This tab represents the first of several tabs dedicated to the statistical study of beer, specifically the DIPA taste analysis of Double IPA (DIPA) beer. The DIPA taste analysis is performed as part of an overarching statistical study of beer for the purpose of examining all aspects affecting its ‘Tasteability’.
The term ‘Tasteability‘ is used throughout the text to describe the overall taste quality of the sampled brews in terms of their four graded taste parameters and associated DIPA rating.
The first topic of study focuses on characterizing the DIPA beer ‘Tasteability’. This involves extracting that combination of average graded taste parameters from the graded feature database that maximizes the likelihood for each of the four DIPA ‘Tasteability’ categories: “Must Try Before You Die”; “Try It, You’ll Like It”; “Take It, or Leave It”; “Don’t Bother, Save Your Money”. Details and results of this analysis are presented below.
Other aspects of the DIPA taste analysis that will be discussed in subsequent tabs include key statistical metrics, distribution functions, and estimation procedures essential to a better understanding of the overall statistical study of beer. Selected topics include:
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- ANOVA ( Analysis of Variance ) – statistical technique that analyzes the differences among group means in the sampled data set;
- moment calculations ( mean, variance, skewness, kurtosis );
- the generation of probability distribution functions ( histograms, cumulative distribution functions ).
The obvious first step in performing a DIPA taste analysis is the actual consumption of beer; i.e. “It’s a well-known fact that consumption of beer leads to improved statistical quality analysis”, quoth one Minitab Blog editor. Please visit this link for “the rest of the story”.
The following overview summarizes the contents of this blog.
Overview
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- Introduction to the MY4PAX method of characterizing DIPA beer ‘Tasteability’;
- Background;
- Methodology used to characterize the DIPA beer ‘Tasteability’;
- Results and Conclusions.
INTRODUCTION
As already mentioned, the primary goal of this tab is to discuss the MY4PAX method of characterizing the DIPA beer ‘Tasteability’ in terms of the four taste parameters – Appearance, Aroma, Mouthfeel, and Flavor. Results of the DIPA taste analysis are presented in the Results and Conclusions sections listed below.
Bayes’ Theorem is the statistical analysis tool that we use to perform this study. It calculates the likelihood of a given ‘Tasteability’ category (TCAT), given a joint set of graded taste parameters – the higher the Bayes probability, the more likely it is that the graded taste parameters craft the given ‘Tasteability’.
BACKGROUND
The web tab DIPA Rating Method gives a detailed description of the methodology used to grade and rate the DIPA beer ‘Tasteability’.
Once the DIPA samples have been graded and rated, and the corresponding DIPA ‘Tasteability’ categories have been determined, Bayes’ Theorem is used to characterize the DIPA ‘Tasteability’ in terms of the aforementioned graded taste parameters.
Bayes’ Theorem is a powerful statistical tool that relates the probability of a particular ‘Tasteability’ category (TCAT) without any prior information, to the probability (posterior probability) of the ‘Tasteability’ category given a joint set of graded taste parameters – the higher the Bayes (posterior) probability, the more likely it is that the graded taste parameters Characterize the given TCAT.
Other soon-to-be-added tabs will describe in detail the statistical study of beer that relate to the measurement of statistical moments and the generation of distribution functions that are essential to the taste analysis of beer.
These quantitative measurements provide information on the location (mean) and variability (variance) of the individual groups of graded taste parameters associated with each of the four ‘Tasteability’ categories, thus providing relevant information on the nature of the individual taste parameter distributions (as illustrated in a histogram, for example).
A third statistical moment, the skewness, is a measure of the symmetry of the shape of the DIPA taste parameter distributions. A negatively skewed distribution indicates a bias towards higher graded taste scores, while a positively skewed distribution indicates a preference for lower graded taste scores.
The results of the statistical study of beer as it relates to the location (mean) and variability (variance) of the individual DIPA taste parameters will be presented in later tabs.
The current tab focuses primarily on the results of the DIPA taste analysis as it pertains to the Bayes’ characterization of the DIPA beer ‘Tasteability’.
METHODOLOGY
Each of the four DIPA taste parameters for each sampled DIPA are graded on a scale of 0 to 5 (5 being the highest); weight averaged using the MY4PAX rating formula (see illustrated example above); and ratings thresholded to assign a ‘Tasteability’ classification to each of the sampled DIPAs.
The measured data set is used to calculate each of the joint probability terms present in the Bayes‘ Equation shown below:
Bayes’ Equation calculates the conditional likelihood of a given ‘Tasteability’ category – “You Must Try Before You Die”; “Try It, You Will Like It”; “Take It, or Leave It”; and “Don’t Bother, Save Your Money” – given the joint probability of the four graded taste parameters, i.e. Appearance, Aroma, Mouthfeel, and Flavor.
