scholarly journals Black swans in astronomical data

2021 ◽  
Author(s):  
David Kipping
Keyword(s):  
Recurrence Time ◽  
P Value ◽  
Cost Ratio ◽  
A Posteriori ◽  
Basic Premise ◽  
Look Ahead ◽  
Posteriori Distribution ◽  
A Posteriori Distribution ◽  
Scientific Value ◽  
New Phenomena

Abstract Astronomy has always been propelled by the discovery of new phenomena lacking precedent, often followed by new theories to explain their existence and properties. In the modern era of large surveys tiling the sky at ever high precision and sampling rates, these serendipitous discoveries look set to continue, with recent examples including Boyajian’s Star, Fast Radio Bursts and ‘Oumuamua. Accordingly, we here look ahead and aim to provide a statistical framework for interpreting such events and providing guidance to future observations, under the basic premise that the phenomenon in question stochastically repeat at some unknown, constant rate, λ. Specifically, expressions are derived for 1) the a-posteriori distribution for λ, 2) the a-posteriori distribution for the recurrence time, and, 3) the benefit-to-cost ratio of further observations relative to that of the inaugural event. Some rule-of-thumb results for each of these are found to be 1) $\lambda < \lbrace 0.7, 2.3, 4.6\rbrace \, t_1^{-1}$ to $\lbrace 50, 90, 95\rbrace {{\ \rm per\ cent}}$ confidence (where t1 = time to obtain the first detection), 2) the recurrence time is t2 < {1, 9, 99} t1 to $\lbrace 50, 90, 95\rbrace {{\ \rm per\ cent}}$ confidence, with a lack of repetition by time t2 yielding a p-value of 1/[1 + (t2/t1)], and, 3) follow-up for ≲ 10 t1 is expected to be scientifically worthwhile under an array of differing assumptions about the object’s intrinsic scientific value. We apply these methods to the Breakthrough Listen Candidate 1 signal and tidal disruption events observed by TESS.

High‐resolution velocity gathers and offset space reconstruction

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1169-1177 ◽  
Author(s):  
Mauricio D. Sacchi ◽  
Tadeusz J. Ulrych
Keyword(s):  
Spectral Analysis ◽  
High Resolution ◽  
Probability Density Function ◽  
Probability Density ◽  
Maximum Entropy ◽  
A Posteriori ◽  
Unknown Parameters ◽  
Maximum Entropy Spectral Analysis ◽  
Posteriori Distribution ◽  
A Posteriori Distribution

We present a high‐resolution procedure to reconstruct common‐midpoint (CMP) gathers. First, we describe the forward and inverse transformations between offset and velocity space. Then, we formulate an underdetermined linear inverse problem in which the target is the artifacts‐free, aperture‐compensated velocity gather. We show that a sparse inversion leads to a solution that resembles the infinite‐aperture velocity gather. The latter is the velocity gather that should have been estimated with a simple conjugate operator designed from an infinite‐aperture seismic array. This high‐resolution velocity gather is then used to reconstruct the offset space. The algorithm is formally derived using two basic principles. First, we use the principle of maximum entropy to translate prior information about the unknown parameters into a probabilistic framework, in other words, to assign a probability density function to our model. Second, we apply Bayes’s rule to relate the a priori probability density function (pdf) with the pdf corresponding to the experimental uncertainties (likelihood function) to construct the a posteriori distribution of the unknown parameters. Finally the model is evaluated by maximizing the a posteriori distribution. When the problem is correctly regularized, the algorithm converges to a solution characterized by different degrees of sparseness depending on the required resolution. The solutions exhibit minimum entropy when the entropy is measured in terms of Burg’s definition. We emphasize two crucial differences in our approach with the familiar Burg method of maximum entropy spectral analysis. First, Burg’s entropy is minimized rather than maximized, which is equivalent to inferring as much as possible about the model from the data. Second, our approach uses the data as constraints in contrast with the classic maximum entropy spectral analysis approach where the autocorrelation function is the constraint. This implies that we recover not only amplitude information but also phase information, which serves to extrapolate the data outside the original aperture of the array. The tradeoff is controlled by a single parameter that under asymptotic conditions reduces the method to a damped least‐squares solution. Finally, the high‐resolution or aperture‐compensated velocity gather is used to extrapolate near‐ and far‐offset traces.

