Marseille study was 72 months (range 12-125 months) and in the literature it was 17 months (range 3-146 months). In the Marseille study, the median follow-up period was 33.9 months (range 12-96 months), and 8 of 9 patients (88.9%) had initial pain cessation with a median of 6.5 days (range 1-180 days). The actuarial rate for new hypesthesia was 33.3% at 6 months and 50% at 1 year, which remained stable for 7 years. The actuarial probabilities of maintaining pain relief without medication at 6 months and 1 year were 100% and 75%, respectively, and remained stable for 7 years. The systematic review analyzed 20 peer-reviewed studies reporting outcomes for repeat GKS for recurrent TN, with a total of 626 patients. Both the selection of the cases for retreatment and the way of reporting outcomes vary widely among studies, with a median rate for initial pain cessation of 88% (range 60%-100%) and for new hypesthesia of 33% (range 11%-80%). Conclusions Results from the Marseille study raise the question of surgical alternatives after failed GKS for TN. The rates of initial pain cessation and recurrence seem comparable to, or even better than, those of the first GKS, according to different studies, but toxicity is much higher, both in the Marseille study and in the published data. Neither the Marseille study data nor literature data answer the 3 cardinal questions regarding repeat radiosurgery in recurrent TN: which patients to retreat, which target is optimal, and which dose to use.

Activity in inferior parietal and medial prefrontal cortex signals the accumulation of evidence in a probability learning task.

In an uncertain environment, probabilities are key to predicting future events and making adaptive choices. However, little is known about how humans learn such probabilities and where and how they are encoded in the brain, especially when they concern more than two outcomes. During functional magnetic resonance imaging (fMRI), young adults learned the probabilities of uncertain stimuli through repetitive sampling. Stimuli represented payoffs and participants had to predict their occurrence to maximize their earnings. Choices indicated loss and risk aversion but unbiased estimation of probabilities. BOLD response in medial prefrontal cortex and angular gyri increased linearly with the probability of the currently observed stimulus, untainted by its value. Connectivity analyses during rest and task revealed that these regions belonged to the default mode network. The activation of past outcomes in memory is evoked as a possible mechanism to explain the engagement of the default mode network in probability learning. A BOLD response relating to value was detected only at decision time, mainly in striatum. It is concluded that activity in inferior parietal and medial prefrontal cortex reflects the amount of evidence accumulated in favor of competing and uncertain outcomes.

MAMOT: hidden Markov modeling tool.

Hidden Markov models (HMMs) are probabilistic models that are well adapted to many tasks in bioinformatics, for example, for predicting the occurrence of specific motifs in biological sequences. MAMOT is a command-line program for Unix-like operating systems, including MacOS X, that we developed to allow scientists to apply HMMs more easily in their research. One can define the architecture and initial parameters of the model in a text file and then use MAMOT for parameter optimization on example data, decoding (like predicting motif occurrence in sequences) and the production of stochastic sequences generated according to the probabilistic model. Two examples for which models are provided are coiled-coil domains in protein sequences and protein binding sites in DNA. A wealth of useful features include the use of pseudocounts, state tying and fixing of selected parameters in learning, and the inclusion of prior probabilities in decoding. AVAILABILITY: MAMOT is implemented in C++, and is distributed under the GNU General Public Licence (GPL). The software, documentation, and example model files can be found at http://bcf.isb-sib.ch/mamot