scholarly journals On the theory of errors and least squares

1932 ◽  
Vol 138 (834) ◽  
pp. 48-55 ◽  
Keyword(s):  
Least Squares ◽  
Prior Probability ◽  
Alternative Form ◽  
Probability Of Error ◽  
The Third ◽  
True Value ◽  
Scientific Inference ◽  
Two Measures ◽  
Normal Law

1. In my “Scientific Inference,” chapter V, I found that the usual presentation of the theory of errors of observation needed some modification, even where the probability of error is distributed according to the normal law. One change made was in the distribution of the prior probability of the precision constant h . Whereas this is usually taken as uniform (or ignored), I considered it better to assume that the prior probability that the constant lies in a range dh is proportional to dh/h . This is equivalent to assuming that if h 1 / h 2 = h 3 / h 4 , h is as likely to lie between h 1 and h 2 as between h 3 and h 4 ; this was thought to be the best way of expressing the condition that there is no previous know­ ledge of the magnitude of the errors. The relation must break down for very small h , comparable with the reciprocal of the whole length of the scale used, and for large h comparable with the reciprocal of the step of the scale; but for the range of practically admissible values it appeared to be the most plausible distribution. The argument for this law can now be expressed in an alternative form. The normal law of error is supposed to hold, but the true value x and the pre­cision constant h are unknown. Two measures are made: what is the pro ability that the third observation will lie between them ? The answer is easily seen to be one-third.

scholarly journals On the relation between direct and inverse methods in statistics

1937 ◽  
Vol 160 (902) ◽  
pp. 325-348 ◽  
Keyword(s):  
Standard Error ◽  
Inverse Method ◽  
Posterior Probability ◽  
Direct Methods ◽  
Previous Knowledge ◽  
Inverse Probability ◽  
True Value ◽  
Scientific Inference ◽  
Normal Law ◽  
True Values

1—In my “Scientific Inference” (1931) I gave a discussion of the posterior probability of a parameter based on a series of observations derived from the normal law of errors, when the parameter and its standard error are originally unknown. I afterwards (1932) generalized the result to the case of several unknowns. Dr J. Wishart pointed out to me that the form that I obtained by using the principle of inverse probability is identical with one obtained by direct methods by “Student” (1908). A formula identical with my general one was also given by T. E. Sterne (1934). The direct methods, however, deal with a different problem from the inverse one. They give results about the probability of the observations, or certain functions of them, the true values and the standard error being taken as known; the practical problem is usually to estimate the true value, the observations being known, and this is the problem treated by the inverse method. As the data and the propositions whose probabilities on the data are to be assessed are interchanged in the two cases it appeared to me that the identity of the results in form must be accidental. It turns out, however, that there is a definite reason why they should be identical, and that this throws a light on the use of direct methods for estimation and on their relation to the theory of probability. Suppose that the true value and the standard error are x and σ; the observed values are n in number with mean x̅ and standard deviation σ'. Then my result (1931, p. 69) was, for previous knowledge k expressing the truth of the normal law but nothing about x and σ, P ( dx | x̅ , σ', k ) ∝ {1 + ( x - x̅ ) 2 /σ' 2 } -½ n dx ; (1)

scholarly journals Retrograde Approach for Intra-arterial Chemotherapy Delivery in Retinoblastoma

2021 ◽  
Author(s):  
Giancarlo Saal-Zapata ◽  
Walter Durand ◽  
Alfredo Ramos ◽  
Raúl Cordero ◽  
Rodolfo Rodríguez
Keyword(s):  
Internal Carotid ◽  
Middle Meningeal Artery ◽  
Posterior Circulation ◽  
Alternative Form ◽  
Chemotherapeutic Drugs ◽  
Retrograde Approach ◽  
First Line ◽  
The Third ◽  
Cure Rates ◽  
Meningeal Artery

AbstractIntra-arterial chemotherapy (IAC) is currently, the first-line treatment for retinoblastomas with successful cure rates. In difficult access or unsuccessful catheterization of the ophthalmic artery (OA), the middle meningeal artery is a second alternative followed by the Japanese technique using balloon. Nevertheless, when a well-developed posterior communicating artery is present, a retrograde approach to the OA through this vessel can be performed to deliver the chemotherapeutic drugs.We present a case of an unsuccessful catheterization of the OA through the internal carotid artery due to a challenging configuration of the OA/carotid siphon angle and describe an alternative form of navigation and catheterization through the posterior circulation.To our knowledge, this is the third report of a successful retrograde catheterization of the OA for IAC and constitutes an alternative route to deliver chemotherapy.

