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An example of where the ability to display a surface can be used is in visualizing a probability density function (see Chapter 8) hiv infection on tongue quality starlix 120 mg. Contour plots show lines of constant surface values antiviral state starlix 120mg on line, similar to topographical maps hiv infection skin rash buy cheap starlix line. The pcolor function shows the same information that is in a contour plot by mapping the surface height to a set of colors stages of hiv infection cdc buy 120 mg starlix with visa. We then calculate the z values that correspond to the function evaluated at each x and y. For example, lighting and color can help highlight structure or features on functions that have many bumps or a jagged surface. We will see some examples of how to use these techniques in the next section and in the exercises at the end of the chapter. The various options that are available for creating contour plots are illustrated in Example 5. Chapter 5: Exploratory Data Analysis 141 10 5 0 -5 -10 2 0 -2 -3 -2 -1 0 1 2 3 Finally, a 3-D contour plot is easily obtained using the contour3 function as shown below. We can extend this to any number of dimensions over a partition of the space [Scott, 1992]. However, in this section we restrict our attention to the bivariate histogram given by k ^ (x) = -f nh 1 h 2 x in B k, (5. We use the optimal bin width for data generated from a standard bivariate normal given in Scott [1992]. We postpone discussion of the optimal bin width and how to obtain it until Chapter 8. Therefore, a surf or mesh plot of the bivariate histogram bin heights is a linear interpolation between adjacent bins. The colors are mapped to the column number of the Z matrix, not to the heights of the bins. Compare the estimated density given by the surface with the one shown in Figure 5. Chapter 5: Exploratory Data Analysis 145 that relate the marker size and color to the height of the bins. The reader might want to compare this plot with the scatterplot of the sample shown in Figure 5. Analogous to the bivariate case, you can also use the plot3 function using a symbol for the marker style to obtain a 3-D scatterplot. Simply type this in at the command line, and you will be able to rotate your graphic using the mouse. One reason for looking at scatterplots of the data is to look for interesting structures. The ability to view these structures for 3-D data is dependent on the viewpoint or projection to the screen. When looking at 3-D scatterplots, the analyst should rotate them to search the data for patterns or structure. These data were originally used in cluster analysis [Lindsey, Herzberg, and Watts, 1987]. What we would like to see from the scatterplot is whether the data for each species can be separated from the others. In other words, is there clear separation or clustering between the species using these variables? This view of the scatterplot indicates that using these variables for pattern recognition or clustering (see Chapter 9) is reasonable. Here we consider applications where we are trying to explore data that has more than three dimensions (d > 3). These include the scatterplot matrix, slices, 3-D contours, star plots, Andrews curves, and parallel coordinates. We finish this section with a description of projection pursuit exploratory data analysis and the grand tour. The grand tour provides a dynamic display of projections of multi-dimensional data, and projection pursuit looks for structure in 1-D or 2-D projections. It should be noted that some of the methods presented here are not restricted to the case where the dimensionality of our data is greater than 3-D.
The carton must be both large enough and strong enough to accommodate the analyzer hiv infection time purchase starlix without prescription. Surround the analyzer with three to four inches of packing material and prevent the analyzer from moving in the carton hiv infection asymptomatic order 120 mg starlix visa. Wrapping the analyzer several times in this material should both protect the analyzer and prevent it from moving in the carton xylometazolin antiviral order starlix toronto. The designations employed and the presentation of the material in this publication do not imply the expression of any opinion whatsoever on the part of the World Health Organization and the Food and Agriculture Organization of the United Nations concerning the legal status of any country hiv infection symptoms after 6 months discount 120 mg starlix amex, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. Dotted lines on maps represent approximate border lines for which there may not yet be full agreement. Errors and omissions excepted, the names of proprietary products are distinguished by initial capital letters. All reasonable precautions have been taken by the World Health Organization and the Food and Agriculture Organization of the United Nations to verify the information contained in this publication. However, the published material is being distributed without warranty of any kind, either express or implied. In no event shall the World Health Organization and the Food and Agriculture Organization of the United Nations be liable for damages arising from its use. Cover illustration by Victoria Menezes Miller Typeset in China, Hong Kong Special Administrative Region Printed in France Contents List of tables List of figures Foreword Preface List of authors Acknowledgements Abbreviations Glossary Part I. The role of food fortification in the control of micronutrient malnutrition Chapter 1 Micronutrient malnutrition: a public health problem 1. Evaluating the public health significance of micronutrient malnutrition Introduction Chapter 3 Iron, vitamin A and iodine 3. Fortificants: physical characteristics, selection and use with specific food vehicles Introduction Chapter 5 Iron, vitamin A and iodine 5. Implementing effective and sustainable food fortification programmes Introduction Chapter 7 Defining and setting programme 7. One of the main reasons for the increased interest is the realization that micronutrient malnutrition contributes substantially to the global burden of disease. In addition to the more obvious clinical manifestations, micronutrient malnutrition is responsible for a wide range of non-specific physiological impairments, leading to reduced resistance to infections, metabolic disorders, and delayed or impaired physical and psychomotor