Spiking band‐limited traces with a relative‐entropy algorithm

Geophysics ◽  
1991 ◽  
Vol 56 (7) ◽  
pp. 1003-1014 ◽  
Author(s):  
F. J. Jacobs ◽  
P. A. G. van der Geest
Keyword(s):  
Relative Entropy ◽  
Fourier Coefficients ◽  
A Priori ◽  
Map Estimation ◽  
A Posteriori ◽  
Novel Method ◽  
Band Limited ◽  
Posteriori Distribution ◽  
A Priori Distribution ◽  
A Posteriori Distribution

A novel method for the inversion of band‐limited seismic traces to full bandwidth reflectivity traces, is based on a probabilistic spiky model of the reflectivity trace, in which position indicators and amplitudes of the spikes occur as random variables, and relies on relative entropy inference from information theory. First, an a priori model for general reflectivity traces in the prospect is derived from nearby wells. Second, the a priori distribution is updated into an a posteriori distribution for the specific trace being studied by the addition of the Fourier data of the seismic trace within a passband. Uncertainty about the Fourier coefficients can be accounted for by specification of a noise variance, which implicitly is infinite outside the passband. The update with relative entropy inference is justified because of its relationship with Bayesian inference. Application of maximum a posteriori (MAP) estimation to the a posteriori distribution results in the most likely spiky reflectivity trace of full bandwidth. A numerical algorithm for obtaining the MAP estimates of spike positions and spike amplitudes is derived from the concept of continuation and is described in detail. The algorithm avoids searching among all possible patterns of spike positions.

scholarly journals Effect of feed texture, meal frequency and pre-slaughter fasting on behaviour, stomach content and carcass microbial quality in pigs

2007 ◽  
Vol 87 (4) ◽  
pp. 479-487 ◽  
Author(s):  
L. Saucier ◽  
D. Bernier ◽  
R. Bergeron ◽  
A. Giguère ◽  
S. Méthot ◽  
...  
Keyword(s):  
Microbial Contamination ◽  
Stomach Contents ◽  
P Value ◽  
Microbial Quality ◽  
Meal Frequency ◽  
A Posteriori ◽  
E Coli ◽  
Key Words Animal ◽  
Stomach Weight ◽  
Study Behaviour

In this study, behaviour in lairage, weight and composition of stomach contents and carcass microbial contamination were studied in 96 barrows assigned to the following treatments: feed texture (FT; mash vs. pellets), meal frequency (MF; 2 vs. five meals per day) and fasting time (WT; 4, 14 and 24 h) according to a 2 × 2 × 3 factorial design. Pigs fed two meals had heavier stomach weights at slaughter than those fed five times per day (P = 0.01). An interaction was found between WT and FT (P = 0.002) for stomach weight. With respect to the contamination of the mouth, total aerobic mesophilic counts were higher than 104 cfu cm-2 but not significantly different between treatments. Coprophagy behaviour in lairage was not correlated with mouth contamination at slaughter. The treatment resulting in the lowest Escherichia coli counts on the thoracic area was feeding the pigs pellets five times per day followed by a 24-h fast. In contrast, the highest E. coli counts were observed in pigs fed mash five times per day followed by a 4-h fast. Comparison a posteriori of these two extreme scenarios yielded a P value of 0.03. Key words: Animal behaviour, carcass hygiene, fasting, feeding, pigs, stomach

scholarly journals A signature predictive of early versus late recurrence after radiation (RT) for breast cancer that may inform the biology of early, aggressive recurrences.

