Maximum Entropy estimation of probability distribution of variables in higher dimensions from lower dimensional data

A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively straightforward. For example, if Y1 and Y2 are independent random variables, each uniform on [0, 1], one can determine the distribution of X = Y1 + Y2; here m=2 and n=1. However, biological and physical situations can arise where n>m. In general, in the absence of additional information, there is no unique solution to Q in those cases. Nevertheless, one may still want to draw some inferences about Q. To this end, we propose a novel maximum entropy (MaxEnt) approach that estimates Q(x) based only on the available data, namely, P(y). The method has the additional advantage that one does not need to explicitly calculate the Lagrange multipliers. In this paper we develop the approach, for both discrete and continuous probability distributions, and demonstrate its validity. We give an intuitive justification as well, and we illustrate with examples.Comment: in revie

Yarkovsky Drift Detections for 247 Near-Earth Asteroids

The Yarkovsky effect is a thermal process acting upon the orbits of small celestial bodies, which can cause these orbits to slowly expand or contract with time. The effect is subtle (da/dt ~ 10^-4 au/My for a 1 km diameter object) and is thus generally difficult to measure. We analyzed both optical and radar astrometry for 600 near-Earth asteroids (NEAs) for the purpose of detecting and quantifying the Yarkovsky effect. We present 247 NEAs with measured drift rates, which is the largest published set of Yarkovsky detections. This large sample size provides an opportunity to examine the Yarkovsky effect in a statistical manner. In particular, we describe two independent population-based tests that verify the measurement of Yarkovsky orbital drift. First, we provide observational confirmation for the Yarkovsky effect's theoretical size dependence of 1/D, where D is diameter. Second, we find that the observed ratio of negative to positive drift rates in our sample is 2.34, which, accounting for bias and sampling uncertainty, implies an actual ratio of $2.7^{+0.3}_{-0.7}$. This ratio has a vanishingly small probability of occurring due to chance or statistical noise. The observed ratio of retrograde to prograde rotators is two times lower than the ratio expected from numerical predictions from NEA population studies and traditional assumptions about the sense of rotation of NEAs originating from various main belt escape routes. We also examine the efficiency with which solar energy is converted into orbital energy and find a median efficiency in our sample of 12%. We interpret this efficiency in terms of NEA spin and thermal properties.Comment: 27 pages, 9 figures, published in the Astronomical Journal, 159, 92, 202

Comparison of the linkage results of two phenotypic constructs from longitudinal data in the Framingham Heart Study: analyses on data measured at three time points and on the average of three measurements

BACKGROUND: Family studies are often conducted in a cross-sectional manner without long-term follow-up data. The relative contribution of a gene to a specific trait could change over the lifetime. The Framingham Heart Study offers a unique opportunity to investigate potential gene × time interaction. We performed linkage analysis on the body mass index (BMI) measured in 1970, 1978, and 1986 for this project. RESULTS: We analyzed the data in two different ways: three genome-wide linkage analyses on each exam, and one genome-wide linkage analysis on the mean of the three measurements. Variance-component linkage analyses were performed by the SOLAR program. Genome-wide scans show consistent evidence of linkage of quantitative trait loci (QTLs) on chromosomes 3, 6, 9, and 16 in three measurements with a maximum multipoint LOD score > 2.2. However, only chromosome 9 has a LOD score = 2.14 when the mean values were analyzed. More interestingly, we found potential gene × environment interactions: increasing LOD scores with age on chromosomes 3, 9, and 16 and decreasing LOD scores on chromosome 6 in the three exams. CONCLUSION: The results indicate two points: 1) it is possible that a gene (or genes) influencing BMI is (are) up- or down-regulated as people aged due to aging process or changes in lifestyle, environments, or genetic epistasis; 2) using mean values from longitudinal data may reduce the power to detect linkage and may have no power to detect gene × time, and/or gene × gene interactions

Comparison of the linkage results of two phenotypic constructs from longitudinal data in the Framingham Heart Study...

Background: Family studies are often conducted in a cross-sectional manner without long-term follow-up data. The relative contribution of a gene to a specific trait could change over the lifetime. The Framingham Heart Study offers a unique opportunity to investigate potential gene x time interaction. We performed linkage analysis on the body mass index (BMI) measured in 1970, 1978, and 1986 for this project. Results: We analyzed the data in two different ways: three genome-wide linkage analyses on each exam, and one genome-wide linkage analysis on the mean of the three measurements. Variance-component linkage analyses were performed by the SOLAR program. Genome-wide scans show consistent evidence of linkage of quantitative trait loci (QTLs) on chromosomes 3, 6, 9, and 16 in three measurements with a maximum multipoint LOD score > 2.2. However, only chromosome 9 has a LOD score = 2.14 when the mean values were analyzed. More interestingly, we found potential gene x environment interactions: increasing LOD scores with age on chromosomes 3, 9, and 16 and decreasing LOD scores on chromosome 6 in the three exams. Conclusion: The results indicate two points: 1) it is possible that a gene (or genes) influencing BMI is (are) up- or down-regulated as people aged due to aging process or changes in lifestyle, environments, or genetic epistasis; 2) using mean values from longitudinal data may reduce the power to detect linkage and may have no power to detect gene x time, and/or gene x gene interactions