development. Another reason for the increased attention to the problem of micronutrient malnutrition is that, contrary to previous thinking, it is not uniquely the concern of poor countries. While micronutrient deficiencies are certainly more frequent and severe among disadvantaged populations, they do represent a public health problem in some industrialized countries. This is particularly true of iodine deficiency in Europe, where it was generally assumed to have been eradicated, and of iron deficiency, which is currently the most prevalent micronutrient deficiency in the world. In addition, the increased consumption in industrialized countries (and increasingly in those in social and economic transition) of highly-processed energy-dense but micronutrient-poor foods, is likely to adversely affect micronutrient intake and status. The control of iodine deficiency disorders through salt iodization, for example, has been a major accomplishment in public health nutrition over the last 30 years. Unfortunately, this is far from being achievable everywhere since it requires universal access to adequate food and appropriate dietary habits. From this standpoint, food fortification has the dual advantage of being able to deliver nutrients to large segments of the population without requiring radical changes in food consumption patterns. In fact, fortification has been used for more than 80 years in industrialized countries as a means of restoring micronutrients lost by food processing, in particular, some of the B vitamins, and has been a major contributory factor in the eradication of diseases associated with deficiencies in these vitamins. Because of the increased awareness of the widespread prevalence and harmful effects of micronutrient malnutrition, and in consideration of changes in food systems (notably an increased reliance on centrally processed foods), and successful fortification experiences in other regions, increasing numbers of developing countries are now committed to , or are considering, fortification programmes. With so much accumulated experience, the conditions under which food fortification can be recommended as a strategic option for controlling micronutrient malnutrition are now better understood. Its limitations are also well known: food fortification alone cannot correct micronutrient deficiencies when large numbers of the targeted population, either because of poverty or locality, have little or no access to the fortified food, when the level of micronutrient deficiency is too severe, or when the concurrent presence of infections increases the metabolic demand for micronutrients. Various safety, technological and cost considerations can also place constraints on food fortification interventions.
Generate a random sample that is uniformly distributed over the interval (0 hiv infection rate nepal discount starlix 120mg overnight delivery, 1) antiviral netflix order starlix 120 mg with mastercard. There is also a function in the Statistics Toolbox called cdfplot that will do this antiviral wipes order 120mg starlix free shipping. Generate a random sample of size 100 from a normal distribution with mean 10 and variance of 2 (use randn(1 antiviral yahoo cheap starlix 120mg free shipping,100)*sqrt(2)+10). What is the value of the empirical cumulative distribution function evaluated at a point that is greater than the largest observation in your random sample? Another measure of skewness, called the quartile coefficient of skewness, for a sample is given by ^ ^ ^ q 0. Investigate the bias in the maximum likelihood estimate of the variance that is given in Equation 3. Repeat this process (generate a random sample from the standard normal distribution, estimate the variance, save the value) many times. Once you are done with this procedure, you should have many estimates for the variance. Take the mean of these estimates to get an estimate of the expected 2 ^2 value of. Does this indicate that the maximum likelihood estimate for the variance is biased? This is at the heart of Monte Carlo simulation for statistical inference (Chapter 6), bootstrap and resampling methods (Chapters 6 and 7), Markov chain Monte Carlo techniques (Chapter 11), and the analysis of spatial point processes (Chapter 12). In addition, we use simulated random variables to explain many other topics in this book, such as exploratory data analysis (Chapter 5), density estimation (Ch apter 8), and statistical pattern recognition (Chapter 9). There are many excellent books available that discuss techniques for generating random variables and the underlying theory; references will be provided in the last section. Our purpose in covering this topic is to give the reader the tools they need to generate the types of random variables that often arise in practice and to provide examples illustrating the methods. We first discuss general techniques for generating random variables, such as the inverse transformation and acceptance-rejection methods. However, we have to caution the reader that the numbers generated by computers are really pseudorandom because they are generated using a deterministic algorithm. The techniques used to generate uniform random variables have been widely studied in the literature, and it has been shown that some generators have serious flaws [Gentle, 1998]. There are several optional arguments, and we take a moment to discuss them because they will be useful in simulation. The function rand with no arguments returns a single instance of the random variable U. This can sometimes be an advantage in situations where we would like to obtain a specific random sample, as we illustrate in the next example. To accomplish this, the state of the uniform random number generator should be specified at each iteration of the loop. The inverse transform method can be used to generate random variables from a continuous distribution. It uses the fact that the cumulative distribution function F is uniform (0, 1) [Ross, 1997]: U = F(X). Say we would like to generate a discrete random variable X that has a probability mass function given by P (X = xi) = pi; x0 < x1 < x2 <. We generate random variables for X according to the following scheme 0; X = 1; 2; U 0. This will be useful when we describe a method for generating Poisson random variables. Chapter 4: Generating Random Variables 85 else X(i) = x(3); % It has to be between 0. These values are reasonable when compared with the desired probability mass values.