2019 ◽  
Vol 5 (suppl) ◽  
pp. 112-112
Author(s):  
Corey Wayne Speers ◽  
S. Laura Chang ◽  
Benjamin Chandler ◽  
Andrea Pesch ◽  
Anna Michmerhuizen ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Gene Expression ◽  
Cox Regression ◽  
External Validation ◽  
Rank Correlation ◽  
Local Therapy ◽  
Feature Reduction ◽  
Recurrence Time ◽  
P Value ◽  
Treatment Intensification

112 Background: Unmet clinical needs in breast cancer (BC) management include the identification of patients at high risk to fail locally despite standard local therapy and an understanding of the biology of these recurrences. We previously reported a radiation response signature and here extend those studies to identify a signature predictive of timing of recurrence after RT. Methods: 2 independent patient cohorts were used for training (119 pts) and validation (112 pts). All patients received RT after BCS and systemic therapy as appropriate. Spearman’s rank correlation to correlate gene expression to recurrence time was used for feature selection. Significant genes were used to train a linear model which was locked before validation. Cox regression was used for both UVA and MVA. Results: Spearman’s correlation identified 485 genes whose expression was significantly associated with recurrence time (+/-3 yrs). Feature reduction refined the list to 41 genes retained within the signature. In training, the correlation of score to recurrence time was 0.85, p-value < 1.3x10-31; AUC of 0.91. External validation in an independent BC validation set accurately identified patients with early vs. late recurrences (correlation= 0.75, p-value = 0.001, AUC = 0.92, sens.=0.75, spec.= 1.0, PPV = 1.0, NPV = 0.8). Unique associations of breast cancer intrinsic subtype to timing of local recurrence were found. In UVA and MVA the signature remained the most significant factor associated with recurrence. GSEA analysis of the 41 genes retained within the signature identified proliferation and EGFR concepts associated with early recurrences and luminal and ER-signaling pathways associated with late recurrences. Knockdown of genes associated with the early and late recurrences demonstrated novel effects on proliferation and clonogenic survival, respectively. Conclusions: We report a BC gene expression signatures that may be useful in identifying patients unlikely to respond to adjuvant RT and may be used to predict timing of recurrences, with implications for potential treatment intensification and duration of follow-up for women with breast cancer treated with RT.

scholarly journals Study of magnitude of anaemic problem in rural tertiary care centre in outpatient department

2018 ◽  
Vol 6 (11) ◽  
pp. 3499
Author(s):  
Anjaneya Prasad V. ◽  
Anjani Kumar C. ◽  
Neelima V. ◽  
Sai Prasanth R.
Keyword(s):  
Public Health ◽  
Low Cost ◽  
Tertiary Care ◽  
Outpatient Department ◽  
P Value ◽  
Cost Ratio ◽  
Care Hospital ◽  
Care Centre ◽  
Tertiary Care Centre ◽  
Major Health Problem