Comparison of plasma progesterone profiles in cyclic, pregnant, pseudopregnant and hysterectomized pigs between 8 and 27 days after oestrus

1988 ◽  
Vol 119 (1) ◽  
pp. 111-116 ◽  
Author(s):  
G. J. King ◽  
R. Rajamahendran
Keyword(s):  
Least Squares ◽  
Analysis Of Variance ◽  
The Other ◽  
Corpora Lutea ◽  
Plasma Progesterone ◽  
The Third ◽  
Secretory Potential ◽  
The Mean

ABSTRACT Plasma progesterone concentrations were compared in cyclic (n = 12), pregnant (n =12), oestradiol-induced pseudopregnant (n=12) and hysterectomized gilts (n=10) between days 8 and 27 after oestrus. The results were grouped into periods covering days 8–13, 14–20 and 21–27 and analysed by least-squares analysis of variance. Plasma progesterone concentrations were significantly (P<0·001) higher in hysterectomized compared with other groups between days 8 and 13. Progesterone concentrations declined rapidly after day 14 in cyclic females and gradually in the other groups. Throughout the third and fourth weeks the mean progesterone concentrations for hysterectomized animals were consistently higher than for pseudopregnant animals (P<0·05). The pregnant group means were below but not significantly different from the hysterectomized means in both of the last two periods. The greater progesterone concentrations in hysterectomized gilts indicated that secretion is high without any conceptus-produced or -mediated luteotrophin, and corpora lutea in cyclic, pregnant or pseudopregnant gilts may never reach full secretory potential. J. Endocr. (1988) 119, 111–116

On Gauss's proof of the normal law of errors

1933 ◽  
Vol 29 (2) ◽  
pp. 231-234 ◽  
Author(s):  
Harold Jeffreys
Keyword(s):  
Arithmetic Mean ◽  
Practical Case ◽  
Apparent Discrepancy ◽  
True Value ◽  
The Mean ◽  
Normal Law

Gauss gave a well-known proof that under certain conditions the postulate that the arithmetic mean of a number of measures is the most probable estimate of the true value, given the observations, implies the normal law of error. I found recently that in an important practical case the mean is the most probable value, although the normal law does not hold. I suggested an explanation of the apparent discrepancy, but it does not seem to be the true one in the case under consideration.

The crystal and molecular structure of tribromo-m-carborane

1976 ◽  
Vol 54 (11) ◽  
pp. 1771-1776 ◽  
Author(s):  
Alice Ann Sayler ◽  
Herbert Beall
Keyword(s):  
Molecular Structure ◽  
Least Squares ◽  
Electrophilic Substitution ◽  
Crystal And Molecular Structure ◽  
Structural Parameters ◽  
Bromine Atom ◽  
Theoretical Work ◽  
Crystal Data ◽  
The Third ◽  
The Subject

The sequence of electrophilic substitution for o- and m-carborane has been the subject of much experimental and theoretical work. The molecular structure of tribromo-m-carborane (m-B10Br3H7C2H2) shows that the third bromine atom to be substituted is found bonded to boron atom 12 (or 5). The crystal data are: space group, Pbcm; a = 8.47(4), b = 12.19(8), and c = 12.25(8) Å; ρo = 1.98(2) and ρc = 2.00 g/cm3 for Z = 4. Data were collected using Weissenberg geometry and Ni-filtered CuK, radiation. The visually estimated intensities of 920 reflections were used in the anisotropic block-diagonalized least-squares refinement of the 76 structural parameters. The final value of the conventional residual index was 0.087.

scholarly journals Three problems in robotics

2002 ◽  
Vol 216 (1) ◽  
pp. 73-80 ◽  
Author(s):  
J M Selig
Keyword(s):  
Least Squares ◽  
Potential Function ◽  
Equilibrium Position ◽  
Screw Theory ◽  
Rigid Motion ◽  
The Body ◽  
The Third ◽  
Second Derivatives ◽  
Spring System ◽  
The Stability