As part of the DIPA taste analysis of the MY4PAX database, Venn diagrams are used to visually represent the relationship between the individual scored taste parameters for each of the four different taste events (or parameters).
The Venn diagram shown below illustrates the joint intersection of four different taste events within an enclosed, contiguous, partition space. Each enclosed circle within the Venn diagram represents the complete set of graded taste parameters for all DIPA samples per taste category, and taste event. The hashed lines at the center of the figure represent those DIPA samples whose graded taste parameters jointly satisfy the four taste requirements for a given taste scenario.
Essential to the application of Bayes’ Theorem is the calculation of the joint probability terms present in Bayes’ equation. The algorithm extracts those DIPA samples from the MY4PAX database whose multi-valued taste function satisfies a given taste scenario – e.g. Appearance = [ 2 to 3 ], Aroma = [ 1 to 2 ], Mouthfeel = [ 4 to 5 ], and Flavor = [ 3 to 4 ] – and computes the corresponding joint probability for each of the terms present in the equation above.
In our application, the Bayes’ algorithm loops over all possible combinations of the multi-valued taste function (in steps of one), and extracts that combination of graded taste parameters that satisfies a given taste scenario.
The Likelihood Ratio (LR) is a separate calculation used in conjunction with Bayes’ Theorem to measure the odds of the graded taste set in favor of a particular ‘Tasteability’ category. The higher the LR, the more likely it is that the corresponding set of graded taste parameters characterizes the ‘Tasteability’ of the particular TCAT – as the LR for each ‘Tasteability’ category, A and B, ( shown below ) increases, so too does the corresponding Bayes’ Probability (P(A|BCDE). For a more detailed discussion of the Likelihood Ratio, click here.
RESULTS
As stated in the Introduction, our objective is to use Bayes’ Theorem in the overarching statistical study of beer to characterize the four DIPA ‘Tasteability’ categories.
Four plots were generated, one for each taste parameter. Each plot consists of three sub-plots, each corresponding to a different ‘Tasteability’ category.
The colored dots in each sub-plot denote the midpoint of each grading interval; e.g. the grading interval [ 4 to 5 ] is represented by a colored dot located at the center of the grading interval, i.e. [ 4.5 ].
Sub-plot 1, denoted by the numeral 1 located next to the y-axis, displays the results for the ‘Tasteability’ category, “You Must Try Before You Die”; sub-plot 2 displays the results for the ‘Tasteability’ category, “Try It, You will Like It”; and sub-plot 3, the results for the ‘Tasteability’ category, “Take It, Or Leave It”. The last TCAT, “Don’t Bother, Save Your Money”, contained only a limited number of samples, and was therefore excluded from the study.
Bayes’ results for the four individual taste parameters are shown below:
Sub-plot no.1 (denoted by the red circles) shows that there is a 94% likelihood that the ‘Tasteability’ category, “Must Try, Before You Die”, is characterized by the graded taste parameters: Appearance [ 4 to 5 ], Aroma [ 3 to 4 ], Mouthfeel [ 4 to 5 ], and Flavor [ 4 to 5 ].
Sub-plot no. 2 (denoted by the green circles) illustrates the results for the second rated TCAT, “Try It, You Will Like It”. These results show that there is a 32% likelihood that this ‘Tasteability’ category has an Excellent [ 4 to 5 ] Mouthfeel and Flavor, and Good [ 3 to 4 ] Appearance and Aroma.
Sub-plot no. 3 (denoted by the blue circles) illustrates the results for the third rated ‘Tasteability’ category, “Take It, or Leave It”. These results show that there is a 77% likelihood that this ‘Tasteability’ category has a Good [ 3 to 4 ] Appearance, Aroma, Flavor, and Mouthfeel.
CONCLUSIONS
Bayes’ Theorem was used to characterize the ‘Tasteability’ of each of the four, MY4PAX ‘Tasteability’ categories; i.e. determine the joint set of graded taste parameters that maximizes the Bayes likelihood for each TCAT. The analysis results presented herein pertain only to the MY4PAX data base.
Bayes’ characteristic taste sets for each of the four ‘Tasteability’ categories are tabulated below.
Please visit the following sites for a review and discussion of the best double IPA beers in America, as rated by 4PAX: Top Rated Dipas; DIPA Champion; DIPA of the Year; DIPA of the Month; 2018 DOM Winners; 2019 DOM Winners; 2020 DOM Winners; 2021 DOM WINNERS; 2022 DOM Winners