Designing Case-control Studies: Decisions About The Controls

The authors quantified, first, the effect of misclassified controls (i.e., individuals who are affected with the disease under study but who are classified as controls) on the ability of a case-control study to detect an association between a disease and a genetic marker, and second, the effect of leaving misclassified controls in the study, as opposed to removing them (thus decreasing sample size). The authors developed an informativeness measure of a study's ability to identify real differences between cases and controls. They then examined this measure's behavior when there are no misclassified controls, when there are misclassified controls, and when there were misclassified controls but they have been removed from the study. The results show that if, for example, 10% of controls are misclassified, the study's informativeness is reduced to approximately 81% of what it would have been in a sample with no misclassified controls, whereas if these misclassified controls are removed from the study, the informativeness is only reduced to about 90%, despite the reduced sample size. If 25% are misclassified, those figures become approximately 56% and 75%, respectively. Thus, leaving the misclassified controls in the control sample is worse than removing them altogether. Finally, the authors illustrate how insufficient power is not necessarily circumvented by having an unlimited number of controls. The formulas provided by the authors enable investigators to make rational decisions about removing misclassified controls or leaving them in

Maternal blood cadmium, lead and arsenic levels, nutrient combinations, and offspring birthweight

Abstract Background Cadmium (Cd), lead (Pb) and arsenic (As) are common environmental contaminants that have been associated with lower birthweight. Although some essential metals may mitigate exposure, data are inconsistent. This study sought to evaluate the relationship between toxic metals, nutrient combinations and birthweight among 275 mother-child pairs. Methods Non-essential metals, Cd, Pb, As, and essential metals, iron (Fe), zinc (Zn), selenium (Se), copper (Cu), calcium (Ca), magnesium (Mg), and manganese (Mn) were measured in maternal whole blood obtained during the first trimester using inductively coupled plasma mass spectrometry. Folate concentrations were measured by microbial assay. Birthweight was obtained from medical records. We used quantile regression to evaluate the association between toxic metals and nutrients due to their underlying wedge-shaped relationship. Ordinary linear regression was used to evaluate associations between birth weight and toxic metals. Results After multivariate adjustment, the negative association between Pb or Cd and a combination of Fe, Se, Ca and folate was robust, persistent and dose-dependent (p < 0.05). However, a combination of Zn, Cu, Mn and Mg was positively associated with Pb and Cd levels. While prenatal blood Cd and Pb were also associated with lower birthweight. Fe, Se, Ca and folate did not modify these associations. Conclusion Small sample size and cross-sectional design notwithstanding, the robust and persistent negative associations between some, but not all, nutrient combinations with these ubiquitous environmental contaminants suggest that only some recommended nutrient combinations may mitigate toxic metal exposure in chronically exposed populations. Larger longitudinal studies are required to confirm these findings

Large-scale genome-wide association studies and meta-analyses of longitudinal change in adult lung function.

BACKGROUND: Genome-wide association studies (GWAS) have identified numerous loci influencing cross-sectional lung function, but less is known about genes influencing longitudinal change in lung function. METHODS: We performed GWAS of the rate of change in forced expiratory volume in the first second (FEV1) in 14 longitudinal, population-based cohort studies comprising 27,249 adults of European ancestry using linear mixed effects model and combined cohort-specific results using fixed effect meta-analysis to identify novel genetic loci associated with longitudinal change in lung function. Gene expression analyses were subsequently performed for identified genetic loci. As a secondary aim, we estimated the mean rate of decline in FEV1 by smoking pattern, irrespective of genotypes, across these 14 studies using meta-analysis. RESULTS: The overall meta-analysis produced suggestive evidence for association at the novel IL16/STARD5/TMC3 locus on chromosome 15 (P  =  5.71 × 10(-7)). In addition, meta-analysis using the five cohorts with ≥3 FEV1 measurements per participant identified the novel ME3 locus on chromosome 11 (P  =  2.18 × 10(-8)) at genome-wide significance. Neither locus was associated with FEV1 decline in two additional cohort studies. We confirmed gene expression of IL16, STARD5, and ME3 in multiple lung tissues. Publicly available microarray data confirmed differential expression of all three genes in lung samples from COPD patients compared with controls. Irrespective of genotypes, the combined estimate for FEV1 decline was 26.9, 29.2 and 35.7 mL/year in never, former, and persistent smokers, respectively. CONCLUSIONS: In this large-scale GWAS, we identified two novel genetic loci in association with the rate of change in FEV1 that harbor candidate genes with biologically plausible functional links to lung function

Transcriptomic evidence that von Economo neurons are regionally specialized extratelencephalic-projecting excitatory neurons.

von Economo neurons (VENs) are bipolar, spindle-shaped neurons restricted to layer 5 of human frontoinsula and anterior cingulate cortex that appear to be selectively vulnerable to neuropsychiatric and neurodegenerative diseases, although little is known about other VEN cellular phenotypes. Single nucleus RNA-sequencing of frontoinsula layer 5 identifies a transcriptomically-defined cell cluster that contained VENs, but also fork cells and a subset of pyramidal neurons. Cross-species alignment of this cell cluster with a well-annotated mouse classification shows strong homology to extratelencephalic (ET) excitatory neurons that project to subcerebral targets. This cluster also shows strong homology to a putative ET cluster in human temporal cortex, but with a strikingly specific regional signature. Together these results suggest that VENs are a regionally distinctive type of ET neuron. Additionally, we describe the first patch clamp recordings of VENs from neurosurgically-resected tissue that show distinctive intrinsic membrane properties relative to neighboring pyramidal neurons