Three rather different problems in robotics are studied using the same technique from screw theory. The first problem concerns systems of springs. The potential function is differentiated in the direction of an arbitrary screw to find the equilibrium position. The second problem is almost identical in terms of the computations; the least-squares solution to the problem of finding the rigid motion undergone by a body given only data about points on the body is sought. In the third problem the Jacobian of a Stewart platform is found. Again, this is achieved by differentiating with respect to a screw. Furthermore, second-order properties of the first two problems are studied. The Hessian of second derivatives is computed, and hence the stability properties of the equilibrium positions of the spring system are found.

scholarly journals Analysis of the development of the livestock sector in agricultural enterprises of Ukraine for 1995-2017

2019 ◽  
pp. 16-22
Author(s):  
A. Nepochatenko ◽  
V. Nepochatenko
Keyword(s):  
Logistic Regression ◽  
Least Squares ◽  
Numerical Method ◽  
Least Squares Method ◽  
Crisis Period ◽  
Sheep And Goats ◽  
Agricultural Enterprises ◽  
Exponential Regression ◽  
The Third ◽  
Livestock Sector

The theoretical analysis of possible single-factor regressions, which correspond to the decrease in the number of livestock of agricultural animals during the crisis period and increase their number at the exit from the crisis state, is made in the work. It is shown that during the crisis period, the dynamics of the reduction of the livestock correspond to the modified exponential regression. It is proposed to find two parameters of these regressions using the least squares method, the third one to be determined by the numerical method with a minimum of MAPE. With the growth of livestock caused by an increase in investments, this evolution corresponds to a modified logistic regression. The two logistic regression parameters find using the least squares method, the third and fourth parameters were determined by numerical method with a minimum of MAPE, as functions of two variables. The obtained theoretical conclusions are in good agreement with the statistical data that correspond to the dynamics of the number of cows, pigs, sheep, goats and poultry in Ukraine for the period 1995-2017. It was shown that changes in the number of cows during the whole period under investigation correspond to the modified exponential regression. The stock of pigs from 1995 to 2001 in agricultural enterprises of Ukraine also decreased under the exponential law. Since 2002 there has been a gradual increase in the number of pigs - including until 2013. In this period, the dynamics corresponded to the logistic regression of Pearl-Reed. Beginning in 2014, due to the loss of part of Ukraine's controlled areas and the complicated epizootic situation (African swine fever), the gradual decrease in the number of pigs began. The modified exponential regression also corresponded to the change in livestock of sheep and goats in agricultural enterprises of Ukraine in 1995-2005. From 2006 to 2010 there was a slight increase in livestock, then its gradual decrease, and from 2014 the total number of sheep and goats was again in line with the modified exponential regression. The dynamics of the number of poultry in agricultural enterprises in Ukraine resembles the process of changing the number of pigs. At first, it decreased, then grew. Between 1995 and 2000, the number of poultry decreased by exponential dependence. Starting from 2001 to 2013, the number of poultry increased annually, which is explained by the significant increase in the volume of state support for the poultry industry. During this period, the change in the size of the poultry fitted well with the modified logistic regression of Pearl-Reed. In 2014-2016, the number of poultry decreased annually, primarily due to changes in the geographical structure of exports. In order to begin the outbreak of the livestock sector from the crisis, it is necessary to increase the volume of domestic and foreign investment in fixed capital, increase the purchasing power of the population, the level of purchasing prices for milk and meat, improve the credit policy, and increase the amount of state aid to agricultural producers. In addition, it is necessary to create appropriate conditions for the expansion of product markets, first of all, by ensuring the process of modernization of production on an innovative basis, which will contribute to improving the quality characteristics of manufactured products in accordance with modern requirements of European and international standards. The said will allow to significantly increase the volume of agricultural production and will contribute to increasing the competitiveness of national agrarian commodity producers both in the domestic and world markets. Key words: animal husbandry in agricultural enterprises, logistic and exponential regression, forecasting.

scholarly journals Effects of environmental factors on multiple ovulation of zebu donors

2006 ◽  
Vol 58 (4) ◽  
pp. 567-574 ◽  
Author(s):  
M.G.C.D. Peixoto ◽  
J.A.G. Bergmann ◽  
C.G. Fonseca ◽  
V.M. Penna ◽  
C.S. Pereira
Keyword(s):  
Environmental Factors ◽  
Least Squares ◽  
Inbreeding Coefficient ◽  
Corpora Lutea ◽  
Data Sets ◽  
Data Set ◽  
The Third ◽  
Multiple Ovulation ◽  
The Mean ◽  
Best Responses