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Technological limits are not necessarily fixed; as a result of technological innovation hiv symptoms urinary tract infection purchase genuine starlix line. Most ongoing food fortification programmes operate with price increases in the range 0 antiviral medication for warts cheap starlix 120mg free shipping. It is recommended that fortification programme managers discuss with industry at an early stage of programme development what an acceptable increment in production costs and product price would be garlic antiviral properties purchase starlix with amex, i stages of hiv infection and symptoms starlix 120mg on-line. If more than one micronutrient is to be added, then their combined cost should fall within this predefined permitted increment. When conducted on a relatively large-scale industrial basis, by far the largest share of the incremental cost of fortification (90% or more) can be attributed to the cost of the fortificant itself. This being the case, the cost limit can be calculated according to Equation 2, where the cost of the fortificant micronutrient(s) is used to substitute for the cost of the entire fortification programme. This approximation does not apply to some rice fortification processes, which rely on the use of rice premixes in low dilution rates (1:100 or 1:200). In this case, the cost of manufacturing of the premix exceeds that of the fortificant compounds. Equation 2 1 A more accurate calculation may consider losses during distribution and storage, as well as losses during food preparation. The variability in the micronutrient content of a fortified food depends on the nature of the food vehicle and the amount of micronutrient added. Generally speaking, the inherent variability in the fortification process is lowest for liquids and greatest for coarse solids. In general, most mineral contents, with the exception of iodine in raw salt, should remain more or less constant, but vitamin contents are more liable to change with time, depending on the product. For other nutrients it may not be necessary to specify this parameter in regulations, something which reduces the complexity of the enforcement system required. Consequently, the general population is at risk of deficiencies in vitamin A, riboflavin (vitamin B2), folate, vitamin B12, iron and zinc. The government is considering introducing a mass fortification programme to counteract the risk of multiple micronutrient deficiencies and to this end has requested its public health nutritionists to 300 D. On the grounds that they are consumed by at least 50% of the population, sugar, oil and wheat flour were singled out as being the most appropriate vehicles for mass fortification. Although rice is also consumed in large amounts by the population, much of the supply is produced at small-scale, local mills, and thus much more difficult to fortify. Although reasonable coverage can be achieved by the fortification of the three nominated food vehicles, there was nevertheless some concern that up to 30% of the target population might not benefit from the planned fortification programme. The sector of the population falling into this category is that which resides in rural areas and whose accessibility to industrially-processed foods is likely to be limited. Since it is technically possible to add vitamin A to all three vehicles, coverage is likely to be the greatest for this vitamin. However, for some of the other nutrients under consideration, which can only be easily added to one of the three proposed vehicles. It was concluded that the potential coverage made vitamin A fortification of all three products worthwhile, but that it would be necessary to provide micronutrient supplements in various forms. The question then arises whether or not it is technologically feasible to add these levels of vitamin A to the chosen food vehicles. As food technologists warned that price increases in food products due to fortification in excess of 2% for sugar and oil, and 0. On the basis of these computations, it is evident that the addition of vitamin A to sugar at a level of 12 mg/kg is barely cost compatible. On the other hand, of the three food vehicles, sugar has the best penetration (see Table D. On balance, it was decided to proceed with the fortification of sugar, despite the fact that the relative high cost might make the implementation of this intervention much more difficult. The above analysis also demonstrates the benefits of fortifying three vehicles with lower amounts of vitamin A rather than just one with a relatively high amount. Furthermore, the coverage of the intervention would be limited to those consuming the single chosen food vehicle.
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