Background: Prevalence of anaemia is very high in rural tertiary care hospital O.P.D patients. Anemia is the most common morbidity among micronutrients and affects health, education, economy, and productivity of the entire nation. Anemia, like fever, is a manifestation and not a disease per se. The most common group among the causes for anemia is malnutrition and among that group, iron deficiency makes up the bulk of it. Girls are more likely to be a victim due to various reasons. In a family with limited resources, the female child is more likely to be neglected. She is deprived of good food and education and is utilized as an extra working hand to carry out the household chores. The added burden of menstrual blood loss, normal or abnormal, precipitates the crises too often. Anemia can usually be prevented at a low cost, and the benefit/cost ratio of implementing preventive programs is recognized as one of the highest in the realm of public health. This information has equipped everyone in public health to take action against this long-standing problem and to do whatever is needed to be done.Methods: In our study 200 people attending medical outpatient department at a tertiary care centre were enrolled. Assessment of the anaemic problem is worked out.Results: Out of 200 patients, 107 were females and 93 were males. 49 females out of 107 had haemoglobin less than 10 and 9 males out of 93 are having haemoglobin less than 10. Among people with hemoglobin less than 10, 84.5% are females. Significant p value was observed in females (<0.0001).Conclusions:Anemia continues to be a major health problem in developing countries like India, particularly rural India. Despite different strategies and programs have been taken by government of India the growing menace of anaemia is not solved. So newer strategies must be taken.Background: Prevalence of anaemia is very high in rural tertiary care hospital O.P.D patients. Anemia is the most common morbidity among micronutrients and affects health, education, economy, and productivity of the entire nation. Anemia, like fever, is a manifestation and not a disease per se. The most common group among the causes for anemia is malnutrition and among that group, iron deficiency makes up the bulk of it. Girls are more likely to be a victim due to various reasons. In a family with limited resources, the female child is more likely to be neglected. She is deprived of good food and education and is utilized as an extra working hand to carry out the household chores. The added burden of menstrual blood loss, normal or abnormal, precipitates the crises too often. Anemia can usually be prevented at a low cost, and the benefit/cost ratio of implementing preventive programs is recognized as one of the highest in the realm of public health. This information has equipped everyone in public health to take action against this long-standing problem and to do whatever is needed to be done.Methods: In our study 200 people attending medical outpatient department at a tertiary care centre were enrolled. Assessment of the anaemic problem is worked out.Results: Out of 200 patients, 107 were females and 93 were males. 49 females out of 107 had haemoglobin less than 10 and 9 males out of 93 are having haemoglobin less than 10. Among people with hemoglobin less than 10, 84.5% are females. Significant p value was observed in females (<0.0001).Conclusions: Anemia continues to be a major health problem in developing countries like India, particularly rural India. Despite different strategies and programs have been taken by government of India the growing menace of anaemia is not solved. So newer strategies must be taken.

scholarly journals Measuring the Uncertainty of Predictions in Deep Neural Networks with Variational Inference

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6011 ◽  
Author(s):  
Jan Steinbrener ◽  
Konstantin Posch ◽  
Jürgen Pilz
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Network Architecture ◽  
Deep Neural Networks ◽  
Variational Inference ◽  
Model Parameters ◽  
A Posteriori ◽  
Novel Approach ◽  
Credible Intervals ◽  
Posteriori Distribution

We present a novel approach for training deep neural networks in a Bayesian way. Compared to other Bayesian deep learning formulations, our approach allows for quantifying the uncertainty in model parameters while only adding very few additional parameters to be optimized. The proposed approach uses variational inference to approximate the intractable a posteriori distribution on basis of a normal prior. By representing the a posteriori uncertainty of the network parameters per network layer and depending on the estimated parameter expectation values, only very few additional parameters need to be optimized compared to a non-Bayesian network. We compare our approach to classical deep learning, Bernoulli dropout and Bayes by Backprop using the MNIST dataset. Compared to classical deep learning, the test error is reduced by 15%. We also show that the uncertainty information obtained can be used to calculate credible intervals for the network prediction and to optimize network architecture for the dataset at hand. To illustrate that our approach also scales to large networks and input vector sizes, we apply it to the GoogLeNet architecture on a custom dataset, achieving an average accuracy of 0.92. Using 95% credible intervals, all but one wrong classification result can be detected.

2-D Bayesian deconvolution

Geophysics ◽  
1991 ◽  
Vol 56 (12) ◽  
pp. 2008-2018 ◽  
Author(s):  
Marc Lavielle
Keyword(s):  
Objective Function ◽  
Seismic Data ◽  
Layer Structure ◽  
A Priori ◽  
A Priori Information ◽  
The Earth ◽  
Markov Random ◽  
Posteriori Distribution ◽  
A Posteriori Distribution ◽  
Priori Information