Data on 1,294 superovulations of Brahman, Gyr, Guzerat and Nellore females were used to evaluate the effects of: breed; herd; year of birth; inbreeding coefficient and age at superovulation of the donor; month, season and year of superovulation; hormone source and dose; and the number of previous treatments on the superovulation results. Four data sets were considered to study the influence of donors’ elimination effect after each consecutive superovulation. Each one contained only records of the first, or of the two firsts, or three firsts or all superovulations. The average number of palpated corpora lutea per superovulation varied from 8.6 to 12.6. The total number of recovered structures and viable embryos ranged from 4.1 to 7.3 and from 7.3 to 13.8, respectively. Least squares means of the number of viable embryos at first superovulation were 7.8 ± 6.6 (Brahman), 3.7 ± 4.5 (Gyr), 6.1 ± 5.9 (Guzerat) and 5.2 ± 5.9 (Nellore). The numbers of viable embryos of the second and the third superovulations were not different from those of the first superovulation. The mean intervals between first and second superovulations were 91.8 days for Brahman, 101.8 days for Gyr, 93.1 days for Guzerat and 111.3 days for Nellore donors. Intervals between the second and the third superovulations were 134.3, 110.3, 116.4 and 108.5 days for Brahman, Gyr, Guzerat and Nellore donors, respectively. Effects of herd nested within breed and dose nested within hormone affected all traits. For some data sets, the effects of month and order of superovulation on three traits were importants. The maximum number of viable embryos was observed for 7-8 year-old donors. The best responses for corpora lutea and recovered structures were observed for 4-5 year-old donors. Inbreeding coefficient was positively associated to the number of recovered structures when data set on all superovulations was considered.

scholarly journals Parameters of the synthesized model of management of technosphere safety in the region

2020 ◽  
Vol 164 ◽  
pp. 07011
Author(s):  
Vyacheslav Burlov ◽  
Oleg Lepeshkin ◽  
Michael Lepeshkin
Keyword(s):  
Differential Equations ◽  
Social Economic ◽  
Integrated Management ◽  
Nonlinear Differential Equations ◽  
Phase Portraits ◽  
Technological Systems ◽  
The Third ◽  
Model Of Management ◽  
Two Measures ◽  
Management Method

The purpose of the study is to select and justify the conditions for guaranteed provision of the required level of technosphere security in the region based on the development of a synthesized model of integrated management. Method of research is the dynamic model based on the synthesis is formalized as a system of nonlinear differential equations. Three main system-forming indicators of social, economic, technical and technological systems, corresponding according to the law of preservation of integrity of object of V. G. Burlov. The solution is to construction phase portraits in MathCAD, which sufficiently fully and succinctly reflect the properties of differential equations under consideration, showing how it needs to change two measures that could be made to change the third.

Realism + Its Discontents: Determinism Noir

ARTMargins ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 100-114
Author(s):  
Amanda Beech
Keyword(s):  
Twentieth Century ◽  
Life Events ◽  
Real Life ◽  
Working Environment ◽  
Alternative Form ◽  
Philosophical Argument ◽  
Art World ◽  
The Third ◽  
Ongoing Work

This short comic based narrative depicts the challenges to and climate of an alternative form of realism in the art-world as a new project for art's politics and construction. Determinism Noir, Realism and Its Discontents calls upon the classic genre of noir narratives to situate themes of agency, mastery, rationalism and metaphysics. These ideas and images are generated in the nihilistic climate of alienation, itself borne out through the machinic, technological and capitalistic forces of the Twentieth Century. The comic presents three parts: first we see the formation of a project base to insinuate a rational determinism: A world of cause that is unpredictable but nevertheless, a pragmatic working environment; second we see a report, based on real life events, showing arguments from politics and the art-world that continue to voice the fear that it is representation itself that has blighted art's real political purchase. The comic criticizes these arguments as having left art with either a naive commitment to an abstract and essential mythology of present-ness or an antirealist self-contortion that dispossesses it of power. The third part of this narrative re-joins the work of the epistemological detective work that is the exercise for this new realist project. Beech's abstract story gels painterly construction, philosophical argument and political diatribe to extend her ongoing work. Here she argues that art must surpass the egotistic self-consciousness that have wrongly subtended claims to realism, whilst condemning those that aspire to exit realism altogether.

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