Inverse problems can be solved in different ways. One way is to define natural criteria of good recovery and build an objective function to be minimized. If, instead, we prefer a Bayesian approach, inversion can be formulated as an estimation problem where a priori information is introduced and the a posteriori distribution of the unobserved variables is maximized. When this distribution is a Gibbs distribution, these two methods are equivalent. Furthermore, global optimization of the objective function can be performed with a Monte Carlo technique, in spite of the presence of numerous local minima. Application to multitrace deconvolution is proposed. In traditional 1-D deconvolution, a set of uni‐dimensional processes models the seismic data, while a Markov random field is used for 2-D deconvolution. In fact, the introduction of a neighborhood system permits one to model the layer structure that exists in the earth and to obtain solutions that present lateral coherency. Moreover, optimization of an appropriated objective function by simulated annealing allows one to control the fit with the input data as well as the spatial distribution of the reflectors. Extension to 3-D deconvolution is straightforward.

scholarly journals Bayesian Modelling of the effects of nitrogen doses on the morphological characteristics of braquiaria grass

2018 ◽  
Vol 12 (4) ◽  
pp. 245 ◽  
Author(s):  
Luiz Henrique Marra da Silva Ribeiro ◽  
Matheus De Souza Costa ◽  
Luiz Alberto Beijo ◽  
Alberto Frank Lázaro Aguirre ◽  
Tatiane Gomes de Araújo ◽  
...  
Keyword(s):  
Bayesian Approach ◽  
Regression Models ◽  
A Priori ◽  
Morphological Characteristics ◽  
Linear Regression Models ◽  
Interval Model ◽  
Distribution Ranges ◽  
Posteriori Distribution ◽  
A Posteriori Distribution ◽  
The Bayesian Approach

The Bayesian approach in regression models has shown good results in parameter estimations, where it can increase accuracy and precision. The objective of the current study was to analyze the application of Bayesian statistics to the modeling yield for leaf dry matter (LM) and stem (SM), in kg ha-1, leaf ratio (LR), crude protein content for leaves (CPL) and stem (CPS) (%) of Brachiaria grass as a function of varying N doses (0; 100; 200 and 300 kg ha-1 yr-1). Simple and two degree polynomial linear regression models were analyzed. Information for a priori distributions was obtained from the literature. A posteriori distribution was generated using a Monte Carlo method via Markov chains. Parameters significance was assyed with HPD (Highest Posteriori Density) with a 95% interval. Model selections was performed using DIC (Deviance Information Criterion); and adjustment quality estimated with means and 95% HPD for Bayesian R2 distribution ranges. The models selected for the variables LM, SM and CPS were linear, while for LR and CPL, they were second level polynomial. The lowest doses that maximize response variables were: LM: 274 ha-1yr-1, SM: 280 ha-1yr-1, LR: 113 ha-1yr-1, CPL: 265 ha-1yr-1, CPS: 289 ha-1yr-1. The Bayesian approach allowed the inclusion of literatureverified a priori information, and the identification of evidence optimization range intervals.

The Strategic Role of Party Ideology When Voters Are Uncertain about How the Economy Works

1994 ◽  
Vol 88 (2) ◽  
pp. 327-335 ◽  
Author(s):  
John E. Roemer
Keyword(s):  
Public Good ◽  
Economic Outcomes ◽  
The Public ◽  
The Poor ◽  
Strategic Role ◽  
The Rich ◽  
The Government ◽  
Posteriori Distribution ◽  
A Posteriori Distribution

A continuum of voters, indexed by income, have preferences over economic outcomes. Two political parties each represent the interests of given constituencies of voters: the rich and the poor. Parties/candidates put forth policies—for instance, tax policy, where taxes finance a public good. Voters are uncertain about the theory of the economy, the function that maps policies into economic outcomes. Parties argue, as well, for theories of the economy. Each voter has a prior probability distribution over possible theories of the economy; after parties announce their theories of the economy, each voter constructs an a posteriori distribution over such theories. Suppose that voters are unsure how efficiently the government converts tax revenues into the public good. Under reasonable assumptions the party representing the rich argues that the government is very inefficient and the party representing the poor argues the opposite. What appear as liberal and conservative ideological views emerge as simply good strategies in the electoral game.

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